A Comparative Study IS800

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A Comparative Study of Design Specifications in IS 800-2007 and IS 800-1984
Abstract The introduction of New IS 800-2007 based on Limit State approach as against the previous version based on Working stress approach has generated disarray in the Indian Design industry regarding the basic design approach and the results obtained. This study is a step in bridging the gap and helps throw light on the difference between basic design procedures for Limit State and Working Stress approach. A numerical evaluation of a field example has also been undertaken to depict the differences in the results generated by both the approaches. Introduction Bureau of Indian Standards made a revision of IS 800 – Code of Practice for General Construction in Steel in December 2007. This new revised code is based on the Limit State Approach as against Working Stress Approach in the earlier versions. The two philosophies are explained in brief as follows. Working Stress Method (WSM) This method forms the basis of traditional design of almost all structures irrespective of their material of construction. The method basically assumes that the structural material behaves in a linear elastic manner , and that adequate safety can be ensured by suitably restricting the stresses in the material due to the expected working loads ( service loads) on the structure. He stresses under the working loads are obtained by applying the methods of “Strength of materials”, such as the simple bending theory. The first attainment of yield stress of steel is taken to be the onset of failure. The limitation due to the non linearity (geometric as well as material) and buckling are neglected. The stresses caused by the characteristic loads are checked against the permissible (allowable) stress, which is a fraction of yield stress. Thus the permissible stress may be defined in terms of a factor of Safety, which takes care of the overload or other unknown factors. Thus, Permissible (allowable) stress = Yield Stress__ Factor of Safety Thus in working Stress method Working Stress ≤ Permissible Stress Each member of the structure is checked for a number of different combinations of loadings. Usually a FOS of 1.67 is adopted fro tension members and beams. A value of 1.92 is used for long columns and 1.67 for short columns. A value of 2.5-3 is used for connections (However using the WSM, the ‘real’ safety against ‘failure’ is unknown.). Since dead load, live load and wind load are all unlikely to act on the structure simultaneously the stresses are checked as follows. Stresses due to live load + Dead load < Permissible stress Stresses due to Dead load + Wind Load < Permissible stress Stresses due to Dead Load + Live Load + Wind Load < 1.33 (permissible stress)

Limitations of the Working Stress Method 1) The main assumptions of Linear Elastic behaviour and the implied assumption that the stresses under Working loads can be kept within the ‘permissible stresses’ are not found to be realistic. 2) It does not consider the consequence of material non linearity and the non-linear behaviour of the materials in the post buckled State. 3) Steel components have the ability to tolerate high elastic stress by yielding locally and redistributing the loads, which is not considered in WSM. 4) It fails to discriminate between different types of load that acts simultaneously, but have different degree of uncertainty, which can lead to nonconservative designs at times when two different loads have counteracting effects. Inspite of the above shortcomings, the structures designed with WSM have performed well. The size of Tension members is about the same in both LSM and WSM when the LL to DL rate (LDR) is about 3. When DL becomes more predominant, there will be slight economy in using LSM. When LDR greater than 3, WSM will be slightly more economical (3%) However, for other members, WSM results in relatively larger member sizes and hence in less deflection. There are instances where WSM results in considerable over design and where it is not safe (Allen 1972 and Gordon 1978). The WSM is noted for its simplicity in concept as well as application. Limit State Method (LSM) It aims for a comprehensive and rational approach to the design problem, by considering safety at ultimate loads and serviceability at working loads. The selection of various multiple safety factors is supposed to have a sound probabilistic basis, involving the separate considerations of different kinds of failure, types of materials, and types of loads (Kulak and Grondin 2002) Limit State of Strength The objective of limit state design is to ensure that the probability of any limit state being reached acceptably low. This is made possible by specifying appropriate multiple safety factors for each limit state (Level reliability). Of course, in order to b e meaningful, the specified values of safety factors should result in ‘target reliability’ (the reliability that will produce designs which will provide the required amount of safety and at the same time result in economic structures). The multiple safety factor adopted by the Indian code is in the so-called partial safety factor format, which is expressed as Rd ≥ ∑ γif Qid Where Rd is the design strength computed using the reduced material strength Ru/γm , where Ru is the characteristic material strength and γm is the partial safety factor for the material, and allows for uncertainties of element behaviour and possible strength reduction due to manufacturing tolerances and imperfections in the material. The values are given in the Table 4 of IS code. These values are directly taken from Eurocode 3 and have no statistical backing (N Subramanian, 2008)The Partial Safety factors for loads γf make allowances for possible deviation of loads and the reduced possibility of all loads acting together. Even these are based on Eurocode 3 with slight modifications. It is to be noted that the

load factors are reduced when different types of Loads (DL, LL, WL or WL) are acting simultaneously at their peak values. This is because of the reduced probability of all the loads acting concurrently. Structural Stability The code deals with 3 forms of structural Stability. They are 1) General Stability 2) Stability against Overturning 3) Sway Stability General Stability It should be ensured that the structure as a whole and each of its elements remain stable from the commencement of erection until demolition. When two members are incapable of keeping themselves in equilibrium then sufficient external bracing should be provided for stability. Stability against Overturning The structure as a whole or any part of it should be designed to prevent instability due to overturning or sliding, while designing tall or cantilever structures. While checking for overturning, uplift or sliding, the loads should be multiplied by the relevant γf factors .The code suggests the following a) The loads and forces should be divided into components aiding instability and those resisting instability. b) The forces and loads causing instability should be combined using the appropriate load facto are given. c) The permanent loads and effects causing resistance should be multiplied by a partial safety factor of 0.9 and added together with design resistance( after being multiplied by the appropriate partial safety factor) d) The resistance effect should be greater than or equal to the destabilising effect. Sway Stability This condition imposes that there must not be excessive lateral deformation under applied loads. a) When the structures are sheltered by an adjoining building, b) When the structure is entirely enclosed, c) When the building is wide in relation to the applied load In order to prevent these situations being critical, the code requires all structures to be checked for a minimum notional horizontal load. The notional loads are specified in Section 4.3.6 of the code as 0.5% of the factored load. The notional horizontal loads should not be 1) applied while considering overturning 2) combined with other horizontal loading such as wind or Earthquake 3) taken to contribute to net shear on the foundation. The notional horizontal load should be applied on the whole structure, in both orthogonal directions, in one direction at a time, and should not be taken to act simultaneously with the factored gravity load. Moreover when the ratio of height to the lateral width of a building is less than unity, such notional loads need not be considered.

Serviceability Limit States In Limit states of serviceability, the variable to be considered is a serviceability parameter (representing deflection, vibration etc.) .A limit state or failure is considered to occur when a specified maximum limit of serviceability, ∆all exceeded (as shown in fig) In the Fig. Pf is the Probability of failure and f∆(∆) is the frequency distribution curve for D. Serviceability limit states relate to satisfactory performance and correspond to excessive deflection, vibration, local deformation, durability and fire resistance. The Load factor γf should be taken as unity for all serviceability limit state calculations, since they relate to the criteria governing normal use.

Probability Density

f∆(∆) Pf

∆all Serviceability Variable D (Deflection, Crack width) Fig. 1 Reliability Model for Serviceability Design

CODAL PROVISON COMPARISON In the newly revised IS 800, stress is laid to make optimum utilisation of the structural member along with provision of making adequate checks for restricting local buckling. Comparison of the critical parameters/clauses of two versions of the code (i.e. IS 800-1984 and IS 800-2007) is as follows
SR NO Clause Description IS:800-1984 IS:800-2007 Comments

1.0 1.1

Material Structural Steels

(REFER IS:2062) TABLE-1, (Pg.2) • Steel conforming to IS: 2062 (General purpose steel) - Steels designated as Fe410WA, Fe410WB and Fe410WC. This standard covers the requirements of steel plates, strips, sections, flats, bars etc. for use in structural work. The steel is suitable for welded, bolted and riveted structures. • Steel conforming to IS:8500 - Weldable structural steel (medium and high-strength qualities). Steels designated as Fe-440-HT, Fe-490-HT, Fe-540-HT, Fe-570-HT and Fe-590HT. • Steel conforming to IS:961- Structural steel ( high tensile )-Steels designated as Fe-570-HT and Fe-540 W -HT.

1.1.1

Yield stress

TABLE-1, (Pg.2) IS 2062 Fe 410 ( WA/WB/WC ) (MPa ) Upto 20mm thk. - 250 20-40 mm - 240 > 40mm - 230

TABLE-1, (Pg.2) • Steel conforming to IS:2062 (General purpose steel) - Steels designated as Fe410WA, Fe410WB and Fe410WC. This standard covers the requirements of steel plates, strips, sections, flats, bars etc. for use in structural work. The steel is suitable for welded, bolted and riveted structures. • Structural Steel other than that specified in IS 2062 can be used provided that the permissible stresses and other design provisions are suitably modified and the steel is also suitable for the type of fabrication adopted • Steel that is not supported by mill test result may be used in structural system after confirming their quality according to IS 1608, or they should be used for unimportant members TABLE-1, (Pg.2)IS 2062 No change Fe 410 ( WA/WB/WC ) (MPa) Upto 20mm thk. - 250 20-40 mm - 240 > 40mm - 230

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

1.1.2

1.2

2.0 2.1

YS - Yield Stress Ultimate TABLE-1, (Pg.2) tensile Fe 410 (WA / WB / WC ) strength 410 MPa Fasteners / Black bolts made from mild Bolts steel-IS:2062. High strength friction grip(HSFG) bolts made from high tensile steel.IS:961 GENERAL DESIGN REQUIREMENTS Load Combination s Clause no. 3.4.2 (Pg.-24) 1) DL + IL 2) DL + IL + WL or EL 3) DL + WL or EL

TABLE-1, (Pg.2) Fe 410 (WA / WB / WC ) 410 MPa Black bolts made from mild steel-IS:2062. High strength friction grip(HSFG) bolts made from high tensile steel.-IS:961 Clause no. 3.5 (Pg.-16) 1) DL + IL 2) DL + IL + WL or EL 3) DL + WL or EL 4) DL + ER (Erection Load) Clause no. 3.7 (Pg. 17) The Sections are classified based on its local buckling strength and the ability to allow rotation before failing. They are a) Class 1 (Plastic) b) Class 2 (Compact) c) Class 3(Semi-compact) & d) Class 4 (Slender) Clause no. 5.3.3 (Pg-29) Partial safety factors have to be considered and no increase or decrease of stresses have to be considered for individual loads Clause no. 5.5.1 (Pg-30) the structure should satisfy 2 limit states 1) Limit state of strength and 2) Limit state of serviceability. The structure should adhere

No Change

No Change

More Importance is given to Erection loading The Class of section governs its design

2.2

Section Classificatio n

No such classification has been made

2.3

Increase of Stresses

2.4

Stability

Clause no. 3.9 (Pg-31) & IS:816-Cl.7.3(Pg.17) Wind / Earthquake Loads • Strl. Steel members 33.33 % • Rivets, bolts, Welds etc. 25 % Clause no. 3.12 (Pg-34) Restoring moment > 1.2 x max. Overturning moment (due to DL) + 1.4 x max. Overturning moment (due to IL and WL/EL) IS-800 : In cases where Dead load provides the restoring

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

moment, only 0.9 times DL shall be considered.

to 1) Stability against Overturning – The loads and effects contributing to the resistance shall be multiplied with 0.9 and added together to get design resistance. 2) Sway Stability Clause no. 5.6.1 (Pg-31) Deflection limits have been provided separately for Industrial buildings and Other Buildings and separate limits have been mentioned for different members.

2.5

Limiting Deflection

Clause no. 3.13 (Pg-34) • Max. Deflection for all applicable loads (Vertical / Horizontal ) = 1/325 of the Span / height.

More importance is given to serviceability requirements for various members in a structure. Additional provision for block shear has been incorporated

3.0 3.1

TENSION MEMBERS Axial Clause no. 4.1 (Pg-37) Stresses Stress on the net effective area not to exceed σat = 0.6 fy (in MPa)

3.2

Maximum Slenderness Ratio

Clause no. 3.7 (Pg-30) • Tension member = 400 • Tension Member ( Reversal of stress occurs due to loads other than WL / EL) = 180 • Tension member (subject to possible reverse of stresses due to WL, EL) =350 Clause no. 4.2 (Pg-37) For area calculation, this clause may be referred.

Clause no.6 (Pg-32-34) The design strength of a tension member should be lowest of 1) Strength due to yielding of gross c/s 2) Strength due to rupture of critical c/s 3) Strength due to block shear • No change has been made

3.3

Net Effective Area

Clause no. 6.3 &6.4 (Pg 3234) This clause may be referred.

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

4.0 4.1

COMPRESSION MEMBERS Axial Clause no. 5.1 (Pg-38) stresses The direct stress shall not exceed 0.6fy or as calculated by equation given in Cl.-5.1.1. Permissible stress σac shall be taken from Table - 5.1 (Pg39), for corresponding slenderness ratio.

Clause no. 7.1.2.1 (Pg-34) The allowable axial stress or design compressive stress (fcd) shall be calculated using the formulas given in the clause or can be calculated using tables 9(a),9(b),9(c),9(d) on the basis buckling class of the section Clause no. 7.2 (Pg-35-45) ‘K’ values shall be taken appropriately based on degree of end restraint of member as given in Table-11 (Pg. 45). 2) For Truss & braced frame members buckling in the plane of truss, effective length ‘1’ shall be taken as between 0.7 and 1.0 times the distance between the centres of intersections, depending on degree of end restraint. For members buckling in the plane perpendicular to truss, ‘1’ shall be taken as distance between centres of intersection. Clause no. B7 (Pg-5-37) • Comp. Member (DL, IL) = 180 • Comp. Member (WL, EL) = 250
1)

The concept of imperfection factor and buckling class of the section has been introduced

4.2

Effective Length (l), l = KL

4.3

Maximum Slenderness Ratio

Clause no. 5.2 (Pg-38) 1) ‘K’ values shall be taken appropriately based on degree of end restraint of member as given in Table -5.2 (Pg-41&42) OR follow the procedure given I n Appendix-C. 2) Truss members buckling in the plane of truss, ‘l’ shall be taken as between 0.7 and 1.0 times the distance between the centres of intersections, depending on degree of end restraint. For members buckling in the plane perpendicular to truss, ‘l’ shall be taken as distance between points of restraint. Clause no. 3.7 (Pg-30) • Comp. Member (DL, IL) = 180 • Comp. Member (WL, EL) = 250 Clause no. 5.7 (Pg-47) 1) Lacing of comp. member shall be designed for a transverse shear equal to

‘K’ values given in both the codes are same.

Clause 3.8 (Table 3)(Pg20) No changes made No changes have been made in the load

4.4

BUILT-UP MEMBERS - Lacing

1)

Clause no. 7.6 (Pg-48-50) Lacing of comp. member shall be designed for a transverse shear equal to

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

4.5

at least 2.5 % of the axial force in the member. 2) Slenderness ratio of the lacing bars shall not exceed 145. 3) Angle of Inclination with 3) Angle of Inclination with the axis of member - (for the axis of member - (for both single & double both single & double lacing) - 40° to 70°to the lacing) - 40° to 70°. axis of built up section. 4) The max. spacing of 4) The max. spacing of lacing shall be such that lacing shall be such that min. slenderness ratio min. slenderness ratio (l/r) (l/r) of the components of of the components of the the member between member between consecutive connection is consecutive connection is not greater than 50 OR not greater than 50 OR 0.7 0.7 times the most times the most unfavourable (l/r) of the unfavourable (l/r) of the member as a whole, member as a whole, whichever is less. whichever is less. BUILT-UP Clause no. 5.8(Pg-51) Clause no. 7.7(Pg-50-52) MEMBERS - 1) Battens shall be designed 1) Battens shall be Battening / to carry the bending designed to carry the Tie plates moment & shears arising bending moment & from transverse shear shears arising from force ‘V’ of 2.5 % of the transverse shear force total axial force on the ‘V’ of 2.5 % of the total axial force on whole comp. member, at the whole comp. any point in the length of the member, divided member, at any point equally between parallel in the length of the planes of battens. member, divided equally between 2) The spacing of battens parallel planes of centre to centre of end battens fastenings shall be such 2) The spacing of that the slenderness ratio battens centre to (l/r) of the lesser main centre of end component over that fastenings shall be distance shall be not such that the greater than 50 OR greater slenderness ratio (l/r) at least 2.5 % of the axial force in the member. 2) Slenderness ratio of the lacing bars shall not exceed 145.

calculation and basic design requirements.

No changes have been made in the load calculation and basic design requirements.

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

than 0.7 time the slenderness ratio of the member as a whole, about it’s x-x axis. (axis parallel to the battens)

4.6

Column Base Clause no. 5.4 (Pg-44) Plate Dimension & thickness of base plate shall be calculated using formulas provided in this clause.

of the lesser main component over that distance shall be not greater than 50 OR greater than 0.7 time the slenderness ratio of the member as a whole, about it’s x-x axis. (axis parallel to the battens) Clause no. 7.4 (Pg-46-48) Dimension & thickness of base plate shall be calculated using formula provided in this clause.

The concept of effective area for load transfer has been introduced.

5.0 5.1

MEMBERS SUBJECTED TO BENDING Bending Clause no. 6.2 (Pg-55) Clause no 8 (Pg-52-559) Stress 1) Max. permissible, σbt or 1) For Laterally Supported σbc = 0.66fy (For Strong & Beams: The design Weak axis bending ) strength in bending shall be calculated as per the 2) Max. permissible σbc for Iformulas given on the beams & Channels (based basis whether the section on section properties and is susceptible to shear l/ry ) shall be referred from Table-6.1A to 6.1F buckling before yielding (Pgs-57 to 62). 2) For Laterally 3) For beams & plate girders, Unsupported Beams, the max. permissible σbc shall design strength in be computed as per bending shall be equation given in Cl. 6.2.3 calculated as per the (Pg-56) OR Table-6.2 formulas given and (Pg-64) may be referred resistance to lateral for σbc calculated from fcb torsional buckling should for different values of fy. not be checked for ( All stresses in MPa) a) bending is about minor axis b) Section is hollow or a solid bar c) In case of major axis bending, the non dimensional

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

slenderness ratio is less than 0.4. 5.2 Bearing Stress Clause no. 6.3 (Pg-68) Max. permissible bearing stress, on net area of contact is, σp = 0.75 ƒy Clause no. 6.4 (Pg-68) 1) Max. permissible Shear stress is, Tvm = 0.45 ƒy 2) Average shear stress in member calculated on the cross section of the web shall not exceed the limits as mentioned in Cl. No. 6.4.2 (Pg-69). Also refer Table-6.6A, B, C (Pg-7375) for stiffened webs. Clause no. 8.7.4 (Pg-67) Should be less than the yield stress of the steel divided by Partial safety factor (ie. fy/1.1) Clause no. 8.4 (Pg-59-60) The nominal plastic shear resistance under pure shear should be calculated using the formulas =, based on the shear areas specified for various sections. Resistance to shear buckling can be verified based on the value of ratio of depth to web thickness.2 methods have been specified for calculation of nominal shear strength. They are 1) Simple Post Critical Method (can be used for beams with or without intermediate transverse Stiffeners 2) Tension Field Method (can be used for beams with intermediate transverse stiffeners) Clause no. 8.6.1.2 (Pg. 64) No specific criteria are mentioned. But in order to avoid buckling of the compression flange into the web, the web thickness shall satisfy the criteria’s specified

5.3

Shear stresses

5.4

Effective length of Compression Flanges & max. Slenderness Ratio

Clause no. 6.6 (Pg-76) & Clause no. 3.7 (Pg-30) 1) To calculate permissible bending stress as explained above in 4.0 (I), appropriate effective length shall be considered referring this clause. 2) Max. Slenderness Ratio for Compression flange of beam =300

SR NO

Clause Description

IS:800-1984
3)

IS:800-2007

Comments

For cantilever beams of projecting length ‘L’, refer Cl. No. 6.6.3 (Pg.77).

6.0 6.1

COMBINED STRESSES Axial Clause no. 7.1.1 (Pg-90) Compression The requirements of this & Bending clause (Equations) shall be satisfied.

Clause no. 9.3.1 & 9.3.2.2 (Pg. 70-71) The requirements in the above clauses should be satisfied.

6.2

Axial Tension & Bending

Clause no. 7.1.2 (Pg-90) The condition as per this clause shall be satisfied.

Clause no. 9.3.1 & 9.3.2.1(Pg 70-71) The requirements in the above clauses should be satisfied.

Separate governing equations are specified for different types of sections. Separate governing equations are specified for different types of sections. The moment reduction is dictated by the percentage of shear force wrt. allowable shear force in the section.

6.3

Bending & Shear

Clause no. 7.1.4 (Pg-91) The equivalent stress calculated by the equation given in this clause shall not exceed the value, σe = 0.9Fy.

Clause no 9 (Pg 69-70) The Moment carrying capacity of the section shall be reduced by the amount as specified in the code ( for high shear force). No reduction is required for Shear force value < 60% of allowable shear capacity of the section.

6.4

Bearing, Bending & Shear

7.0 7.1 7.1.1

Clause no. 7.1.5 (Pg-92) The equivalent stress calculated by the equation given in this clause shall not exceed the value, σe = 0.9Fy. CONNECTIONS. BOLTED :Permissible Clause no. 8.9.4 - (Pg-95) Stresses for IS:2062 bolts :(Material) MPa ksi a) Axial tension 120 17.4 b) Shear 80 11.6 c ) Bearing 250 36.25

No specific criteria are mentioned.

Clause no. 10 (Pg 73-77) No specific value prescribed. Procedure given for calculation of permissible loads (Axial Tension, Shear, & Bearing).

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

7.1.2

Combined shear and tension in bolts

7.1.3

7.1.4

Clause no. 8.9.4.5 - (Pg-96) The individual stresses should not exceed allowable values and combined stress ratio should not exceed 1.40 Minimum Clause no. 8.10.1-(Pg-96) pitch Shall not be less than 2.5 times the nominal diameter of the bolt. Minimum Clause no. 8.10.2-(Pg-97) edge distance As given in Table 8.2 on page 97

7.1.5

Maximum pitch

Clause no. 8.10.1-(Pg-96) Shall not exceed 32t or 300 mm whichever is less, where t is the thickness of the thinner outside plate.

7.1.6

Maximum edge distance No specific criteria are mentioned.

Clearance for Clause no.3.6.1.1 (Pg 28) fastener 1.5 mm for dia. Of bolt <= Holes 25mm, and 2 mm for dia. of bolt > 25mm

Clause no. 10.4.6 (Pg-77) No specific value provided. Procedure given for calculation of permissible loads. Clause no. 10.2.2(Pg-73) Shall not be less than 2.5 times the nominal diameter of the fastener (Bolt/Rivet). Clause no. 10.2.4.2(Pg-74) Should be >1.7 times hole dia. for sheared or handflame cut edges, & >1.5 times hole dia. for rolled, machine-flame cut, sawn and planed edges, from the centre of the hole. Clause no.10.2.3(Pg-74) Shall not exceed 32t or 300 mm whichever is less, where t is the thickness of the thinner outside plate. Clause no. 10.2.4.3 (Pg-74) Shall not exceed 12tε ,where t is the thickness of the thinner outer plate, and ε = (250/fy)1/2 Clause no. 10.2.1 (Pg-73) As given in table 19

No change has been made. Not much variation is observed in the end results.

No change has been made.

More practical aspect for clearance has been considered.

7.2 7.2.1 7.2.1.1

WELDED :Fillet welds : Permissible stresses.

Refer IS:816 Clause no. 7.1.2-(Pg-17) Shear stress Shall not exceed 110 Mpa

7.2.12

Effective area of weld

Clause no. 6.2.3-(Pg-10) Effective length X Effective throat thickness

Clause no. 10.5-(Pg-78) Shear stress Shall not exceed 110 Mpa nor as calculated using clause 10.5.7 (Pg. 7981) Clause no. 6.2.3-(Pg-10) Effective length X effective throat thickness

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

7.2.1.3

Effective throat thickness

Clause no. 6.2.3-(Pg-10) shall not be less than 3 mm. for calculations it shall be taken as K times the fillet size, where K is a constant. Of a complete penetration weld shall be taken as the thickness of the thinner part joined. And that of an incomplete/partial penetration butt weld shall be taken as minimum thickness of the weld metal common to the parts joined, excluding reinforcement.

7.2.1.4

Effective length

Clause no. 6.2.4-(Pg-11) Shall be the overall length of weld including end returns.

7.2.1.5

Minimum length of weld Minimum size of the weld

Clause no. 6.2.4.1-(Pg-11) shall not be less than four times the size of the weld. Clause no. 6.2.2-(Pg-10) shall not be less than 3 mm. The minimum size of the first run or the single run weld shall be as given in Table 1 in IS:816 Clause no. 7.2-(Pg-17) Permissible stresses in shear and tension reduced to 80%.

Clause no. 10.5.3-(Pg-78) shall not be less than 3 mm and not > 0.7t, where t is the thickness of the thinner plate. for calculations of stresses at faces inclined to each other it shall be taken as K times the fillet size, where K is a constant. Of a complete penetration weld shall be taken as the thickness of the thinner part joined. And that of an incomplete/partial penetration butt weld shall be taken as minimum thickness of the weld metal common to the parts joined, excluding reinforcement. Clause no. 10.5.4-(Pg-78) Shall be the overall length of weld excluding end returns in case of Fillet welds and shall be the overall length of weld including end returns for Butt weld. Clause no. 10.5.4(Pg-78) shall not be less than four times the size of the weld. Clause no. 10.5.2-(Pg-78) shall not be less than 3 mm. The minimum size of the first run or the single run weld shall be as given in Table 21 (Pg 78) Clause no. 10.5.7.2 (Pg. 79) A partial safety factor of 1.5 is to be used for calculation design strength in shear and tension.

No Changes have been suggested

No Changes have been suggested No Changes have been suggested

7.2.1.6

7.2.1.8

Field /site weld

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

7.2.2 7.2.2.1

Butt/Groove Weld :Permissible stresses.

Clause no. 7.1.1-(Pg-16) Shear stress through throat of butt shall not exceed that of the base material. Tension or compression on section through throat of butt weld shall not exceed the stress in the base metal.

7.2.2.2

8.0 8.1

Clause no.6.1.61-(Pg-7) Effective length times the effective throat thickness GANTRY GIRDER Increase in Clause no.3.9.3-(Pg-31) stresses While considering the simultaneous effects of vertical & horizontal surge loads of cranes for the combination given in cl. No. 3.4.2.3 & 3.4.2.4, the permissible stresses may be increased by 10 %.

Effective area of weld

Clause no. 10.5.7(Pg. 79) Permissible stresses I fillet weld shall be calculated as per eqn. in Cl. 10.5.7.1.1 Butt Welds shall be treated a parent metal with a thickness equal to the throat thickness, and shall not exceed those permitted in the parent metal Clause no. 10.5.4(Pg-78-79) Effective length times the effective throat thickness

No specific criteria are given.

Stresses are to be calculated using adequate Partial Safety factors.

8.2 9.0 9.1

9.2

Limiting Clause no.3.13.1.3-(Pg-35) Clause no. 5.6.1 (Pg. 31) deflection This clause shall be referred. Table 6 should be referred. DESIGN AND DETAILING FOR EARTHQUAKE LOADS Load Clause no. 12.2 (Pg. 87) Combination No such criteria are given Two more combinations s have to be considered 1) 1.2 DL + 0.5 LL ± 2.5 EL 2) 0.9 DL ± 2.5 EL Lateral Load No such classification has The Building has been Resisting been made classified as System 1) Braced Frame System a) Ordinary concentrically Braced Frames (OCBF) b) Special Concentrically Braced Frame(SCBF)

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

Eccentrically Braced Frame (EBF) 2) Moment Frame System a) Ordinary Moment Frame (OMF) b) Special Moment Frame (SMF) Various criteria for loads on members are specified for different lateral load resisting systems 10.0 10.1 FATIGUE Reference design Condition No such criteria are mentioned. Clause no. 13.2.1 (Pg. 91) The conditions when Fatigue design becomes necessary are mentioned, along with a plot of standard S-N curve for each category. A capacity reduction factor µ r is to be applied when plates greater than 25 mm tk. are joined by transverse fillet or butt welding Clause no. 13.2.3 (Pg. 92) Based on consequences of fatigue failure , component details have been classified and Partial Safety Factors are given for each type.(Refer Table 25 - Pg. 92) Clause no. 13.3 (Pg. 92-98) Tables 26 (a) to (d) indicate the classification of different details into various categories for the purpose of assessing fatigue strength. Clause no. 13 ( Pg. 105-110) The following points have been discussed and relevant design standards have been mentioned 1) Fire Resistance Level

c)

10.2

Partial Safety No such criteria are Factors mentioned.

10.3

Detail Category

No such criteria are mentioned.

11 11.1

FIRE RESISTANCE No such criteria are mentioned.

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

2) Period of Structural Adequacy 3) Variation of mechanical properties of Steel with Temperature 4) Limiting Steel Temperature 5) Thermal Increase with Time in Protected Members 6) Temperature Increase with Time in Unprotected Members 7) Determination of Period of Structural Adequacy from a single test 8) Three-Sided Fire Exposure Condition. 12.0 USEFUL TABLES 1) Maximum Slenderness ratio - Table 3.1 (Pg-30) 2) Permissible stress in Axial Compression Table 5.1 (Pg-39) 3) Effective length of compression member of constant Dimension Table 5.2 (Pg-41-43) 4) Max. permissible bending stress in I-beams or Channels - Table 6.1A/B (Pg-57,58) 5) Permissible avg. shear stress - Table 6.6A (Pg73) 6) Minimum Thickness of web for Plate Girders with solid web – Table 6.7 (Pg. 83) 7) Max. permissible stress in Rivets and Bolts - Table 8.1 (Pg.-95) 8) Edge Distance of Holes -

1)

2) 3)

4)

5) 6) 7) 8) 9)

10)

Tensile Properties of Structural steel products (Pg. 13-14) Limiting Width to Thickness Ratio (Pg. 18) Maximum Values of Effective Slenderness Ratios (Pg.20) Partial Safety Factors for Loads, for Limit States (Pg. 29) Partial Safety Factor for Materials (Pg. 30) Deflection Limits (Pg. 31) Imperfection Factor (Pg. 35) Stress Reduction Factor for columns (Pg. 36-39) Design Compressive Stress for columns (Pg. 40-43) Buckling Class of C/S (Pg. 44)

SR NO

Clause Description

IS:800-1984

IS:800-2007
11)

Comments

9)

Table 8.2 (Pg. 97) Section Properties - SP(6) & IS:808.

12)

13)

14) 15)

16) 17) 18) 19) 20)

21)

22)

23)

24)

25) 26)

Effective Length of Prismatic Compression Members (Pg. 45) Constants k1,k2,k3 for calculation of Flexural Torsional buckling in Angle Struts (Pg. 48) Design Bending Compressive Stress Corresponding to Lateral Buckling (Pg. 55-56) Critical Stress wrt elastic Lateral Buckling (Pg. 57) Effective length of Simply Supported Beams (Pg. 58) Effective Length for Cantilever (Pg. 61) Constants α1 & α2 (Pg. 71) Equivalent uniform Moment Factor (Pg. 72) Clearances for Fastener Holes (Pg. 73) Typical Average Values fro coefficient of Friction (Pg. 77) Minimum Size of First run or of a single run Fillet Weld (Pg. 78 Values of K for Different Angles Between Fusion Faces (Pg. 78) Response Reduction Factor for a Building System (Pg. 87) Multiplying Factors for Calculated Stress Range (Pg. 92) Partial Safety Factors for Fatigue Strength (Pg. 92) Detail Category Classification for fatigue strength assessment (Pg.

SR NO

Clause Description

IS:800-1984

IS:800-2007

Comments

27)

28) 29)

30) 31)

32)

33) 34)

93-98) Factors to allow for Variability of Structural Units ( Pg. 103) Environmental Exposure Condition (Pg. 103) Protection Guide for Steel Work Application (Pg. 104-105) Regression Coefficient , k (Pg. 107) Fire Resistance Rating – Encased Steel Columns (Pg. 110) Fire Resistance Rating – Encased Steel Beams (Pg. 111) Normal Tolerance after Erection (Pg. 115) Straightness Tolerance Incorporated in Design Rules (Pg. 115_

Shelter Definition Shelter is a steel structure with roof, and with or without wall cladding provided for equipment to protect from sunshine, rain, show, wind and temperature and noise, which is either fully enclosed or fully opened according to the requirements of equipment. 1) Compressor Shelter For compressor shelter and its related equipment, which would be required in most of the plant facilities. It is usually fully enclosed or partially enclosed with operation platform, hoisting devices such as hoist or crane for maintenance and operation of compressor 2) Ordinary Shelter For equipment other than compressor such as pump, emergency generator, package equipment and etc. include sunshades for truck loading and car parking. It is usually partially enclosed or fully opened and in some cases with operation platform on ground and hoist or crane for maintenance and operation of equipment.

A typical example of shelter for table top type compressor is shown below.

Fig. 2 Typical Shelter for Table Type Compressor Type of Structure Conventional Steel Frame Building Type A pitched roof of building with rigid forming combined with framing, which are furnished with operating platforms, equipment support, piping support and etc. as required. A typical figure is shown below

Fig. 3 Typical Steel Frame Building Type Compressor Shelter Pre Engineered Building (PEB) Type Manufacturer’s standard of Steel framed building with its own materials specification and design code fro steel structure, connection, purlin, girth, cladding material. PEB type, of which the steel weight is less than conventional type, is suitable for simple structure without support for heavy loads nor lots of supports like a warehouse.

Comparison of Compressor Shelter members Designed by WSM and LSM Load Combinations The following load combinations have been considered in the analysis of the Portal. IS 800-2007
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 1.5 (DL+CL)+1.05 (IL) 1.2 (DL+CL)+1.05 IL+0.6WL(-X PREESSURE) 1.2 (DL+CL)+1.05 IL+0.6WL(-X SUCTION) 1.2 (DL+CL)+1.05 IL+0.6WL(X PREESSURE) 1.2 (DL+CL)+1.05 IL+0.6WL(X SUCTION) 1.2 (DL+CL)+1.05 IL+0.6ELX 1.2 (DL+CL)+1.05 IL-0.6ELX 1.2 (DL+CL)+1.05 IL+0.6ELY 1.2 (DL+CL)+1.05 IL-0.6ELY 1.2 (DL+CL+WL(-X PRESSURE))+0.53 IL 1.2 (DL+CL+WL(-X SUCTION))+0.53 IL 1.2 (DL+CL+WL(X PRESSURE))+0.53 IL 1.2 (DL+CL+WL(X SUCTION))+0.53 IL 1.2 (DL+CL+ELX)+0.53 IL 1.2 (DL+CL-ELX)+0.53 IL 1.2 (DL+CL+ELY)+0.53 IL 1.2 (DL+CL-ELY)+0.53 IL 1.5 (DL +WL(-X PRESSURE) 1.5 (DL +WL(-X SUCTION) 1.5 (DL +WL(X PRESSURE) 1.5 (DL +WL(X SUCTION) 1.5 (DL +ELX) 1.5 (DL -ELX) 1.5 (DL +ELY) 1.5 (DL -ELY) 0.9 DL+1.5WL(-X PRESSURE) 0.9 DL+1.5WL(-X SUCTION) 0.9 DL+1.5WL(X PRESSURE) 0.9 DL+1.5WL(X SUCTION) 0.9 DL+1.5ELX 0.9 DL-1.5ELX 0.9 DL+1.5ELY 0.9 DL-1.5ELY 1.2 DL+0.5(IL+CL)+2.5 ELx 1.2 DL+0.5(IL+CL)-2.5 ELx 1.2 DL+0.5(IL+CL)+2.5 ELy 1.2 DL+0.5(IL+CL)-2.5 ELy 0.9 DL+2.5 ELx 0.9 DL-2.5 ELx 0.9 DL+2.5 ELy 0.9 DL-2.5 ELy

IS 800-1984 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)
DL + IL + WL(-X PRESSURE) DL + IL + WL(-X-SUCTION) DL + IL + WL (X-PRESSURE) DL + IL + WL (X-SUCTION) DL + IL DL + IL + CL DL + IL + CL+ WL (-X-PRESSURE) DL + IL + CL+WL (-X-SUCTION) DL + IL + CL+ WL (X-PRESSURE) DL + IL + CL+WL (X-SUCTION) DL + IL + VX + VY DL + IL -VX + VY DL + IL + CL + VX +VY

Note: Kindly note that in the LSM , Crane Load is considered as the Leading Live load and the actual Live Load is considered as the accompanying Live Load.

Member Forces The compressor Shelter is assumed to comprise of the following Different Types of Sections: 1) 2 ISMB 400 Placed at a c/c distance of 1000mm (R1)(Main Columns upto Gantry Girder) 2) ISMB 450 (R2)(Columns supporting Roof Truss) 3) ISA 75 x 75 x 8 (R3)( Truss Top and Bottom Chord Members) 4) ISA 65 x 65 x 6 (R4)( Truss Inclined Members) 5) ISA 50 x 50 x 6 (R5)( Truss Vertical Members) 6) ISMB 150 (R6)(Monitor Portal)

Fig. 4 Staad Model for Portal Frame indicating the locations of Various Members

The member wise STAAD Pro Analysis Output after applying the above mentioned load combinations are as follows: Forces as per LSM
Section ISMB400BB100 ISMB450 ISA75X75X8 ISA65X65X6 ISA50X50X6 ISMB150 Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Axial Max Fx kN 1067.917 -9.306 349.129 -86.659 376.31 -387.325 232.33 -139.311 77.453 -237.676 17.084 -17.603 Shear Max Fy kN 171.777 -222.799 223.019 -154.811 11.804 -11.696 0.502 -0.528 1.031 -1.618 0.647 -0.71 Max Fz kN 0 0 0 0 0 0 0 0 0 0 0 0 Torsion Max Mx kNm 0 0 0 0 0 0 0 0 0 0 0 0 Bending Max My kNm 0 0 0 0 0 0 0 0 0 0 0 0 Max Mz kNm 1366.781 -1505.794 280.178 -198.128 3.467 -3.016 0.587 -0.488 0.794 -0.797 0.416 -0.566

Forces as per WSM
Section ISMB400BB100 ISMB450 ISA75X75X8 ISA65X65X6 ISA50X50X6 ISMB150 Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Max+ve Max -ve Axial Max Fx kN 779.694 199.834 -41.206 166.838 -181.083 90.21 -84.566 90.303 -61.541 11.365 -11.781 Shear Max Fy kN 144.088 -119.851 145.209 -106.198 7.847 -7.566 0.327 -0.421 0.645 -0.554 0.58 -0.426 Max Fz kN 0 0 0 0 0 0 0 0 0 0 0 0 Torsion Max Mx kNm 0 0 0 0 0 0 0 0 0 0 0 0 Bending Max My kNm 0 0 0 0 0 0 0 0 0 0 0 0 Y Max Mz kNm 887.13 -1072.455 178.89 -119.623 1.728 -2.067 0.446 -0.312 0.329 -0.3 0.432 -0.283

Saad Pro Sign Convention: + ve Axial Force Denotes Compression - ve Axial Force denotes Tension + ve Shear Force Denotes Shear Force along +ve Y axis - ve Shear Force Denotes Shear Force along -ve Y axis + ve Moment denotes Hogging moment - ve Moment denotes Sagging moment
X

Z

Fig. 5 Staad Global Axis

DESIGN OF TRUSS MEMBER (2 ISA 50x50x6, Single Leg Connection) IS 800-1984 Design for Tension MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Ultimate Strength of Steel Partial Safety Factors

γm0 γm1

= = = = =

200000 250 410 1.1 1.25

MPa MPa MPa

LOADS ACTING ON MEMBER : Axial Force- Tension GEOMETRY : No. of bolts usedfor load Transfer Nominal Dia. Of Bolts Spacing between bolts Edge Distance End Distance Effective Length in "x " dirn. Effective Length in "y " dirn. SECTION PROPERTIES : Section details Gross Area of section (Ag) (one angle) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Net Area of Total Cross Section (An) Net Area of Connected Leg (Anc) Gross Area of Ourstanding Leg (Ago) Clearance for Bolts Minimum Gross area in Shear Along Bolt line (Avg) Minimum Net Area in Sheat Along Bolt Line (Avn) Minimum Gross Area in tension (Atg) Minimum Net Area in Tension (Atn) w1 SUMMARY OF DESIGN : TYPE OF STRESSES Yielding of Gross C/s Failure of Critical Section ACTUAL FORCE 30.77 KN 30.77 KN

=

30.764

KN

= = = = = = =

6.00 20.00 60.00 30.00 30.00 892.50 892.5

no. mm mm mm mm mm mm

= = = = = = = = = = = = = =

2 ISA 50 x 50 x 6, Single Leg connection 568.00 mm2 50.00 mm 50.00 mm 6.00 mm 436.00 mm2 150.00 mm2 282.00 mm3 2.00 mm (Table 19, Pg 73) 1980.00 mm 1254.00 180.00 114.00 20.00 mm mm mm mm

PERMISSIBLE FORCE 85.2 KN 48.51 KN

CHECK SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength of Member under Axial Tension σper = 150 MPa T per = 85200.00 N

> SAFE

30764

Design Strength due to Rupture of Critical Section Effective C/s area of Connected Leg (A1) A1 = 150.00 Gross C/s area of un connected Leg A2 = 282.00 k = 3*A1/(3*A1+A2) Net Effective Area (Aeff) Tensile force resisted by the section

mm2 mm2 = = = = 0.61 A1 + A2*k σper * Aeff 48504.1 = > SAFE 323.36 30764 mm2 N

Design for Compression LOADS ACTING ON MEMBER : Axial Force- Compression SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Radius of Gyratiojn about minor Axis Radius of Gyratiojn about major Axis SUMMARY OF DESIGN :

=

133.729

kN

= = = = = = =

2 ISA 50x50x6, Connected Back to back 1136.00 mm2 50.00 mm 50.00 mm 6.00 mm 15.10 mm 23.10 mm

TYPE OF CHECKS Axial Force

ACTUAL FORCE 133.729 KN

PERMISSIBLE FORCE 139.77 KN

CHECK SAFE

Slenderness Check ( Table 3.1, Pg. 30) leff/rmin λ= AXIAL FORCE Allowable Axial stress σal = fcc = = σal = Allowable Comp Force =

=

59.11

< SAFE

180

(Cl. 5.1) 0.6*fcc*fy/(fcc1.4+fy1.4)1/1.4 π2*E/(leff/rmin)2 564.45 123.03 139765.27 MPa Mpa > 133729 N SAFE

IS 800-2007 Design for Tension LOADS ACTING ON MEMBER : Factored Loads Axial Force- Tension SUMMARY OF DESIGN :

=

118.838

kN-m

TYPE OF CHECKS Yielding of Gross C/s Failure of Critical Section Block Shear

ACTUAL FORCE 118.84 KN 118.84 KN 118.84 KN

PERMISSIBLE FORCE 129.1 KN 125.14 KN 283.78 KN

CHECK SAFE SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength iof Member under Axial Tension (Tdg) (Cl. 6.2, Pg. 32) Tdg Ag*fy/γm0 = = 129090.91 N = > SAFE Design Strength due to Rupture of Critical Section For Single Angles (Cl. 6.3.3, Pg. 33) 1.4 - 0.076*(w/t)*(fy/fu)*(bs/Lc) β = = β Tdn = = = 1.26 1.26 0.9*Anc*fu/γm1 + β *Ago*fy/γm0 125131.81 > SAFE

129.0909 KN 118.838 KN

≤ ≥ ≤ ≥

{fu*γm0/(fy*γm1)} 0.7 1.44 0.7

118838 N

Design Strength due to Block Shear (Cl. 6.4,Pg 33) Tdb1 Tdb2 = = = [Avg*fy/(30.5*γm0)+0.9*Atnfu/γm1] 293460.42 (0.9*Avn*fu/(30.5*γm1)+Atg*fy/γm0) 283777.26 283777.26 > SAFE 118838

Tdb

=

Design for Compression LOADS ACTING ON MEMBER : Factored Loads Axial Force- Compression SUMMARY OF DESIGN : TYPE OF CHECKS Axial Force (Fixed Ends) Axial Force (Hinged Ends) ACTUAL FORCE 133.729 KN 133.729 KN PERMISSIBLE FORCE 182.49 KN 138.68 KN CHECK SAFE SAFE = 133.729 KN

Slenderness Check (Table 3, Pg. 20) leff/rmin l =

=

59.11

< SAFE

180

AXIAL FORCE Considering that the angles are loaded only through one Leg Equivalent Slenderness Ratio λe = (k1+k2*λvv2+k3*λϕ2)0.5 λvv λϕ = = = = (l/rvv)/(ε*(π2E/250)0.5) 0.67 (b1+b2)/(2*t)/(ε*(π2E/250)0.5) 0.09

(Cl. 7.5.1.2 & Cl. 7.5.2.2)

Considering Fixed condition at the Ends k1 = 0.2 k2 = 0.35 k3 = 20 λe φ = 0.729 0.5(1+α*(λe-0.2)+λe2) 0.895 1/(φ+(φ2-λe2)0.5) 0.707 X fy/γm0 160.64 182485.16 121656.78 > SAFE

(Table 12, Pg. 48) (Table 12, Pg. 48) (Table 12, Pg. 48)

= = X = = Design Compressive Stress fcd =

Design Comp Force = Allowable Comp force =

133729

Considering Hinged condition at the Ends k1 = 0.7 k2 = 0.6

(Table 12, Pg. 48) (Table 12, Pg. 48)

k3 λe φ

= =

5 1.005 0.5(1+α*(λe-0.2)+λe2) 1.202 1/(φ+(φ2-λe2)0.5) 0.537 X fy/γm0 122.07 138674.03 92449.35 > SAFE

(Table 12, Pg. 48)

= = X = = Design Compressive Stress fcd = = Design Comp Force = Allowable Comp force =

133729

Considering Concentric Axial Force (Angles loaded through both the legs)(Cl. 7.5.1.1, Pg. 47) λ φ = 0.67 0.5(1+α*(λe-0.2)+λe2) 0.836 1/(φ+(φ2-λe2)0.5) 0.746 X fy/γm0 169.53 Design Comp Force = Allowable Comp force = 192581.25 128387.50 N > SAFE 133729

= = X = = Design Compressive Stress fcd =

DESIGN OF TRUSS MEMBER (2 ISA 65x65x6, Single leg connection) IS 800-1984 Design for Tension MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Ultimate Strength of Steel Partial Safety Factors

γm0 γm1

= = = = =

200000 250 410 1.1 1.25

MPa MPa MPa

LOADS ACTING ON MEMBER : Axial Force- Tension GEOMETRY : No. of bolts used for load Transfer Nominal Dia. Of Bolts Spacing between bolts Edge Distance End Distance Effective Length in "x " dirn. Effective Length in "y " dirn. SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Net Area of Total Cross Section (An) Net Area of Connected Leg (Anc) Gross Area of Ourstanding Leg (Ago) Clearance for Bolts Minimum Gross area in Shear Along Bolt line (Avg) Minimum Net Area in Sheat Along Bolt Line (Avn) Minimum Gross Area in tension (Atg) Minimum Net Area in Tension (Atn) w1 SUMMARY OF DESIGN : TYPE OF STRESSES Yielding of Gross C/s Failure of Critical Section ACTUAL FORCE 66.63 KN 66.63 KN

=

66.624

kN

= = = = = = =

6.00 20.00 60.00 35.00 35.00 1530.00 1400.00

no. mm mm mm mm mm mm

= = = = = = = = = = = = = =

2 ISA 65 x 65 x 6, Single Leg connection 744.00 mm2 65.00 mm 65.00 mm 6.00 mm 612.00 mm2 240.00 mm2 372.00 mm3 2.00 mm (Table 19, Pg 73) 2010.00 mm 1284.00 210.00 144.00 30.00 mm mm mm mm

PERMISSIBLE FORCE 111.6 KN 73 KN

CHECK SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength of Member under Axial Tension σper = 150 T per = 111600.00 N

> SAFE

100000 N

Design Strength due to Rupture of Critical Section Effective C/s area of Connected Leg (A1) A1 = 240.00 Gross C/s area of un connected Leg A2 = 372.00 k = 3*A1/(3*A1+A2) Net Effective Area (Aeff) Tensile force resisted by the section

mm2 mm2 = = = = 0.66 A1 + A2*k σper * Aeff 72791.21 = > SAFE 485.27 66624 mm2 N

Design for Compression LOADS ACTING ON MEMBER : Axial Force- Compression SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Radius of Gyratiojn about minor Axis Radius of Gyratiojn about major Axis SUMMARY OF DESIGN :

=

90.197

kN

= = = = = = =

2 ISA 65x65x6, Connected Back to back 1488.00 mm2 65.00 mm 65.00 mm 6.00 mm 19.80 mm 28.90 mm

TYPE OF CHECKS Axial Force

ACTUAL FORCE 90.197 KN

PERMISSIBLE FORCE 154.27 KN

CHECK SAFE

Slenderness Check( Table 3.1, Pg. 30) leff/rmin λ = AXIAL FORCE Allowable Axial stress σal = fcc = = σal = Allowable Comp Force =

=

77.27273

< SAFE

180

(Cl. 5.1) 0.6*fcc*fy/(fcc
1.4

+fy1.4)1/1.4

π2*E/(leff/rmin)2 330.25 MPa 103.67 Mpa 154265.39 >

90197

SAFE

IS 800-2007 Design for Tension LOADS ACTING ON MEMBER : Factored Loads Axial Force- Tension SUMMARY OF DESIGN :

=

69.66

kN-m

TYPE OF CHECKS Yielding of Gross C/s Failure of Critical Section Block Shear

ACTUAL FORCE 69.66 KN 69.66 KN 69.66 KN

PERMISSIBLE FORCE 169.1 KN 192.87 KN 296.41 KN

CHECK SAFE SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength iof Member under Axial Tension (Tdg) (Cl. 6.2, Pg. 32) Tdg Ag*fy/γm0 = = 169090.91 N = > SAFE Design Strength due to Rupture of Critical Section For Single Angles (Cl. 6.3.3, Pg. 33) 1.4 - 0.076*(w/t)*(fy/fu)*(bs/Lc) β = = β Tdn = = = 2.23 1.44 0.9*Anc*fu/γm1 + β *Ago*fy/γm0 192864.00 > SAFE

169.09 KN 150 KN

≤ ≥ ≤ ≥

{fu*γm0/(fy*γm1)} 0.7 1.44 0.7

69655.50 N

Design Strength due to Block Shear (Cl. 6.4,Pg 33) Tdb1 Tdb2 = = = [Avg*fy/(30.5*γm0)+0.9*Atnfu/γm1] 306252.90 (0.9*Avn*fu/(30.5*γm1)+Atg*fy/γm0) 296405.68 296405.68 > SAFE 69655.5

Tdb

=

Design for Compression LOADS ACTING ON MEMBER : Factored Loads Axial Force- Compression SUMMARY OF DESIGN : TYPE OF CHECKS ACTUAL FORCE PERMISSIBLE FORCE 208.45 KN 162.26 KN 209.11 KN = 77.27 < SAFE CHECK FAILS FAILS SAFE 180 = 223.33 kN

Axial Force (Fixed Ends) 223.33 KN Axial Force (Hinged Ends) 223.33 KN Concentric Axial Force 223.33 KN Slenderness Check (Table 3, Pg. 20) leff/rmin l =

AXIAL FORCE Considering that the angles are loaded only through one Leg Equivalent Slenderness Ratio λe = (k1+k2*λvv2+k3*λϕ2)0.5 λvv λϕ = = = (l/rvv)/(ε*(π2E/250)0.5) 0.87 (b1+b2)/(2*t)/(ε*(π2E/250)0.5) 0.12

(Cl. 7.5.1.2 & Cl. 7.5.2.2)

Considering Fixed condition at the Ends k1 = 0.2 k2 = 0.35 k3 = 20 λe = 0.873 = = X = = Design Compressive Stress fcd = φ 0.5(1+α*(λe-0.2)+λe2) 1.046 1/(φ+(φ2-λe2)0.5) 0.616 X fy/γm0 140.08 208442.72 138961.82 N

(Table 12, Pg. 48) (Table 12, Pg. 48) (Table 12, Pg. 48)

MPa < FAILS 223330

Design Comp Force = Allowable Comp force =

Considering Hinged condition at the Ends k1 = 0.7 k2 = 0.6 k3 = 5

(Table 12, Pg. 48) (Table 12, Pg. 48) (Table 12, Pg. 48)

λe φ

=

1.108 0.5(1+α*(λe-0.2)+λe2) 1.337 1/(φ+(φ2-λe2)0.5) 0.480 X fy/γm0 109.04 162254.75 108169.83 N

= = X = = Design Compressive Stress fcd =

MPa < FAILS 223330

Design Comp Force = Allowable Comp force =

Considering Concentric Axial Force (Angles loaded through both the legs)(Cl. 7.5.1.1, Pg. 47) λ = 0.87 = = X = = Design Compressive Stress fcd = = Design Comp Force = Allowable Comp force = φ 0.5(1+α*(λe-0.2)+λe2) 1.043 1/(φ+(φ2-λe2)0.5) 0.618 X fy/γm0 140.53 209107.71 139405.14 N

MPa < FAILS 223330

DESIGN OF TRUSS MEMBER (2 ISA 75x75x8, Single Leg connection) IS 800-1984 Design for Tension MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Ultimate Strength of Steel γm0 Partial Safety Factors γm1 LOADS ACTING ON MEMBER : Axial Force- Tension GEOMETRY : No. of bolts usedfor load Transfer Nominal Dia. Of Bolts Spacing between bolts Edge Distance End Distance Effective Length in "x " dirn. Effective Length in "y " dirn. SECTION PROPERTIES : (one angle) Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Net Area of Total Cross Section (An) Net Area of Connected Leg (Anc) Gross Area of Ourstanding Leg (Ago) Clearance for Bolts Minimum Gross area in Shear Along Bolt line (Avg) Minimum Net Area in Sheat Along Bolt Line (Avn) Minimum Gross Area in tension (Atg) Minimum Net Area in Tension (Atn) w1 SUMMARY OF DESIGN : TYPE OF STRESSES Yielding of Gross C/s Failure of Critical Section ACTUAL FORCE 106.44 KN 106.44 KN PERMISSIBLE FORCE 170.7 KN 109.84 KN CHECK SAFE SAFE

= = = = =

200000 250 410 1.1 1.25

MPa MPa MPa

=

106.4315 kN

= = = = = = =

11.00 24.00 60.00 40.00 40.00 1120.00 1400

no. mm mm mm mm mm mm

= = = = = = = = = = = = = =

2 ISA-75x75x8, Single Leg connection 1138.00 mm2 75.00 mm 75.00 mm 8.00 mm 930.00 mm2 360.00 mm2 568.00 mm3 2.00 mm (Table 19, Pg 73) 5120.00 mm 2936.00 mm 320.00 mm 216.00 mm 35.00 mm

Design Strength Due to Yielding of Gross Cross Section

Design Strength of Member under Axial Tension σper = 150.00 T per = 170700.00

Mpa N > 100000 N

Design Strength due to Rupture of Critical Section Effective C/s area of Connected Leg (A1) A1 = 360.00 Gross C/s area of un-connected Leg A2 = 568.00 k = 3*A1/(3*A1+A2) = 0.66 Net Effective Area (Aeff) Tensile force resisted by the section

mm2 mm2

= = =

A1 + A2*k σper * Aeff 109835

= > SAFE

732.23

mm2

100000 N

Design for Compression LOADS ACTING ON MEMBER : Axial Force- Compression SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Radius of Gyratiojn about minor Axis Radius of Gyratiojn about major Axis SUMMARY OF DESIGN :

=

220

kN

= = = = = = =

2 ISA 75 x75 x 8, Back to back 2276.00 mm2 75.00 mm 75.00 mm 8.00 mm 22.80 mm 34.90 mm

TYPE OF CHECKS Axial Force

ACTUAL FORCE 220 KN

PERMISSIBLE FORCE 274.69 KN

CHECK SAFE

Slenderness Check ( Table 3.1, Pg. 30) leff/rmin λ = AXIAL FORCE Allowable Axial stress σal = fcc = = σal = Allowable Comp Force =

=

61.40

< SAFE

180

(Cl. 5.1) 0.6*fcc*fy/(fcc 523.00 120.69 274686.27
1.4

+fy1.4)1/1.4 MPa Mpa > 220000 SAFE

π2*E/(leff/rmin)2

IS 800-2007 Design for Tension LOADS ACTING ON MEMBER : Factored Loads Axial Force- Tension SUMMARY OF DESIGN :

=

193.66 kN

TYPE OF CHECKS Yielding of Gross C/s Failure of Critical Section Block Shear

ACTUAL FORCE 193.67 KN 193.67 KN 193.67 KN

PERMISSIBLE FORCE 258.64 KN 250.23 KN 641.36 KN

CHECK SAFE SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength iof Member under Axial Tension (Tdg) (Cl. 6.2, Pg. 32) Tdg Ag*fy/γm0 = = 258636.36 N = > SAFE Design Strength due to Rupture of Critical Section For Single Angles (Cl. 6.3.3, Pg. 33) 1.4 - 0.076*(w/t)*(fy/fu)*(bs/Lc) β = = β Tdn = = = 1.12 1.12 0.9*Anc*fu/γm1 + β *Ago*fy/γm0 250220.17

258.64 KN 150 KN

≤ ≥ ≤ ≥

{fu*γm0/(fy*γm1)} 0.7 1.44 0.7

> SAFE

193662.5 N

Design Strength due to Block Shear (Cl. 6.4,Pg 33) Tdb1 Tdb2 = = = = = [Avg*fy/(30.5*γm0)+0.9*Atnfu/γm1] 735588.97 (0.9*Avn*fu/(30.5*γm1)+Atg*fy/γm0) 641356.40 641356.40 > SAFE 193662.5

Tdb

Design for Compression MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Ultimate Strength of Steel

= = =

200000 250 410

MPa MPa MPa

Partial Safety Factors

γm0 γm1

= =

1.1 1.25

LOADS ACTING ON MEMBER : Factored Loads Axial Force- Compression SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Leg (t) Radius of Gyratiojn about minor Axis Radius of Gyratiojn about major Axis SUMMARY OF DESIGN : TYPE OF CHECKS ACTUAL FORCE

=

376.31

kN

= = = = = = =

2 ISA-75x75x8, Back to back 2276.00 mm2 75.00 mm 75.00 mm 8.00 22.80 34.90 mm mm mm

PERMISSIBLE FORCE 365.88 KN 288.66 KN 420.45 KN = 49.12 < SAFE

CHECK FAILS FAILS SAFE 180.0

Axial Force (Fixed Ends) 376.31 KN Axial Force (Hinged Ends) 376.31 KN Concentric Axial Force 376.31 KN Slenderness Check (Table 3, Pg. 20) leff/rmin l =

AXIAL FORCE Considering that the angles are loaded only through one Leg Equivalent Slenderness Ratio λe = (k1+k2*λvv2+k3*λϕ2)0.5 (Cl. 7.5.1.2 & Cl. 7.5.2.2) λvv λϕ = = = (l/rvv)/(ε*(π2E/250)0.5) 0.55 (b1+b2)/(2*t)/(ε*(π2E/250)0.5) 0.11 Considering Fixed condition at the Ends k1 = 0.2 k2 = 0.35 k3 = 20 λe = 0.728 0.5(1+α*(λe-0.2)+λe2) φ = = X = = Design Compressive Stress 0.894 1/(φ+(φ2-λe2)0.5) 0.707

(Table 12, Pg. 48) (Table 12, Pg. 48) (Table 12, Pg. 48)

fcd

=

X fy/γm0 160.75 365872.31 243914.87

Mpa < FAILS 376310

Design Comp Force = Allowable Comp force =

Considering Hinged condition at the Ends k1 = 0.7 k2 = 0.6 k3 = 5 λe = 0.969 0.5(1+α*(λe-0.2)+λe2) φ = = 1.158 1/(φ+(φ2-λe2)0.5) X = = 0.558 Design Compressive Stress X fy/γm0 fcd = 126.83 Design Comp Force = Allowable Comp force = 288653.98 192435.99 < FAILS

(Table 12, Pg. 48) (Table 12, Pg. 48) (Table 12, Pg. 48)

376310

Considering Concentric Axial Force (Angles loaded through both the legs)(Cl. 7.5.1.1, Pg. 47) = 0.55 0.5(1+α*(λe-0.2)+λe2) = = 0.739 φ+(φ2-λe2)0.5) 1/( X = = 0.813 Design Compressive Stress fcd X fy/γm0 = = 184.73 Design Comp Force = Allowable Comp force = 420449.33 280299.55 N > SAFE 376310 λ φ

DESIGN OF TRUSS MEMBER (ISMB 150) IS 800-1984 Design for Tension MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Ultimate Strength of Steel Partial Safety Factors

γm0 γm1

= = = = =

200000 250 410 1.1 1.25

MPa MPa MPa y

LOADS ACTING ON MEMBER : Axial Force- Tension GEOMETRY : No. of bolts usedfor load Transfer Nominal Dia. Of Bolts Spacing between bolts Edge Distance End Distance Distance between bolt lines Effective Length in "x " dirn. Effective Length in "y " dirn. SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Web (tw) Thickness of flange (t) Net Area of Total Cross Section (An) Net Area of Connected Leg (Anc) Gross Area of Ourstanding Leg (Ago) Clearance for Bolts Minimum Gross area in Shear Along Bolt line (Avg) Minimum Net Area in Sheat Along Bolt Line (Avn) Minimum Gross Area in tension (Atg) Minimum Net Area in Tension (Atn) w1 SUMMARY OF DESIGN : TYPE OF STRESSES Yielding of Gross C/s Failure of Critical Section ACTUAL FORCE 11.79 KN 11.79 KN

=

11.781

kN x

= = = = = = =

6.00 20.00 60.00 35.00 35.00 60.00 2000.00 2000

no. mm mm mm mm mm mm mm

= = = = = = = = = = = = = = =

ISMB 150 (connected via 2 bolt lines) 1900.00 mm2 150.00 mm 40.00 mm 4.80 mm 7.60 mm 1688.80 mm2 485.76 mm2 1143.04 mm3 2.00 mm (Table 19, Pg 73) 1488.00 mm 907.20 288.00 182.40 45.00 mm mm mm mm

PERMISSIBLE FORCE 285 KN 168.96 KN

CHECK SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength of Member under Axial Tension σper = 150 Mpa T per = 285000.00 N Design Strength due to Rupture of Critical Section Effective C/s area of Connected Leg (A1) A1 = 485.76 mm2 Gross C/s area of un connected Leg A2 = 1143.04 mm2 k = 3*A1/(3*A1+A2) = Net Effective Area (Aeff) = Tensile force resisted by the section = = Design for Compression LOADS ACTING ON MEMBER : Axial Force- Compression SECTION PROPERTIES : Section details Gross Area of section (Ag) Width of connected Leg Width of Unconnected Leg (w) Thickness of Web (tw) Thickness of flange (tf) Radius of Gyration about minor Axis Radius of Gyration about major Axis SUMMARY OF DESIGN : TYPE OF CHECKS Axial Force ACTUAL FORCE 11.368 KN

> SAFE

100000 N

0.56 A1 + A2*k σper * Aeff 168951.9

= > SAFE

1126.35 mm2 11781 N

=

11.368

kN

= = = = = = = =

ISMB 150 1900.00 150.00 40.00 4.80 7.60 16.60 61.80

mm2 mm mm mm mm mm mm

PERMISSIBLE FORCE 120.21 KN

CHECK SAFE

Slenderness Check ( Table 3.1, Pg. 30) leff/rmin λ = AXIAL FORCE Allowable Axial stress σal = = = σal = Allowable Comp Force = fcc

=

120.48

<

180

SAFE

(Cl. 5.1) 0.6*fcc*fy/(fcc1.4+fy1.4)1/1.4 π2*E/(leff/rmin)2 135.85 MPa 63.27 Mpa 120204.53 >

11368 N

SAFE

IS 800-2007 Design for Tension LOADS ACTING ON MEMBER : Factored Loads Axial Force- Tension SUMMARY OF DESIGN :

=

17.603

kN-m

TYPE OF CHECKS Yielding of Gross C/s Failure of Critical Section Block Shear

ACTUAL FORCE 17.61 KN 17.61 KN 17.61 KN

PERMISSIBLE FORCE 431.82 KN 518.32 KN 241.16 KN

CHECK SAFE SAFE SAFE

Design Strength Due to Yielding of Gross Cross Section Design Strength iof Member under Axial Tension (Tdg) (Cl. 6.2, Pg. 32) Tdg Ag*fy/γm0 = = 431818.18 N = > SAFE Design Strength due to Rupture of Critical Section For Single Angles (Cl. 6.3.3, Pg. 33) 1.4 - 0.076*(w/t)*(fy/fu)*(bs/Lc) β = = β Tdn = = = 1.53 1.44 0.9*Anc*fu/γm1 + β *Ago*fy/γm0 518313.47 > SAFE 17603 N

431.82 150

KN KN

≤ ≥ ≤ ≥

{fu*γm0/(fy*γm1)} 0.7 1.44 0.7

Design Strength due to Block Shear Tdb1 Tdb2 = = = [Avg*fy/(30.5*γm0)+0.9*Atnfu/γm1] 249093.84 (0.9*Avn*fu/(30.5*γm1)+Atg*fy/γm0) 241156.30 241156.30 > SAFE 17603

Tdb

=

Design for Compression LOADS ACTING ON MEMBER : Factored Loads Axial Force- Compression SUMMARY OF DESIGN : TYPE OF CHECKS Axial Force Slenderness Check (Table 3, Pg. 20) leff/rmin λ= AXIAL FORCE (Cl. 7.1.2.1) h/b = tf = (buckling about y-y axis) α = λ = φ = = = = Design Compressive Stress fcd = X ACTUAL FORCE 17.09 KN PERMISSIBLE FORCE 172.98 KN CHECK SAFE = 17.084 kN

=

120.48

< SAFE

180

1.875 7.6

> <

1.2 40

mm

0.34 (class b) 1.36 0.5(1+α*(λe-0.2)+λe2) 1.617 1/(φ+(φ2-λe2)0.5) 0.401 X fy/γm0 91.04 172979.05 115319.37 N > SAFE 17084

Design Comp Force = Allowable Comp force = (buckling about x-x axis) α = λ = = = X = = Design Compressive Stress fcd = = Design Comp Force = Allowable Comp force = φ

0.21 1.36 0.5(1+α*(λe-0.2)+λe2) 1.542 1/(φ+(φ2-λe2)0.5) 0.440 X fy/γm0 799.60 1519234.09

(class a)

> SAFE

16600

1012822.73 N

DESIGN OF COLUMN ( ISMB 450) IS 800-1984 MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Partial Safety Factors

γm0 γm1

= = = =

200000 250 1.1 1.25

MPa MPa

y LOADS ACTING ON COLUMNS : Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) GEOMETRY : Eff. Length @ x-axis (leffx) Eff. Length @ y-axis (leffy) SECTION PROPERTIES : Section details Area of Combined section (Ax) Moment of inertia @ major axis (Ixx) Moment of inertia @ minor axis (Iyy) Elastic Moduli of section @ major axis (Zexx) Elastic Moduli of section @ minor axis (Zeyy) Plastic Modulus of section @ major axis (Zpxx) Radius of gyration @ major axis (rxx) Radius of gyration @ minor axis (ryy) Weight of section Thickness of flange (Tf) of I Section Thickness of web (tw) Overall depth (D) Clear depth of web (d1) Effective Web Depth (h1) Centre to centre distance between flanges Width of Flange of Individual I section SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses ACTUAL STRESS 21.66 MPa 132.53 MPa 0.00 MPa 0.84 PERMISSIBLE STRESS 93.61 MPa 133.13 MPa 150.00 MPa 1.00 CHECK SAFE SAFE SAFE SAFE = = = 199.818 179 0 kN kN-m kN-m

x

= =

3.13 2.61

m m

= = = = = = = = = = = = = = = = =

ISMB 450 9227.00 303908000 8340000 1350700.00 111200.00 1533360 181.50 30.10 72.40 17.40 9.40 450.00 415.20 379.20 432.60 150.00

mm2 mm4 mm4 mm3 mm3 mm3 mm mm Kg / m mm mm mm mm mm mm mm

CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal)

= =

P / Ax 199818 / 9227

= Actual bending stress @ major axis (σbcx,cal) = = = = = =

Actual bending stress @ minor axis (σbcy,cal)

21.65579278 MPa Mx / Zxx 179000000 / 1350700 132.52 MPa My / Zyy 0 / 111200 0.00 MPa

CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx)

= = = = = = = = = = = = = = = =

Slenderness ratio in minor direction (λy)

lx / rxx 3132 / 181.5 17.26 lY / ryy 2610 / 30.1 86.71 86.71 π2 ∗ Ε / λx2 < SAFE 180 = λperm.

Maximum slenderness ratio ( λmax ) Elastic critical stress in major dir. (fccx )

Elastic critical stress in minor dir. (fccy )

π2 ∗ 200000 / 297.78 6622.15 MPa π2 ∗ Ε / λy2 π2 ∗ 200000 / 7518.8 262.27 MPa 262.27 MPa 0.6 * fcc * fy [(fcc)1.4 + (fy)1.4 ] 1/1.4 0.6 * 262.27 * 250 [(262.27)^1.4 + (250)^1.4 ]^1/1.4 93.60 MPa (as per clause 5.1.1) σac,cal σac 21.66 93.60 0.231

Minimum elastic critical stress ( fcc ) Permissible axial stress (σac )

Ratio of axial compression

= = = =

BENDING STRESS : Y

X

= = = = = = = =

26.5 * 105 / ( l / ryy)2 26.5 * 10^5 / ( 86.72 )^2 352.45 MPa Y * [1+ 1/20 * { (l/ryy)*(T/D) }2 ]0.5 352.46 * [1+ 1/20 * { ( 86.72)*(17.4 / 450) }^2 ]^0.5 440.50 MPa Distance Between NA and Top Extreme Fiber Distance Between NA and Bottom Extreme Fiber

(as per clause 6.2.4)

(as per clause 6.2.4)

C1 C2

C1 K1 K2

= = =

C2 1.0 For ψ = 1.0 For ω = 0.5 (as per table 6.3) (as per table 6.4) (as per clause 6.2.4)

0.0 fcbx K1 * ( X + K2 * Y ) * C1/C2 = = 1 * ( 440.51 + 0 * 352.46 ) * 1.0 = 440.50 ( If T/t < 2.0 and d1/t < 1344 / sqrt(fy), fcbx = 1.2 * fcbx & If T/t > 2.0 or d1/t > 1344 / sqrt(fy) , fcbx = fcbx ) fcbx = = σbcx = = σbcy = = 1.2 * 440.51 528.60 0.66 x fcbx x fy MPa

(as per clause 6.2.4.1)

[(fcbx)1.4 + (fy)1.4 ] 1/1.4 0.66 x 528.61 x 250 [(528.61)^1.4 + (250)^1.4 ]^1/1.4 133.13 MPa 150.00 MPa

(as per clause 6.2.5)

CHECK FOR COMBINED STRESSES : Cmx = 0.6 Cmy = σac,cal σac = σbcx,cal x Cmx 1 - σac,cal x σbcx 0.6 σbcy,cal x Cmy 1 - σac,cal x σbcy 0.6 x fccy 0 x 0.6 1 - 21.66 x 150 0.6 x 262.3 0.00 1.00

(as per 7.1.3) (as per 7.1.3)

21.66 = 93.61 = =

0.6 x fccx 132.53 x 0.6 1 - 21.66 x134 0.6 x 6623 0.23 0.60 0.83 < SAFE

IS 800-2007 LOADS ACTING ON COLUMNS : Factored Loads Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) Shear Force SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal) ACTUAL STRESS 37.84 MPa 207.44 MPa 0 MPa 1.197 PERMISSIBLE STRESS 139.21 MPa 201.28 MPa 0 MPa 1.00 CHECK SAFE FAILS SAFE FAILS

= = = =

349.129 280.178 0 223.019

kN kN-m kN-m KN

= = = = = = = = =

P / Ax 349129/9227 37.84 MPa Mx / Zxx 280178000/1350700 207.43 MPa My / Zyy 0/111200 0.00 MPa

Actual bending stress @ major axis (σbcx,cal)

Actual bending stress @ minor axis (σbcy,cal)

SECTION CLASSIFICATION For Compression Flange b/Tf = Web d/Tw = For Flexure Flange b/Tf = d/Tw = ε = (250/fy)0.5

(Table 2) 4.31 40.34 < < 9.4 ε 42 ε 9.4 ε 84 ε Plastic Semi-Compact Semi Compact Plastic Plastic Plastic

4.31 47.87

< <

CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx) Slenderness ratio in minor direction (λy)

= = = = = =

lx / rxx 3132/181.5 17.26 lY / ryy 2610/30.1 86.71

Maximum slenderness ratio ( λmax )

=

86.71

< SAFE

180 = λperm.

a (As per Table 10) 0.21 (As per Table 7) Imperfection Factor (α2) = 0.34 Moodification factor for effective length (MF) MF = 1 (not required as the column is not built up (Cl. 7.7.1.4)) = Leffx Leffy = = 3.132 m 2.61 m = = = = = = = Euler Buckling stress in major dir. (fccx ) = = = = = = = = = = = = = = fcd 139.21x9227/1000 = = lx / rxx 3132/181.5 17.26 lY / ryy 2610/30.1 86.71 2543.77 MPa π2 ∗ Ε / λy2 (Cl. 7.1.2.1) π2∗200000/297.78 6630.59 MPa 2 2 π ∗ Ε / λy π2∗200000/7518.8 262.60 MPa 0.19 (Cl. 7.1.2.1) 0.98 0.518 1.108 227.56 Mpa 139.20 Mpa 2099714.57 N 1284443.59 N 139.20 Mpa 1284.44 KN

Column Buckling Curve Imperfection Factor (α1)

=

Modified Slenderness ratio in major direction (λx)

Mopdified Slenderness ratio in minor direction (λy)

Euler Buckling stress in minor dir. (fccy )

λxx λyy φχ φγ fcdx = fcdy = Ndx = Ndy =

=(fy/fccx)0.5
0.5

= (250/6630.59)^0.5

=(fy/fccy) = (250/262.6)^0.5 =0.5∗[1+α (λ−0.2)+λ2] =0.5∗[1+α (λ−0.2)+λ2] (fy/γm0)/(φx +[φx 2-λxx 2]0.5)=Xfy/γm0≤fy/γm0 (fy/γm0)/(φy +[φy 2-λyy 2]0.5)=Xfy/γm0≤fy/γm0 fcdx * Ax fcdy * Ax

Permissible compressive Stress Design Compressive Strength.=

BENDING STRESS : (for Laterally Unrestrained Case: )(Cl. - 8.2.2) fcr,b = 365.85 Mcr = 662216997.19 λLT 0.76 = 0.83



0.78223981

λLT

=

0.83



0.4

therefore the member is to be considered as laterally unsupported Check whether webs are susceptible to Shear Buckling before Yielding Shear force = 223019.00 N Permissible Shear Force = 1506884.20 N Ratio V/Vd = 0.15 Therefore the webs are not susceptible to shear buckling before yielding βb αLT φLT X LT fbd = = = = = 0.5[1+αLT(λLT-0.2)+λLT2] 1/(φLT + [ φLT2 - λLT2}0.5) X LT.fy/γm0 Zp/Ze = 1 0.21

<

0.6

(for Plastic Section) (for rolled steel section - Cl. 8.2.2) = = = 0.91 0.78 177.30

Design Bending Moment (Cl. 8.2.2) β *Zp*f Mdx = = b bd Design Bending Stress =

271866985.46 N-mm = 201.28 MPa

271.87 KNm

Check of Resistance of the C/s to the combined action of axial compressive force & BM (Cl. 9.3.1.3) Ag*fy/γmo Nd = = 2097045.45 N = 2097.05 KN Basic Governing Equation (Cl. 9.3.1.3) -------= (349.129 / 2099.72) + (280.178 / 271.87) Check for Overall Member Strength ny nx ψ Cmx Cml λy λx Ky Kx = = = = = = = = = = = = = = N/Ndy N/Nx 0.6 0.4 (fy/fccy)^0.5 (fx/fccx)^0.5 1+(λy-0.2)*ny 1.211 1+(λx-0.2)*nx 0.999 = = = 0.272 0.166 0.00 (As per Table 18, Pg. 72) 0.976 0.194 1+0.8*ny 1.217 1+ 0.8*nx 1.133 N/Nd + My/Mdy +Mz/Mdz <= 1.0 = 1.197 ≥ 1 FAILS

= = < < < <

KLT KLT

1- 0.1*λLTny/(CmLT - 0.25) ≥ 1 - 0.1ny/(CmLT - 0.25) 0.850 ≤ 0.922 0.922 (Cl. 9.3.2.2) FAILS (Cl. 9.3.2.2) SAFE

P/Pdy + KLT.Mx/Mdx ≤ 1.0 1.222 ≥ 1.000

P/Pdx + Kz.Cmx.Mx/Mdx ≤ 1.0 0.784 ≤ 1.000

DESIGN OF MAIN COLUMN (ISMB 400 BB 1000) IS 800-1984 MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel LOADS ACTING ON COLUMNS : Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) Shear Force GEOMETRY : Eff. Length @ x-axis (leffx) Eff. Length @ y-axis (leffy) y b b1 x = = 200000 250 MPa MPa

= = = =

780 1073 0 150

kN kN-m kN-m KN

= =

8.50 3.50

m m

SECTION PROPERTIES : Section details Area of Single Section Moment of Inertia @ major axis of single section Moment of Inertia @ minor axis of single section Plastic Section modulus of section @ major axis Centre to centre distance between 2 ISMB (b1) Area of Combined section (Ax) Moment of inertia @ major axis (Ixx) Moment of inertia @ minor axis (Iyy) Elastic Moduli of section @ major axis (Zexx) Elastic Moduli of section @ minor axis (Zeyy) Plastic Modulus of section @ major axis (Zpxx) Plastic Modulus of section @ minor axis (Zpyy) Radius of gyration @ major axis (rxx) Radius of gyration @ minor axis (ryy) Weight of section Thickness of flange (Tf) of I Section Thickness of web (tw) Overall depth (D) Clear depth of web (d1)

= = = = = = = = = = = = = = = = = = = =

Double ISMB400 BB 1000 7846.00 mm2 204584000.00 mm4 6221000.00 mm4 1176180.00 mm3 1000.00 mm 15692.00 mm2 3935442000.00 mm4 ######## 409168000.00 mm4 ######## 6904284.21 mm3 511460.00 mm3 7846000.00 mm3 2352360.00 mm3 500.79 mm 161.48 mm 123.20 Kg / m 16.00 mm 8.90 mm 400.00 mm 368.00 mm

Effective Web Depth (h1) Width of Flange of Individual I section (b) SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses ACTUAL STRESS 49.71 MPa 155.42 MPa 0.00 MPa 0.92

= =

334.40 mm 140.00 mm

PERMISSIBLE STRESS 147.97 MPa 163.88 MPa 165.00 MPa 1.00

CHECK SAFE SAFE SAFE SAFE

CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal)

= = = = = = = = =

Actual bending stress @ major axis (σbcx,cal)

Actual bending stress @ minor axis (σbcy,cal)

P / Ax 780000 / 15692 49.706857 MPa Mx / Zxx 1073000000 / 6904285 155.41 MPa My / Zyy 0 / 511460 0.00 MPa

CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx)

= = = = = = = = = = = = = = = =

lx / rxx 8500 / 500.8 16.97 lY / ryy 3500 / 161.48 21.67 21.67 = λperm. < 180 2 2 π ∗ Ε / λx π2 ∗ 200000 / 288.09 6844.89 MPa 2 2 π ∗ Ε / λy π2 ∗ 200000 / 469.8 4197.36 MPa 4197.36 MPa 0.6 * fcc * fy [(fcc)1.4 + (fy)1.4 ] 1/1.4 0.6 * 4197.37 * 250 (as per clause 5.1.1) [(4197.37)^1.4 + (250)^1.4 ]^1/1.4 147.97 MPa σac,cal σac SAFE

Slenderness ratio in minor direction (λy)

Maximum slenderness ratio ( λmax ) Elastic critical stress in major dir. (fccx )

Elastic critical stress in minor dir. (fccy )

Minimum elastic critical stress ( fcc ) Permissible axial stress (σac )

Ratio of axial compression

= =

= = BENDING STRESS : Y = = = = = = = = = = =

49.71 147.97 0.336 (as per clause 6.2.4)

X

C1 C2 C1 K1 K2 fcbx

26.5 * 105 / ( l / ryy)2 26.5 * 10^5 / ( 21.68 )^2 5640.70 MPa Y * [1+ 1/20 * { (l/ryy)*(T/D) }2 ]0.5 5640.71 * [1+ 1/20 * { ( 21.68)*(16 / 400) }^2 ]^0.5 5745.72 MPa Distance Between NA and Top Extreme Fiber Distance Between NA and Bottom Extreme Fiber C2 For ψ = 1.0 1.0 For ω = 0.5 0.0

(as per clause 6.2.4)

(as per table 6.3) (as per table 6.4) (as per clause 6.2.4)

K1 * ( X + K2 * Y ) * C1/C2 = = 1 * ( 5745.73 + 0 * 5640.71 ) * 1.0 = 5745.72 ( If T/t < 2.0 and d1/t < 1344 / sqrt(fy), fcbx = 1.2 * fcbx & If T/t > 2.0 or d1/t > 1344 / sqrt(fy) , fcbx = fcbx ) fcbx σbcx = = = = = σbcy = 1.2 * 5745.73 6894.87 0.66 x fcbx x fy MPa

(as per clause 6.2.4.1)

[(fcbx)1.4 + (fy)1.4 ] 1/1.4 0.66 x 6894.87 x 250 [(6894.87)^1.4 + (250)^1.4 ]^1/1.4 163.88 MPa 165.00 MPa

(as per clause 6.2.5)

CHECK FOR COMBINED STRESSES : Cmx = 0.6 Cmy = σac,cal + σac = σbcx,cal x Cmx 1 - σac,cal x σbcx 0.6 + σbcy,cal x Cmy 1 - σac,cal x σbcy

(as per 7.1.3) (as per 7.1.3)

49.71 + = 147.97 = =

0.6 x fccx 0.6 x fccy 155.42 x 0.6 + 0 x 0.6 1 - 49.71 x 164 1 - 49.71 x 165 0.6 x 6845 0.6 x 4197.4 0.34 + 0.58 + 0.00 0.91 < 1.00 SAFE

IS 800-2007 LOADS ACTING ON COLUMNS : Factored Loads Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) Shear Force SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses ACTUAL STRESS 68.06 MPa 218.1 MPa 0 MPa 1.259 PERMISSIBLE STRESS 219.39 MPa 227.28 MPa 0 MPa 1.00 CHECK SAFE SAFE SAFE FAILS

1067.917 1505.79 0 222.799

kN kN-m kN-m KN

CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal)

Actual bending stress @ major axis (σbcx,cal)

Actual bending stress @ minor axis (σbcy,cal)

= = = = = = = = =

P / Ax 1067.917/15692 68.05 MPa Mx / Zxx 1505790000/6904284.22 218.10 MPa My / Zyy 0/511460 0.00 MPa

SECTION CLASSIFICATION For Compression b/Tf Flange d/Tw Web For Flexure b/Tf Flange d/Tw

(Table 2) = = 4.38 37.57 < < 9.4 ε Plastic 42 ε Semi-Compact Semi Compact 42 ε Semi Compact 84 ε Plastic Semi Compact ε = (250/fy)0.5

= =

37.57 4.38

< <

CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx)

= = =

lx / rxx 4500 / 161.48 27.87 lY / ryy 11500 / 400.99

Slenderness ratio in minor direction (λy)

= =

= Maximum slenderness ratio ( λmax ) = < c 0.49

28.68 28.68 180.00 = λperm. SAFE

Column Buckling Curve Imperfection Factor (α)

= =

(As per Table 10) (As per Table 7)

Moodification factor for effective length (MF) MF 1.1 Leffx = 9.35 Leffy = 3.85 Modified Slenderness ratio in major direction (λx)

(for battened Column) m m = = = = = = = = = = = = = = = = = = = = = = = lx / rxx 9350/500.8 18.67 lY / ryy

(Cl. 7.7.1.4)

Mopdified Slenderness ratio in minor direction (λy)

Euler Buckling stress in major dir. (fccx )

Euler Buckling stress in minor dir. (fccy )

3850/161.48 23.84 2543.77 MPa 2 2 π ∗ Ε / λy (Cl. 7.1.2.1) π2∗200000/348.59 5664.14 MPa 2 2 π ∗ Ε / λy π2∗200000/568.46 3473.32 MPa 0.21 0.27 0.525 0.553 226.10 219.38 3548018.48 3442573.99 219.38 3129.61 N N Mpa KN (Cl. 7.1.2.1)

λxx λyy φχ φγ fcdx = fcdy = Ndx = Ndy =

=(fy/fccx)0.5 = (250/5664.15)^0.5 =(fy/fccy)0.5 = (250/3473.32)^0.5 =0.5∗[1+α (λ−0.2)+λ2] =0.5∗[1+α (λ−0.2)+λ2] (fy/γm0)/(φx +[φx 2-λxx 2]0.5)=Xfy/γm0≤fy/γm0 (fy/γm0)/(φy +[φy 2-λyy 2]0.5)=Xfy/γm0≤fy/γm0 fcdx * Ax fcdy * Ax

Permissible compressive Stress, (fcd) Design Compressive Strength. BENDING STRESS : (for Laterally Unrestrained Case: ) (Cl. - 8.2.2) fcr,b Mcr λLT = = = 146503.79 27247573270.14 N N-mm

0.04 < 0.4 therefore the member is to be considered as laterally supported

Check whether webs are susceptible to Shear Buckling before Yielding Shear force = 222799 N

Permissible Shear Force = 1293264.60 N Ratio V/Vd = 0.17 < Therefore the webs are not susceptible to shear buckling before yielding βb = Zp/Ze (Cl. 8.2.1.2) = =

0.6

Design Bending Moment β b*Zp*fy/γmo Mdx = Design Bending Stress

1569155502.39 N-mm 227.27 MPa

=

1569.16 KNm

Check for overall buckling from bending consideration (Considering Push Pull effect) (As shown in Subramanian - Pg 1114) Axial force due to BM in One I section = Maxm. Compressive force in One I section = Compression resistance of the section = 1505790 N 2573707 N 3129612.72 N = = > 2573.71 KN 3129.61 KN 2573.71 KN SAFE Check of Resistance of the C/s to the combined action of axial compressive force & BM (Cl. 9.3.1.3) Nd = Ag*fy/γmo = 3566363.64 N N/Nd + My/Mdy +Mz/Mdz <= 1.0 1.259 > 1 = 3566.36 KN

Basic Governing Equation (Cl. 9.3.1.3) -------1067.917 / 3566.37 + 1505.79 / 1569.16 = Check for Overall Member Strength ny = nx = ψ Cmx CmLT λy λx Ky Kx = = = = = = = = =

FAILS

N/Ndy N/Nx 0.0 0.6 0.4 (fy/fccy)0.5 (fx/fccx)0.5 1+(λy-0.2)*ny 1.021 1+(λx-0.2)*nx 1.003

= =

0.310 0.301 (As per Table 18, Pg. 72)

= = < < < <

0.268 0.210 1+0.8*ny 1.248 1+ 0.8*nx 1.241 (Cl. 9.3.2.2)

P/Pdy + Ky.Cmy.My/Mdy + KLT.Mx/Mdx <= 1.0 0.70 < SAFE

1.000

P/Pdx + 0.6.Ky.Cmy.My/Mdy +Kx.Cmx.Mx/Mdx <= 1.0 0.879 < 1.000 SAFE

(Cl. 9.3.2.2)

DESIGN OF BEAM IS 800-1984 MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel Partial Safety Factors

γm0 γm1

= = = =

200000 250 1.1 1.25

MPa MPa

LOADS ACTING ON COLUMNS : Bending moment @ major axis (Mx) Bending moment @ minor axis (My) GEOMETRY : Eff. Length @ x-axis (leffx) Eff. Length @ y-axis (leffy) SECTION PROPERTIES : Section details Area of section (Ax) Moment of inertia @ major axis (Ixx) Moment of inertia @ minor axis (Iyy) Elastic Moduli of section @ major axis (Zexx) Elastic Moduli of section @ minor axis (Zeyy) Plastic Moduli of section @ major axis (Zpxx) Plastic Moduli of section @ minor axis (Zpyy) Radius of gyration @ major axis (rxx) Radius of gyration @ minor axis (ryy) Weight of section Thickness of flange (T) Thickness of web (t) Overall depth (D) Clear depth of web (d1) Centre to Centre distance of flanges Shear Resisting Area (Av) SUMMARY OF DESIGN : TYPE OF STRESSES Bending stress @ major axis Bending stress @ minor axis ACTUAL STRESS 142.39 MPa 0.00 MPa

= =

145 0

kN-m kN-m

y

= =

6.50 1.10

m m x

= = = = = = = = = = = = = = = = =

ISMB 300+160x10 PLT(T/B) 8826.00 mm2 162942666.67 mm4 11365666.67 mm4 1018391.67 mm3 142070.83 mm3 1147740.00 mm3 126693.59 mm3 135.87 mm 35.89 mm 69.32 Kg / m 20.85 mm 7.50 mm 320.00 mm 275.20 mm 298.34 mm 2400.00 mm2

PERMISSIBLE STRESS 162.35 MPa 165.00 MPa

CHECK SAFE SAFE

CALCULATION OF ACTUAL STRESSES : Actual bending stress @ major axis (σbcx,cal)

Actual bending stress @ minor axis (σbcy,cal)

= = = =

Mx / Zxx 145000000 / 1018392 142.38 MPa My / Zyy

= = CALCULATION OF PERMISSIBLE STRESSES : Slenderness ratio in major direction (λx) = = = = = = =

0 / 142071 0.00

MPa

lx / rxx 6500 / 135.88 47.84 lY / ryy 1100 / 35.89 30.65 47.84 < 250 = λperm. SAFE

Slenderness ratio in minor direction (λy)

Maximum slenderness ratio ( λmax )

BENDING STRESS : Y

= = = = = =

26.5 * 105 / ( l / ryy)2 26.5 * 10^5 / ( 30.66 )^2 2820.28 MPa Y * [1+ 1/20 * { (l/ryy)*(T/D) }2 ] 2820.28 * 3088.75 [1+ 1/20 * { ( 30.66)*(20.85 / 320) }^2 ] MPa

(as per clause 6.2.4)

X

(as per clause 6.2.4)

C1 C2 C1 K1 K2 fcbx

= = = = =

Distance Between NA and Top Extreme Fiber Distance Between NA and Bottom Extreme Fiber C2 For ψ = 1.0 1.0 For ω = 0.5

(as per table 6.3) (as per table 6.4) (as per clause 6.2.4)

0.0 K1 * ( X + K2 * Y ) * C1/C2 = = 1 * ( 3088.76 + 0 * 2820.28 ) * 1.0 = 3088.75 ( If T/t < 2.0 and d1/t < 1344 / sqrt(fy), fcbx = 1.2 * fcbx & If T/t > 2.0 or d1/t > 1344 / sqrt(fy) , fcbx = fcbx ) fcbx σbcx = = = = = σbcy = 1.2 * 3088.76 3706.50 0.66 x fcbx x fy MPa

(as per clause 6.2.4.1)

[(fcbx)1.4 + (fy)1.4 ] 1/1.4 0.66 x 3706.51 x 250 [(3706.51)^1.4 + (250)^1.4 ]^1/1.4 162.35 MPa 165.00 MPa (as per clause 6.2.5)

IS 800-2007 LOADS ACTING ON BEAMS : Factored Loads Bending moment @ major axis (Mx) Bending moment @ minor axis (My) SUMMARY OF DESIGN : TYPE OF STRESSES Bending stress @ major axis Bending stress @ minor axis ACTUAL STRESS 213.58 MPa 0.00 MPa PERMISSIBLE STRESS 227.27 227.27 CHECK SAFE SAFE

= =

217.5 0

kN-m kN-m

SECTION CLASSIFICATION (Cl. 3.7.4, Pg. 18-20) Flange b/(Tf+Tp) be/Tp bi/Tf d/Tw ε = (250/fy)0.5 = = = = 3.56 1.00 14.00 32.20 < < < < 8.4ε 8.4ε 29.3ε 84ε Plastic Plastic Plastic Plastic Plastic

Web

CALCULATION OF ACTUAL STRESSES : Actual bending stress @ major axis (σbcx,cal)

= = = = = =

Mx / Zxx 217500000 / 1018392 213.57 MPa My / Zyy 0 / 142071 0.00 MPa

Actual bending stress @ minor axis (σbcy,cal)

CALCULATION OF PERMISSIBLE STRESSES : Slenderness ratio in major direction (λx) = = = = = = = lx / rxx 6500 / 135.88 47.84 lY / ryy 1100 / 35.89 30.65 47.84 < 250 = λperm. SAFE

Slenderness ratio in minor direction (λy)

Maximum slenderness ratio ( λmax )

BENDING STRESS : (considering beam as laterally Unsupported) : Cl. 8.2.2 - Pg. No. 54 1.1*π2*E/(LLT/ry)2*[1+1/20*((LLT/ry)/(hf/tf))2]0.5 fcr-bxx = fcr-byy Mcr xx = = = = = = = = = 1.1*π2*E/(LLT/rx)2*[1+1/20*((LLT/rx)/(hf/tf))2]0.5 π2*E*Iy*hf/(2LLT)*[1+1/20*((LLT/ry)/(hf/tf))2]0.5 β b*Zp*fcr-b min. of above two values π2*E*Ix*hf/(2LLT)*[1+1/20*((LLT/rx)/(hf/tf))2]0.5 β b*Zp*fcr-b min. of above two values (β b*Zp*fy/Mcr)0.5 0.313 (fy/fcr-b)0.5 <= <= = (1.2*Ze*fy/Mcr)0.5 0.322 0.313

= = = = = = = =

2559.68 10183.07 3063642872.39 3063.64 2937.85 2937.85

Mpa

Mcr xx Mcr yy

N-mm KN-m KN-m KN-m

3268208535.03 N-mm 3268.21 KN-m 1290.13 KN-m 1290.13 KN-m

Mcr yy λLT xx λLT xx

=

λLT xx = 0.313 As λLT is < 0.4 , the beam can be considered as laterally supported. λLT yy λLT yy = = = (β b*Zp*fy/Mcr)0.5 0.157 (fy/fcr-b)0.5 <= <= = (1.2*Ze*fy/Mcr)0.5 0.182 0.157

λLT yy = 0.157 As λLT is < 0.4 , the beam can be considered as laterally supported. Check whether Webs are Susceptible to Shear Buckling before yielding (Cl. 8.2.1.1) Shear Force Acting = Mx*8/Leff2 = 41.18 KN/m Shear force at ends (V) = 133846.15 N 0.6 Design Shear Strength = 314918.3286 N Ratio = V/Vd = 0.43 < Therefore the webs are not susceptible to shear buckling before yielding Design Moment Mdxx = β b*Zp*fy/γm0 = = = = 260850000.00 N-mm 260.85 KN-m 227.27 Mpa 28793998.64 N-mm 28.79 KN-m 227.27 Mpa > 217.5 KN-mSAFE

Permissible Bending Stress Mdyy = β b*Zp*fy/γm0

Permissible Bending Stress

>0

SAFE

Base Plate Design and Anchor Bolt Design
The following examples depict the general procedure for the design of base plates and anchor bolts (if required) as per WSM and LSM for various loading conditions at column end. Base Plate ( Without Moment) IS 800-1984 Input Data Grade of Concrete Yield Stress of Steel Axial Force (P) = = 30 N/mm2 250 N/mm2 266.67 KN

L

Base Plate dimension Length (L) = 450 mm Breadth (B) = 450 mm Pedestal Dimensions Length (Lp) = 500 mm Breadth (Bp) = 500 mm Dimensions of the rectangle circumscribing the column Length = 300 mm Breadth = 250 mm Projection of slab base beyond the rectangle circumscribing the column a = 100 mm b = 75 mm Calculation Allowable stress in steel ( σbs) Stress under Base plate w = = Supporting Area A1 Loaded Area A2 Allowable stress in conc. =

B

w

=

185 (Cl. 5.4.3, pg.45, IS 800-1984)

Px 103/(L x B) 1.32 N-mm 2 = 250000 mm 2 = 202500 mm sqrt(A1/A2)x0.25xfck 8.33 > 1.32

(Cl.34.4,Pg.65, IS 456) SAFE

Thickness of base plate (Cl. 5.4.3, Pg. 45) (3 x w (a2 - b2/4) / σbs)0.5 t = IS 800-2007 Loading Axial Force (P) Calculation Stress under Base plate w = 400 KN

=

13.55

mm

= = Allowable stress in conc. =

Px 103/(L x B) 1.98 N-mm 0.45 x fck (Cl.34.4,Pg.65, IS 456) 13.5 > 1.98

SAFE

Thickness of base plate (Cl. 7.4.3.1, Pg 47) (2.5 x w (a2 - 0.3b2) x γm0 / fy)0.5 = t =

13.44

mm

Base Plate ( With Moment but no tension at base) IS 800-1984 Input Data Grade of Concrete Yield Stress of Steel Column section Axial Force (P) Moment (M) Shear Force (Fx) Shear Force (Fy) Base Plate dimension Length (L) Breadth (B) Pedestal Dimensions Length (Lp) Breadth (Bp) L = 25 250 ISHB 250 333.33 30 0 0 MPa MPa KN KN-m KN KN B = = 540 mm 400 mm

= = = =

= =

600 mm 600 mm w

Dimensions of the rectangle circumscribing the column Length = Breadth =

250 mm 250 mm

Projection of slab base beyond the rectangle circumscribing the column a = 145 mm b = 75 mm Calculation eccentricity Section Modulus Maxm pressure at the base

= = = = Min Pressure at the Base = = Pressure at the critical section of the column = Distance of Critical Section from the face pof the Plate = Supporting Area Loaded Area Allowable stress in conc. A1 A2 =

90 19440000 P/A + M/Z 3.09 P/A - M/Z 0.00 2.22 151.25

mm mm4 MPa MPa mm

= 360000 = 216000 sqrt(A1/A2)x0.25xfck 8.07 > SAFE

(Cl.34.4,Pg.65, IS 456) 3.09

Moment at Critical Section of Column considering Cantilever effect and Trapezoidal Loading = 32007.27 N-mm Allowable stress in steel ( σbs) Thickness = = = 185 MPa (Cl. 5.4.3, pg.45, IS 800-1984)

sqrt(6 M / σbs) 32.22 mm

IS 800-2007 Input Data Column section Axial Force (P) Moment (M) Shear Force (Fx) Shear Force (Fy) Calculation eccentricity Section Modulus Maxm pressure at the base Min Pressure at the Base Pressure at the face of the column Allowable stress in conc. =

= = = =

ISHB 250 500 45 0 0

KN KN-m KN KN

= = = = = = =

90 mm 4 19440000 mm P/A + M/Z 2 4.63 N/mm P/A - M/Z 2 0.00 N/mm 3.39 (Cl.34.4,Pg.65, IS 456) 4.63

0.45 x fck 11.25

> SAFE

Moment at Face of Column considering Cantilever effect and Trapezoidal Loading = 44312.8072 N-mm Allowable BM = Thickness = Zp x fy / γm0 sqrt(M x γm0 / (Zp x fy)) 27.93 < mm sqrt(M x γm0 / (1.5/6 x fy))

Base Plate ( With Moment and tension at base) IS 800-1984 Input Data Grade of Concrete Yield Stress of Steel Column section Axial Force (P) Moment (M) Shear Force (Fx) Shear Force (Fy) Base Plate dimension Length (L) Breadth (B) Pedestal Dimensions Length (Lp) Breadth (Bp) L = 30 N/mm 2 250 N/mm W310x310x143 475.00 KN 333.33 KN-m 0 KN 0 KN
2

g d

g

= = = =

B

= =

750 mm 650 mm k=n

= =

1100 mm 1000 mm T

w

Dimensions of the rectangle circumscribing the column Length = 325 mm Breadth = 325 mm Projection of slab base beyond the rectangle circumscribing the column a = 212.5 mm b = 162.5 mm Bolt Diameter (φ) = No. Of bolts = Edge Distance = = c/c Distance of Bolt hole and CG of Distance of Tension Bolt from Opp Edge (d) = = Net Area of Bolt Permissible Bond Stress (τb) = Calculation eccentricity Section Modulus Maxm pressure at the base Min Pressure at the Base Pressure at the critical section of the column Distance of Critical Section from the face of the Plate Supporting Area Loaded Area A1 A2 30 3 50 325 700 561 mm no. mm mm mm mm2
2

(from IS 1367-1967 & IS 1364-1967) (Table 21, IS 456-2000)

0.9 N/mm

= = = = = = = = = =

701.75 60937500 P/A + M/Z 6.44 P/A - M/Z -4.50 0.00 220.63

mm mm4 N/mm2 N/mm2 mm

2 1100000 mm 2 487500 mm

Allowable stress in conc., (w )

=

sqrt(A1/A2)x0.25xfck 11.27 >

6.44

(Cl.34.4,Pg.65, IS 456) N/mm2 SAFE

Moment at Section of Column considering Cantilever effect and Trapezoidal Loading Taking Moments @ centre of Tension Bolt 0.5nd2pL(1-n/3) = P.d + M n = (3 - sqrt(9 -24*((Pg+M)/(d2wB)))/2 = Length of loaded area , k nd = Balancing Vertical Forces Force in Bolt , T = 0.5 kw B - P M Allowable stress in steel ( σbs) Thickness

= 211.61

0.30 mm

= = = = =

299800.20 N 182792.55 N-mm 185 N/mm2 per mm width of the plate (Cl. 5.4.3, pg.45, IS 800-1984)

sqrt(6 M / σbs) 77.00 mm

Anchor Bolt Design Allowable Tensile Steress in Bolts Tension Capacity of 1 Bolt No. of Bolts Reqd. Tension in each bolt Bond force produced = = πφlτb

= = =

120 (Table 8.1, IS 800 1984) N/mm2 561 x 120 = 67320 N/mm2 299800.21 / 67320 = 5 no. = 59960.04 N

299800.21 / 5 = = T T/(πφτb)

Length of Anchor Bolt Required

=

707.24

mm

Provide 10 no. of 750 mm long, 30 mm dia. bolts.

IS 800-2007 P Input Data Column section Axial Force (P) Moment (M) Shear Force (Fx) Shear Force (Fy) Design Bond Stress of concrete (τbd) Ultimate tensile stress of bolt Yield Tress of the bolt Calculation eccentricity Section Modulus Maxm pressure at the base Min Pressure at the Base Pressure at the face of the column Allowable stress in conc. W310x310x143 712.5 KN 500 KN-m 0 KN 0 KN
2 1.5 N/mm

M T d

= = = = = = =

y w

(Cl. 26.2.1.1, IS 456-2000) (as per IS 1367-Part 3) (as per IS 1367-Part 3)

400 N/mm 2 240 N/mm

2

= = = = = = = =

701.75 60937500 P/A + M/Z 9.67 P/A - M/Z -6.74 6.93 0.45 x fck 13.5

mm mm4 N/mm2 N/mm2

(Cl.34.4,Pg.65, IS 456) N/mm2 > 9.67

SAFE

Length of Loaded Area considering Plastic Deformation L/2+a-[(L/2+g)2-2x(M+Pg)/(0.45xfckxB)]0.5 y = 131.44 < 212.5 < 750

SAFE

Moment at Face of Column considering Cantilever effect and Rectangular Loading = 260450.73 N-mm per mm width of the plate Allowable BM Thickness = Zp x fy / γm0 = sqrt(M x γm0 / (1/4 x fy)) 67.70

< mm

sqrt(M x γm0 / (1.5/6 x fy)) (Cl.

Anchor Bolt Design Force in Anchor Bolt Tensile Capacity of 1 30 mm dia bolt =

= =

0.45 x fck x y x B - P 440873.39 N 0.9 x fub x An / gmb < fyb x Asb / gm0 0.9*400 x 561/1.25 < 240x561/1.1 = = 4 no.

(Cl. 10.3.5) 122400 N

No. of bolts required , (nb)

Length of Anchor Bolt Required (Concrete break out failure in Tension Criteria) = ((Nu/nb)/(k x sqrt(fck)))1/1.5 = (Pull out criteria) = φ x σs /(4 τbd) = Provide 8 no of 1000 mm long, 30 mm dia bolts. 982.34 mm

119.01 mm

Gusseted Base Plate ( With Moment and tension at base)
IS 800-1984 Input Data Grade of Concrete Yield Stress of Steel Column section Axial Force (P) Moment (M) ShearForce (Fx) ShearForce (Fy)

=

= = = =

30 N/mm2 250 N/mm2 W310x310x143 300.00 KN 166.67 KN-m 30 KN 33.33 KN

a

b

Base Plate dimension Length (L) = 520 mm Breadth (B) = 520 mm Pedestal Dimensions Length (Lp) = 600 mm Breadth (Bp) = 600 mm Dimensions of the rectangle circumscribing the column Length = 325 mm Breadth = 325 mm Projection of slab base beyond the rectangle circumscribing the column a = 97.5 mm T b = 97.5 mm Bolt Diameter Edge Distance c/c Diatance of Bolt hole and CG of Column (g) Distance of Tension Bolt from Opp Edge (d) Net Area of Bolt (from IS 1367-1967 & IS 1364-1967) Permissible Bond Stress (τb) (Table 21, IS 456-2000) Calculation eccentricity Section Modulus Maxm pressure at the base = = = = = =

h P M

g

g k = nd

a

w 30 50 210 470 561.00 0.9 d mm mm mm mm mm2 N/mm2

555.56 23434667 = = Min Pressure at the Base = = Pressure at the critical section of the column = Distance of Critical Section from the face of = Supporting Area Loaded Area Allowable stress in conc. A1 A2 =

= =

mm mm4 P/A + M/Z 2 8.22 N/mm P/A - M/Z 2 -6.00 N/mm 5.25 105.63 mm

= 360000 = 270400 sqrt(A1/A2)x0.25xfck 8.65 > SAFE

(Cl.34.4,Pg.65, IS 456) 8.22

Taking Moments @ centre of Tension Bolt 0.5nd2pL(1-n/3) = P.d + M n = (3 - sqrt(9 -24*((Pg+M)/(d2wB)))/2 = Length of loaded area = k nd =

= 268.19

0.57 mm

Moment at Section of Column considering Cantilever effect and Trapesoidal Loading = (5.25+2*8.65)/(5.25+8.65)*(105.63/3)*(5.25+8.65)/2*105.63 = Moment about column face for 1 gusset Shear Force Allowable stress in steel ( σbs) Assume: Gusset Plate Thickness Height of Gusset = = = = = 20968.23357 N-mm 176175.282 N 185 MPa

41936.467 N-mm

(Cl. 5.4.3, pg.45, IS 800-1984) 16 mm 6.52 mm 200 mm

SAY

Let us adopt the gusset plate of size 200 x 97.5 x 15 mm Moment of resistance = = (1/6xtxd2xσbs) 19733333.33 N-mm SAFE Design of Thickness of Base plate (Considering the base plate to act as Simply Supported Beam with overhangs on 2 ends) Moment at the face of gusset = 28740.50481 N-mm Moment at the centre of the SS span = 85517.30769 N-mm Plate thickness required = sqrt(M/(1/6* σbs)) 52.66 Anchor Bolt Design Balancing Vertical Forces Force in Bolt , T = 0.5 kwB - P Allowable Tensile Stress in Bolt Tension Capacity of 1 Bolt No. of Bolts Reqd. on Tension Face Tension in each bolt Bond force produced = = πφlτb = T/(πφτb) = 715.80 mm = = = mm

>

20968.234 N-mm

=

303428.01

N

(Table 8.1, Pg. 95, IS 800 1984) 120 N/mm2 561 x 120 = 67320 N 303428.02 / 67320 = 5 no. = 60685.602 N

303428.02 / 5

Length of Anchor Bolt Required

Provide 10 no. of 750 mm long, 30 mm dia. bolts.

IS 800-2007 P Input Data Column section Axial Force (P) Moment (M) ShearForce (Fx) ShearForce (Fy) Design Bond Stress of concrete Ultimate tensile stress of bolt Yield stress of the bolt Calculation eccentricity Section Modulus Maxm pressure at the base Min Pressure at the Base Pressure at the face of the column Allowable stress in conc. = W310x310x143 450 KN 250 KN-m 45 KN 50 KN 1.5 N/mm 2 400 N/mm 2 240 N/mm
2

= = = = = = =

M T d

y w

(Cl. 26.2.1.1, IS 456-2000) (as per IS 1367-Part 3) (as per IS 1367-Part 3)

= = = = = = = 0.45 x fck 13.5

555.56 23434666.67 P/A + M/Z 12.33 P/A - M/Z -9.00 10.02

mm mm4 N/mm2 N/mm2

> SAFE

(Cl.34.4,Pg.65, IS 456) 12.33

Length of Loaded Area considering Plastic Deformation L/2+d-[(L/2+d)2-2x(M+Pd)/(0.45xfckxB)]0.5 y = 119.64 > 97.5 < 520 SAFE Moment at Face of Column considering Cantilever effect and Rectangular Loading = 33366937.50 N-mm Assume: Gusset Plate Thickness = 20 mm (Considering The Gusset Plate as the outstanding element of compression Flange b/tf = 4.875 < 13.6 h = 272 mm (again considering it as an outstanding element of 300 mm - SAY Let us adopt the gusset plate of size 200 x 97.5 x 15 mm = 16683468.75 N-mm Moment about column face for 1 gusset Shear Force = 419937.7913 N 0.5 0.6xAvxfyw/(3) /γm0 = 472377.5 > 419937.79 Check Vp = (Cl.8.2.1, Pg. 52-53) SAFE Therefore the gusset plate is not succeptible to shear buckling (1/6xtd2fy/γm0) (Considering Elastic limit is not exceeded) Moment of resistance = = 68181818 > 16683469 N-mm N-mm

SAFE Design of Thickness of Base plate Moment at the face of gusset Moment at the centre of the SS span Plate thickness required = = = 40542.19 N-mm 137700 N-mm sqrt(M x γm0 /(1/4* fy)) 49.23 mm

Horizontal Shear Check Resultant Horizontal Shear Permissible horizontal Shear

= =

(Fx2+Fy2)0.5 0.45*P

= = KN

67.27 202.5

> SAFE

67.27 KN

Observation: as the Concrete strength goes on reducing the thickness of the base plate goes on reducing Anchor Bolt Design force in Anchor Bolt, (Nu) = 0.45 x fck x y x B - P 389875.58 N 0.9 x fub x An / γmb < fyb x Asb / γm0 0.9*400 x 561/1.25 < 240x561/1.1 = = 389875.59 / 122400 = (Cl. 10.3.5) 122400 N 4 no.

Tensile Capacity of 1-30 mm dia bolt. = (Cl. 10.3.5) = No. of Bolts Reqd. on Tension Face

Length of Anchor Bolt Required (Concrete break out failure in Tension Criteria) = ((Nu/nb)/(k x sqrt(fck)))1/1.5 = (Pull out criteria) = φ x σs /(4 τbd) = Provide 8 no of 900 mm long, 30 mm dia bolts. 868.71 mm

109.64 mm

Conclusion:
The above examples shows a general approach towards analysing/designing of members through IS 800-2007 based on Limit state design. It can be concluded here that the Limit state approach tends to reduce tension member size in general and increase the size of compression member accompanied with bending, while designing. Though a generalised concept guides us that Limit state theory leads to smaller member size, the same does not hold the ground for steel design according to IS 800-2007.The main contributing factor for the same seems to be a large Factor of Safety and Various Load combinations as mentioned above. Also in the present code the Live load has been bifurcated into two parts namely, Leading and Accompanying Live Load. The example taken here being that of an industrial structure that has sufficiently large amount of Crane load for it to be considered as Leading Live Load. This consideration also amplifies the Loading on the structures as the FOS for the Leading Live load is more than that of Accompanying Live load. The following table shows that Stress utilisation ratio which is the ratio of Actual Stress (Force) to Permissible Stress (Force) which signifies percentage of material utilised for resisting external forces. Out of a total of 15 Cases, 10 Cases indicated that Limit state Method based IS 800-2007 yields results on a higher side as compared to working stress approach based IS 800-1984
Stress Utilisation Ratio Working Stress Limit State Method Method 0.63 0.95 0.96 0.73 0.91 0.41 0.58 1.07 0.97 0.77 0.80 1.03 0.07 0.07 0.09 0.10 0.23 0.31 1.00 0.96 0.84 1.26 0.34 0.31 0.95 0.96 0.92 1.26 0.88 0.94

Section

Action Tension Compression Tension Compression Tension Compression Tension Compression Compression Bending Combined Forces Compression Bending Combined Forces Beam Bending

Remarks LSM is Conservative

2 ISA 50x50x6 2 ISA 65x65x6 2 ISA 75x75x8 ISMB 150 ISMB 450

LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative LSM is Conservative

A ISMB 400 BB 1000 ISMB300+160x10 PLT(T/B)

The same does not hold true in case of Base Plate and Anchor bolt design, where the results of Limit State Design, which yield less thickness of the base plate as compared to Working Stress approach.
Type Base Plate Without Moment Base Plate With Moment but no Tension Base Plate With Moment & Tension Gusseted Base plate- With Moment & Tension Thickness Working Stress Method Limit State Method 13.55 13.44 32.22 27.93 77.00 67.70 52.66 49.23

While carrying out the above exercise it was realised that though the newly developed IS code is quite elaborate, there are some areas that still needs some light to be thrown on, which are as mentioned below 1) Thickness of Flange and centre to centre distance between flanges in Built up members: In the Clause 8.2.2.1, for finding out the value of Mcr, thickness of flange and the centre to centre distance between flanges are required, but the code is yet to provide any guidelines. For Primary compression members , accompanied with bending moment, the code recommends considering Semi Compact and Slender sections only, but for calculation of Section strength of such section , guidelines are given for Plastic and Compact sections. The code is yet to throw any light as to which sections shall be considered in this category. Elastic Lateral Torsional Buckling capacity has to be calculated for beams and columns not restrained laterally, but the code remains silent on the method of calculating the same for unsymmetrical sections and sections symmetric about major axis. For calculation of bearing pressure for size of gusset plate larger than required, a parameter “c” has been introduced, but the code is yet to come up with the guidelines for calculating the same.

2)

3)

4)

Inspite of a few shortcomings (some of which have been mentioned above) in the new code which would be taken care of in the future amendments, the code has explained and given guidelines for almost each and every thing that are required in day to day’s work. Though the results obtained by the new code seems to be conservative as compared to the previous version of the code (which may be because of more importance given to Local Buckling Criteria), the Limit State Method ( as adopted by the new version of the code ) ensures that local failures in the member section are avoided and the structure lives upto its designed life.

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