Steps
Content
DESIGN OF MEMBERS FOR FLEXURE
(NSCP 6TH Edition 2010, Section 506 and AISC 2005 Specifications Chapter F)
Step 1:
Determine the following:
Mu for LRFD Load Combinations (SEI/ASCE 7, Section 2.3)
Ma for ASD Load Combinations (SEI/ASCE 7, Section 2.4)
Step 2:
Assume steel section from AISC Manual. Determine its design load due to self-weight and
add the corresponding values to the dead load of ASD and LRFD load combinations.
Step 3: (NSCP Table 502.4.1 & AISC Table B4.1)
From the assumed section, classify cross-sectional shapes as compact, non-compact or
slender, depending on the values of the width-thickness ratios of the flange and web. For I-shaped
sections:
If
If
If
and the flange is continuously connected to the web, the shape is compact.
the shape is non-compact.
the shape is slender.
For flanges,
√
√
For webs,
√
√
Determine the lateral-torsional buckling modification factor for non-uniform moment diagrams
when both ends of the unsupported segment are braced, Cb.
(NSCP Eq. 506.1-1 & ---)
For doubly symmetric members,
Step 4:
See NSCP Table User Note 506.1.1 and select case that is suitable for the flange and web
slenderness. Determine the value of the nominal flexural strength, Mn from the selected case.
Step 4.1: (NSCP Section 506.2)
If
for both flange and web (compact section) bent about their major axis.
1.
Solve for the limiting lengths Lp and Lr:
(NSCP Eq. 506.2-5 & AISC Eq. F2-5)
√
√
√
√
(
)
(NSCP Eq. 506.2-6 & AISC Eq. F2-6)
For doubly symmetric I-shape:
Note: if the square root term in Eq. 506.2-4 is conservatively taken equal to 1.0, Eq. 506.2-6
becomes
π
√
√
√
(NSCP Eq. 506.2-7 & AISC Eq. F2-7)
(
)
2.
Mn shall be the lower value obtained according to the following limit states:
Yielding (NSCP Section 506.2.1)
(NSCP Eq. 506.2-1 & AISC Eq. F2-1)
Lateral-Torsional Buckling (NSCP Section 506.2.2)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.2-2 & AISC Eq. F2-2)
,
(NSCP Eq. 506.2-3 & AISC Eq. F2-3)
√
(
(NSCP Eq. 506.2-4 & AISC Eq. F2-4)
( )
)
Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0.
The available flexural strength shall be greater than or equal to the maximum required
moment causing compression within the flange under consideration Cb is permitted to be
conservatively taken as 1.0 for all cases.
Step 4.2: (NSCP Section 506.3)
If
(compact web);
If
(non-compact flange) or
(slender flange) bent about their major axis.
1.
Mn shall be the lower value obtained according to the following limit states:
Lateral-Torsional Buckling (NSCP Section 506.3.1)
(Apply provisions in Section 506.2.2)
Compression Flange Local Buckling (NSCP Section 506.3.2)
a. For
,
[
b.
For
(
)(
)]
(NSCP Eq. 506.3-1 & AISC Eq. F3-1)
,
(NSCP Eq. 506.3-2 & AISC Eq. F3-2)
√
kc shall not be taken less than 0.35 nor greater than 0.76
Step 4.3: (NSCP Section 506.4)
If
(compact web) or
1.
(non-compact web) bent about their major axis.
Solve for the limiting lengths Lp and Lr:
√
(NSCP Eq. 506.4-7 & ---)
√
√
√
(
(NSCP Eq. 506.4-8 & ---)
)
The stress FL, is determined as follows:
a.
For
,
(NSCP Eq. 506.4-6a & ---)
b.
For
,
(NSCP Eq. 506.4-6b & ---)
2.
Determine the web plastification factor for compression Rpc:
a.
For
,
(NSCP Eq. 506.4-9a & ---)
b.
For
,
[
3.
(
)(
(NSCP Eq. 506.4-9b & ---)
)]
Determine the web plastification factor for tension Rtc:
a.
For
,
(NSCP Eq. 506.4-9a & ---)
b.
For
,
[
4.
(
)(
(NSCP Eq. 506.4-9b & ---)
)]
Mn shall be the lower value obtained according to the following limit states:
Compression Flange Yielding (NSCP Section 506.4.1)
(NSCP Eq. 506.4-1 & ---)
Lateral-Torsional Buckling (NSCP Section 506.4.2)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.4-2 & ---)
,
(NSCP Eq. 506.4-3 & ---)
(NSCP Eq. 506.4-4 & ---)
√
(
For
(NSCP Eq. 506.4-5 & ---)
( )
)
, J shall be taken as zero.
Compression Flange Local Buckling (NSCP Section 506.4.3)
a. For
, the limit state of LB does not apply.
b. For
,
[
c.
For
(
)(
)]
(NSCP Eq. 506.4-12 & ---)
,
(NSCP Eq. 506.4-13 & ---)
√
kc shall not
Tension Flange
a. For
b. For
be taken less than 0.35 nor greater than 0.76
Yielding (NSCP Section 506.4.4)
, the limit state of TFY does not apply.
,
(NSCP Eq. 506.4-14 & ---)
Step 4.4: (NSCP Section 506.5)
If
(slender web) bent about their major axis.
1.
Solve for the limiting lengths Lp and Lr:
(NSCP Eq. 506.4-7 & ---)
√
(NSCP Eq. 506.5-5 & ---)
√
2.
Determine the bending strength reduction factor Rpg:
(
3.
√ )
Mn shall be the lower value obtained according to the following limit states:
Compression Flange Yielding (NSCP Section 506.5.1)
(NSCP Eq. 506.5-1 & ---)
Lateral-Torsional Buckling (NSCP Section 506.5.2)
(NSCP Eq. 506.5-2 & ---)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.5-3 & ---)
,
`(NSCP Eq. 506.5-4 & ---)
(
)
Compression Flange Local Buckling (NSCP Section 506.5.3)
(NSCP Eq. 506.5-7 & ---)
a. For
,
[
b.
(
For
)(
)]
(NSCP Eq. 506.5-8 & ---)
,
(NSCP Eq. 506.5-9 & ---)
(
)
√
kc shall not
Tension Flange
a. For
b. For
be taken less than 0.35 nor greater than 0.76
Yielding (NSCP Section 506.5.4)
, the limit state of TFY does not apply.
,
(NSCP Eq. 506.5-10 & ---)
Step 4.5: (NSCP Section 506.5)
For I-Shaped members bent about their minor axis.
1. Mn shall be the lower value obtained according to the following limit states:
Yielding (NSCP Section 506.6.1)
(NSCP Eq. 506.6-1 & ---)
Flange Local Buckling (NSCP Section 506.6.2)
a. For
, the limit state of yielding shall apply.
b. For
,
(
c.
For
)(
)
(NSCP Eq. 506.6-2 & ---)
,
(NSCP Eq. 506.6-3 & ---)
(NSCP Eq. 506.6-4 & ---)
(
)
Step 5: (NSCP Section 506.1)
For LRFD, check if the section is capable of resisting the design loads, the section must
satisfy the equation:
For ASD, check if the section is capable of resisting the service loads, the section must
satisfy the equation:
For all provisions of Section 506,
and
.
λ = width-thickness ratio
λf = width-thickness ratio of flange
λp = upper limit for compact category
λr = upper limit for non-compact category
λw = width-thickness ratio of web
λpf = flange upper limit for compact category
λrf = flange upper limit for non-compact category
λpw = web upper limit for compact category
λrw = web upper limit for non-compact category
bf = flange width
Cb = lateral-torsional buckling modification factor
E = modulus of elasticity of steel
Fy = specified minimum yield stress of the type of steel being used
h = web height
ho = distance between the flange centroids
Iy = moment of inertia taken about the y-axis
J = torsional constant
Lb = length between points that are either braced against lateral displacement of
compression flange or braced against twist of the cross-section
Lp = limiting laterally unbraced length for the limit state of yielding
Lr = limiting laterally unbraced length for the inelastic lateral-torsional buckling
MA = absolute value of moment at quarter point of the unbraced segment
MB = absolute value of moment at centerline of the unbraced segment
MC = absolute value of moment at third quarter point of the unbraced segment
Mmax = absolute value of maximum moment in the unbraced segment
Mn = nominal moment capacity
Mp = plastic moment
Rm = cross-section monosymmetry parameter
Sx = elastic section modulus taken about the x-axis
Sy = elastic section modulus taken about the y-axis
rx= radius of gyration with respect to x-axis
ry= radius of gyration with respect to y-axis
tf = flange thickness
tw = web thickness
Zx = plastic section modulus about the x-axis
Zy = plastic section modulus about the y-axis
DESIGN OF MEMBERS FOR FLEXURE
(NSCP 5TH Edition 2001)
Step 1:
Determine the following:
Ma for ASD Load Combinations (SEI/ASCE 7, Section 2.4)
Step 2:
Assume steel section from AISC Manual. Determine its design load due to self-weight and
add the corresponding values to the dead load of ASD load combinations.
Step 3: (NSCP Table 502-1)
From the assumed section, classify cross-sectional shapes as compact, partially compact, or
non-compact, depending on the values of the width-thickness ratios of the flange and web. For Ishaped sections:
For compact sections, the following conditions must be satisfy:
a. Its flanges must be continuously connected to the web.
b. The section must have a flange width-thickness ratio of its compression elements:
c.
√
The section must have a depth to web thickness ratio:
√
For partially compact sections, the following conditions must be satisfy:
a. The section satisfy the requirements for compact sections except that their flanges are
non-compact:
√
√
For non-compact sections, the following conditions must be satisfy:
a. The section must not qualify as compact shapes and must have a flange width-thickness
ratio of its compression elements:
√
Determine the lateral-torsional buckling modification factor for non-uniform moment diagrams
when both ends of the unsupported segment are braced, Cb.
For doubly symmetric members,
Cb is permitted to be conservatively taken as 1.0 for all cases. For cantilevers or overhangs where
the free end is unbraced, Cb=1.0.
Step 4: (NSCP Table 502-1)
From the assumed section, determine the value of Lb, Lc and Lu which will be considered in
the computations. Lb is the laterally unsupported length of the compression flange. Lc shall be the
smaller value of L1 or L2, and Lu shall be the larger value of L1 or L2.
√
Step 5:
Determine the value of the allowable bending stress, Fb depending on the given parameters
that the section has satisfy.
Laterally Supported Beams
a. For compact sections bending about the strong axis (x-axis) and
.
b.
For partially-compact sections bending about the strong axis (x-axis) and
[
c.
.
√ ]
For non-compact sections bending about the strong axis (x-axis) and
.
Laterally Unsupported Beams
a. If
b.
If
(2 Cases)
Case 1:
√
√
Fb is the larger value obtained in the following equations:
( )
[
]
The allowable bending stress shall not exceed 0.6Fy (
Case 2:
)
√
Fb is the larger value obtained in the following equations:
( )
The allowable bending stress shall not exceed 0.6Fy (
Sections bending about its weak axis
a. For compact sections:
b.
For partially-compact sections:
[
c.
)
√ ]
For non-compact sections bending about the strong axis (x-axis) and
.
Step 6:
Solve for the actual bending stress and compare to the allowable bending stress. The
section must satisfy the equation:
(NSCP 6TH Edition 2010, Section 506 and AISC 2005 Specifications Chapter F)
Step 1:
Determine the following:
Mu for LRFD Load Combinations (SEI/ASCE 7, Section 2.3)
Ma for ASD Load Combinations (SEI/ASCE 7, Section 2.4)
Step 2:
Assume steel section from AISC Manual. Determine its design load due to self-weight and
add the corresponding values to the dead load of ASD and LRFD load combinations.
Step 3: (NSCP Table 502.4.1 & AISC Table B4.1)
From the assumed section, classify cross-sectional shapes as compact, non-compact or
slender, depending on the values of the width-thickness ratios of the flange and web. For I-shaped
sections:
If
If
If
and the flange is continuously connected to the web, the shape is compact.
the shape is non-compact.
the shape is slender.
For flanges,
√
√
For webs,
√
√
Determine the lateral-torsional buckling modification factor for non-uniform moment diagrams
when both ends of the unsupported segment are braced, Cb.
(NSCP Eq. 506.1-1 & ---)
For doubly symmetric members,
Step 4:
See NSCP Table User Note 506.1.1 and select case that is suitable for the flange and web
slenderness. Determine the value of the nominal flexural strength, Mn from the selected case.
Step 4.1: (NSCP Section 506.2)
If
for both flange and web (compact section) bent about their major axis.
1.
Solve for the limiting lengths Lp and Lr:
(NSCP Eq. 506.2-5 & AISC Eq. F2-5)
√
√
√
√
(
)
(NSCP Eq. 506.2-6 & AISC Eq. F2-6)
For doubly symmetric I-shape:
Note: if the square root term in Eq. 506.2-4 is conservatively taken equal to 1.0, Eq. 506.2-6
becomes
π
√
√
√
(NSCP Eq. 506.2-7 & AISC Eq. F2-7)
(
)
2.
Mn shall be the lower value obtained according to the following limit states:
Yielding (NSCP Section 506.2.1)
(NSCP Eq. 506.2-1 & AISC Eq. F2-1)
Lateral-Torsional Buckling (NSCP Section 506.2.2)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.2-2 & AISC Eq. F2-2)
,
(NSCP Eq. 506.2-3 & AISC Eq. F2-3)
√
(
(NSCP Eq. 506.2-4 & AISC Eq. F2-4)
( )
)
Note: The square root term in Eq. 506.2-4 may be conservatively taken equal to 1.0.
The available flexural strength shall be greater than or equal to the maximum required
moment causing compression within the flange under consideration Cb is permitted to be
conservatively taken as 1.0 for all cases.
Step 4.2: (NSCP Section 506.3)
If
(compact web);
If
(non-compact flange) or
(slender flange) bent about their major axis.
1.
Mn shall be the lower value obtained according to the following limit states:
Lateral-Torsional Buckling (NSCP Section 506.3.1)
(Apply provisions in Section 506.2.2)
Compression Flange Local Buckling (NSCP Section 506.3.2)
a. For
,
[
b.
For
(
)(
)]
(NSCP Eq. 506.3-1 & AISC Eq. F3-1)
,
(NSCP Eq. 506.3-2 & AISC Eq. F3-2)
√
kc shall not be taken less than 0.35 nor greater than 0.76
Step 4.3: (NSCP Section 506.4)
If
(compact web) or
1.
(non-compact web) bent about their major axis.
Solve for the limiting lengths Lp and Lr:
√
(NSCP Eq. 506.4-7 & ---)
√
√
√
(
(NSCP Eq. 506.4-8 & ---)
)
The stress FL, is determined as follows:
a.
For
,
(NSCP Eq. 506.4-6a & ---)
b.
For
,
(NSCP Eq. 506.4-6b & ---)
2.
Determine the web plastification factor for compression Rpc:
a.
For
,
(NSCP Eq. 506.4-9a & ---)
b.
For
,
[
3.
(
)(
(NSCP Eq. 506.4-9b & ---)
)]
Determine the web plastification factor for tension Rtc:
a.
For
,
(NSCP Eq. 506.4-9a & ---)
b.
For
,
[
4.
(
)(
(NSCP Eq. 506.4-9b & ---)
)]
Mn shall be the lower value obtained according to the following limit states:
Compression Flange Yielding (NSCP Section 506.4.1)
(NSCP Eq. 506.4-1 & ---)
Lateral-Torsional Buckling (NSCP Section 506.4.2)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.4-2 & ---)
,
(NSCP Eq. 506.4-3 & ---)
(NSCP Eq. 506.4-4 & ---)
√
(
For
(NSCP Eq. 506.4-5 & ---)
( )
)
, J shall be taken as zero.
Compression Flange Local Buckling (NSCP Section 506.4.3)
a. For
, the limit state of LB does not apply.
b. For
,
[
c.
For
(
)(
)]
(NSCP Eq. 506.4-12 & ---)
,
(NSCP Eq. 506.4-13 & ---)
√
kc shall not
Tension Flange
a. For
b. For
be taken less than 0.35 nor greater than 0.76
Yielding (NSCP Section 506.4.4)
, the limit state of TFY does not apply.
,
(NSCP Eq. 506.4-14 & ---)
Step 4.4: (NSCP Section 506.5)
If
(slender web) bent about their major axis.
1.
Solve for the limiting lengths Lp and Lr:
(NSCP Eq. 506.4-7 & ---)
√
(NSCP Eq. 506.5-5 & ---)
√
2.
Determine the bending strength reduction factor Rpg:
(
3.
√ )
Mn shall be the lower value obtained according to the following limit states:
Compression Flange Yielding (NSCP Section 506.5.1)
(NSCP Eq. 506.5-1 & ---)
Lateral-Torsional Buckling (NSCP Section 506.5.2)
(NSCP Eq. 506.5-2 & ---)
a. For
, the limit state of LTB does not apply.
b. For
,
[
c.
(
For
)(
)]
(NSCP Eq. 506.5-3 & ---)
,
`(NSCP Eq. 506.5-4 & ---)
(
)
Compression Flange Local Buckling (NSCP Section 506.5.3)
(NSCP Eq. 506.5-7 & ---)
a. For
,
[
b.
(
For
)(
)]
(NSCP Eq. 506.5-8 & ---)
,
(NSCP Eq. 506.5-9 & ---)
(
)
√
kc shall not
Tension Flange
a. For
b. For
be taken less than 0.35 nor greater than 0.76
Yielding (NSCP Section 506.5.4)
, the limit state of TFY does not apply.
,
(NSCP Eq. 506.5-10 & ---)
Step 4.5: (NSCP Section 506.5)
For I-Shaped members bent about their minor axis.
1. Mn shall be the lower value obtained according to the following limit states:
Yielding (NSCP Section 506.6.1)
(NSCP Eq. 506.6-1 & ---)
Flange Local Buckling (NSCP Section 506.6.2)
a. For
, the limit state of yielding shall apply.
b. For
,
(
c.
For
)(
)
(NSCP Eq. 506.6-2 & ---)
,
(NSCP Eq. 506.6-3 & ---)
(NSCP Eq. 506.6-4 & ---)
(
)
Step 5: (NSCP Section 506.1)
For LRFD, check if the section is capable of resisting the design loads, the section must
satisfy the equation:
For ASD, check if the section is capable of resisting the service loads, the section must
satisfy the equation:
For all provisions of Section 506,
and
.
λ = width-thickness ratio
λf = width-thickness ratio of flange
λp = upper limit for compact category
λr = upper limit for non-compact category
λw = width-thickness ratio of web
λpf = flange upper limit for compact category
λrf = flange upper limit for non-compact category
λpw = web upper limit for compact category
λrw = web upper limit for non-compact category
bf = flange width
Cb = lateral-torsional buckling modification factor
E = modulus of elasticity of steel
Fy = specified minimum yield stress of the type of steel being used
h = web height
ho = distance between the flange centroids
Iy = moment of inertia taken about the y-axis
J = torsional constant
Lb = length between points that are either braced against lateral displacement of
compression flange or braced against twist of the cross-section
Lp = limiting laterally unbraced length for the limit state of yielding
Lr = limiting laterally unbraced length for the inelastic lateral-torsional buckling
MA = absolute value of moment at quarter point of the unbraced segment
MB = absolute value of moment at centerline of the unbraced segment
MC = absolute value of moment at third quarter point of the unbraced segment
Mmax = absolute value of maximum moment in the unbraced segment
Mn = nominal moment capacity
Mp = plastic moment
Rm = cross-section monosymmetry parameter
Sx = elastic section modulus taken about the x-axis
Sy = elastic section modulus taken about the y-axis
rx= radius of gyration with respect to x-axis
ry= radius of gyration with respect to y-axis
tf = flange thickness
tw = web thickness
Zx = plastic section modulus about the x-axis
Zy = plastic section modulus about the y-axis
DESIGN OF MEMBERS FOR FLEXURE
(NSCP 5TH Edition 2001)
Step 1:
Determine the following:
Ma for ASD Load Combinations (SEI/ASCE 7, Section 2.4)
Step 2:
Assume steel section from AISC Manual. Determine its design load due to self-weight and
add the corresponding values to the dead load of ASD load combinations.
Step 3: (NSCP Table 502-1)
From the assumed section, classify cross-sectional shapes as compact, partially compact, or
non-compact, depending on the values of the width-thickness ratios of the flange and web. For Ishaped sections:
For compact sections, the following conditions must be satisfy:
a. Its flanges must be continuously connected to the web.
b. The section must have a flange width-thickness ratio of its compression elements:
c.
√
The section must have a depth to web thickness ratio:
√
For partially compact sections, the following conditions must be satisfy:
a. The section satisfy the requirements for compact sections except that their flanges are
non-compact:
√
√
For non-compact sections, the following conditions must be satisfy:
a. The section must not qualify as compact shapes and must have a flange width-thickness
ratio of its compression elements:
√
Determine the lateral-torsional buckling modification factor for non-uniform moment diagrams
when both ends of the unsupported segment are braced, Cb.
For doubly symmetric members,
Cb is permitted to be conservatively taken as 1.0 for all cases. For cantilevers or overhangs where
the free end is unbraced, Cb=1.0.
Step 4: (NSCP Table 502-1)
From the assumed section, determine the value of Lb, Lc and Lu which will be considered in
the computations. Lb is the laterally unsupported length of the compression flange. Lc shall be the
smaller value of L1 or L2, and Lu shall be the larger value of L1 or L2.
√
Step 5:
Determine the value of the allowable bending stress, Fb depending on the given parameters
that the section has satisfy.
Laterally Supported Beams
a. For compact sections bending about the strong axis (x-axis) and
.
b.
For partially-compact sections bending about the strong axis (x-axis) and
[
c.
.
√ ]
For non-compact sections bending about the strong axis (x-axis) and
.
Laterally Unsupported Beams
a. If
b.
If
(2 Cases)
Case 1:
√
√
Fb is the larger value obtained in the following equations:
( )
[
]
The allowable bending stress shall not exceed 0.6Fy (
Case 2:
)
√
Fb is the larger value obtained in the following equations:
( )
The allowable bending stress shall not exceed 0.6Fy (
Sections bending about its weak axis
a. For compact sections:
b.
For partially-compact sections:
[
c.
)
√ ]
For non-compact sections bending about the strong axis (x-axis) and
.
Step 6:
Solve for the actual bending stress and compare to the allowable bending stress. The
section must satisfy the equation:
