D4.B.6.3 Members Subject to Bending

The laterally unsupported length of the compression flange for the purpose of computing the factored moment resistance is specified in STAAD with the help of the parameter UNL. If UNL is less than one tenth the member length (member length is the distance between the joints of the member), the member is treated as being continuously laterally supported. In this case, the moment resistance is computed from Clause 13.5 of the code. If UNL is greater than or equal to one tenth the member length, its value is used as the laterally unsupported length. The equations of Clause 13.6 of the code are used to arrive at the moment of resistance of laterally unsupported members. Some of the aspects of the bending capacity calculations are :

The weak axis bending capacity of all sections except single angles is calculated as

For Class 1 & 2 sections, φ·P_y · F_y

For Class 3 sections, φ · S_y · F_y

where

φ	=	Resistance factor = 0.9
P_y	=	Plastic section modulus about the local Y axis
S_y	=	Elastic section modulus about the local Y axis
F_y	=	Yield stress of steel

For single angles, the bending capacities are calculated for the principal axes. The specifications of Section 5, page 6-283 of AISC-LRFD 1994, 2^nd ed., are used for this purpose because the Canadian code doesn’t provide any clear guidelines for calculating this value.
For calculating the bending capacity about the Z-Z axis of singly symmetric shapes such as Tees and Double angles, CAN/CSA-S16-01 stipulates in Clause 13.6(d), page 1-31, that a rational method, such as that given in SSRC’s Guide to Stability Design Criteria of Metal Structures, be used. Instead, STAAD uses the rules of Section 2c, page 6-55 of AISC-LRFD 1994, 2^nd ed.

Laterally Supported Class 4 members subjected to bending

When both the web and compressive flange exceed the limits for Class 3 sections, the member should be considered as failed and an error message will be thrown.
When flanges meet the requirements of Class 3 but web exceeds the limits for Class 3, resisting moment shall be determined by the following equation.

${M'}_{r} = M_{r} [1 - 0.0005 \frac{A_{w}}{A_{f}} (\frac{h}{w} - \frac{1, 900}{\sqrt{M_{f} / ϕ_{s}}})]$

Where Mr = factored moment resistance as determined by Clause 13.5 or 13.6 but not to exceed ϕMy = factored moment resistance for Class 3 sections = ϕMy

If axial compressive force is present in addition to the moment, modified moment resistance should be as follows.

${M'}_{r} = M_{r} {1 - 0.0005 \frac{A_{w}}{A_{f}} [\frac{h}{w} - 1, 900 \frac{1 - 0.65 C_{f} / (ϕ C_{y})}{\sqrt{M_{f} / ϕ_{s}}}]}$

C_y = A · F_y
- S = Elastic section modulus of steel section.
For sections whose webs meet the requirements of Class 3 and whose flanges exceed the limit of Class 3, the moment resistance shall be calculated as

M_r = ϕ · S_e · F_y

Where:
- S_e = effective section modulus determined using effective flange width.
- For Rectangular HSS section, effective flange width
  
  b_e= 670 · t/√(F_y )
- For I-section, T-section, Channel section, effective flange width and for Angle section, effective length width
  
  b_e= 200 · t/√(F_y )
  
  But shall not exceed 60 · t

Laterally Unsupported Class 4 members subjected to bending

As per clause 13.6(b) the moment resistance for class-4 section shall be calculated as follows

When M_u > 0.67M_y

$M_{r} = 1.15 ϕ M_{y} (1 - \frac{0.28 M_{y}}{M_{u}})$

M_r should not exceed ϕS_eF_y
When M_u ≤ 0.67M_y

M_r=ϕM_u

Where, as per clause 13.6(a),

M_u=(ω₂ π)/L √(EI_y GJ + (πE/L)² I_y C_w )

For unbraced length subjected to end moments-

ω₂=1.75 + 1.05k + 0.3k² ≤ 2.5

When bending moment at any point within the unbraced length is larger than the larger end moment or when there is no effective lateral support for the compression flange at one of the ends of unsupported length-

ω₂ = 1.0

k = Ratio of the smaller factored moment to the larger moment at opposite ends of the unbraced length, positive for double curvature and negative for single curvature.

Se = effective section modulus determined using effective flange width.

For Rectangular HSS section, effective flange width

b_e= 670t/√(F_y )

For I-section, T-section, Channel section, effective flange width and for Angle section, effective length width

b_e= 200t/√(F_y )

But shall not exceed 60t.

This clause is applicable only for I shaped and Channel shaped section as there is no guide line in the code for other sections.