# D8.C.2 Design Procedure

The design procedure according to IS 801 is based on an allowable stress method. In essence, the principle is to determine the maximum allowable design stress for a given section profile. The section properties that are used to calculate the allowable stress are based on the gross section properties or the "effective" section properties, based on the load being applied and the check being considered.

The design procedure varies slightly from profile to profile, based on the characteristics of the elements that form the profile shape. IS 801 classifies the elements (flat plates) that form the section profile into the following element types:
• stiffened element – an element that is supported along two opposite edges either by another element or a stiffening element such as a lip
• unstiffened element – an element that is supported by another element only along one edge
• multiple stiffened element – an element that is supported in between web(s) or stiffened element(s) by intermediate stiffeners that are parallel to the direction of stress

The various checks for a section profile and the design methods adopted depend on the type of the elements that form the profile. The following clauses from IS 801 are implemented and are used as appropriate:

• Cl 5.2.1
• Cl.5.2.1.1
• Cl.5.2.3
• Cl.5.2.4
• Cl.6.1
• Cl.6.1.1.1
• Cl.6.2
• Cl.6.3
• Cl.6.4
• Cl.6.4.1
• Cl.6.4.2
• Cl.6.4.3
• Cl.6.6
• Cl.6.6.1.1
• Cl.6.6.1.2
• Cl.6.6.1.3
• Cl.6.7
• Cl.6.7.1
• Cl.6.7.2
• Cl.6.7.3
• Cl.6.8
Note: Deflection checks based on the effective section properties are not performed.

## D8.D.2.1 Maximum allowable section segment dimensions

Checks will be done to verify the maximum allowable flat width ratios for the flange segments forming section profile as per Cl.5.2.3 and for the web segments as per Cl.5.2.4. Note that Cl.5.2.3(d) will not be considered as this can vary based on the amount of curling.

## D8.D.2.2 Maximum member slenderness

Member slenderness checks will be performed for members subject to compression. The maximum allowable slenderness for a compression member will be limited to 200 as per Cl.6.3.3.

Slenderness for a member about both the z & y local axes will be calculated. If any of these exceeds the limiting value of 200, the program will consider that as a failure criterion. Note that members subject to tension will not have any slenderness checks performed.

## D8.D.2.3 Members subject to tension

The following check will be performed for all members in tension:

 Tensile stress ratio = Factual / F

where
 Factual = the applied stress on the member. = Applied Tension / A A = the net cross section area of the profile
Note: If the parameter list includes the NSF parameter, the net area will be calculated as A × NSF, where A is the gross area of the section. If NSF has not been specified, a default value of 1.0 will be used.

The maximum allowable design stress for members in tension will be calculated as:

 F = 0.6 × Fy

where
 Fy = the minimum yield strength of the section.

If the increase in steel strength due to cold work forming is to be considered (ref. CWY param), then the design stress will be calculated as:

 F = 0.6 × Fya

where
 Fya = the average yield point of the full section and will be calculated as:Fya = C × Fyc + (1 -C) Fyt.( refer to Cl.6.6.1.a for the description of the terms used.)
Note: The FY and FU values are expected to be user inputs. The default value of FY will be taken as 3600 kg/cm2(Table 2 of IS:801) and FU will be taken as 4588 kg/cm2.

## D8.D.2.4 Members subject to compression

The following check will be performed for all members in compression:

 Compression check ratio = Factual / Fcap

where
 Factual = the applied axial stress on the member Fcap = the allowable compressive stress for the member

The compression capacity will be calculated as follows:

• For profile shapes with stiffened elements alone and not susceptible to Flexural torsional buckling (Tube):

The maximum allowable design stress will be calculated as:

 F = 0.6 × Fy

where Fy = the minimum yield strength of the section.
Note: Allowance will be made for cold forming strength as required.

Note that if the effect of cold work forming is to be considered, then the enhanced strength Fya will have to be determined based on the value of the factor Q. Hence to determine the factor Q, the program would use the design stress (= 0.6×Fy ). This factor Q will then be used to determine the enhanced strength Fya, which will then be used for the design checks.

This design stress, F, will be used to calculate the effective area of the section. The procedure to calculate the effective area involves calculating the effective width of each element that forms the profile. The effective width of each element will be calculated as described below:

• For elements without intermediate stiffeners:

The effective width of such elements will be calculated as per the equations in Cl.5.2.1.1 (for closed square and rectangular tubes). The value of ‘f used will be the maximum allowable design stress F as in section 3.2.1 above.

Note: The current implementation does not allow for sections to have multiple stiffened elements as per Cl.5.2.1.2. Hence Cl.5.2.1.2 is not be considered for calculating the effective width of elements.

The maximum allowable compression stress for the member, Fc, will then be determined based on the equations as per Cl.6.6.1.1. Note that the factor Q will be based on the effective area determined using the design stress F as mentioned above.

• For profile shapes with stiffened elements alone (Pipe sections):

The maximum allowable compressive stress for pipes will be determined as per cl.6.8:

For sections with D/t < 232000 / Fy, F = 0.6 × Fy

For section with 232000 / Fy < D/t < 914000 / Fy, F = 46540 / (D/t) + 0.399 Fy

Section with D/t > 914000 / Fy will not be designed.

A check will also be done to make sure that the compressive stress < Fa1 as determined by 6.6.1.1. for a value of Q=1.

• For profile shapes with un-stiffened elements alone (Angle sections):

The maximum allowable design stress Fc will be calculated as per the equations in Cl.6.2 (a), 6.2(b), 6.2(c) or 6.2 (d) as appropriate, based on the plate width-to-thickness ratio of each element.

This design stress, Fc, will be used to calculate the factor Q when checking for flexural/flexural torsional buckling failure modes. Note that since this section is subject to torsional buckling, the factor Q, to be used to calculate the allowable compressive stress Fa1 as per Cl. 6.6.1.2/3, will be calculated as the ratio between the Fc for the element with the largest w/t ratio to the basic design stress as per Cl.6.1 & 6.2.

• For profile shapes with both stiffened and unstiffened elements and /or susceptible to Flexural torsional buckling (Channel, Zee, Hat, Channels with Lips, Zee with Lips, Angle with lip sections sections):

These sections are subject to torsional-flexural buckling. The factor Q will be determined as per Cl.6.6.1.1 (3) as:

Q = Qs × Qa

Qs will be calculated as the ratio between the Fc for the element with the largest w/t ratio to the basic design stress as per Cl.6.1 & 6.2.

Qa will be calculated for the stiffened elements as per Cl.6.6.1.1 (1) but with Fa taken as the stress used to calculate Qs.

If Q =1.0, the allowable stress Fa2 will be calculated as per Cl.6.6.1.2. If however the factor Q < 1.0, the allowable stress Fa2 will be calculated as per Cl.6.6.1.2, but with the term Q being replaced with Q.Fy.

## D.2.5 Members subject to bending

The following check will be performed for all members in bending:

 Bending check ratio = Mactual / Mcap

where
 Mactual = the applied bending stress on the member Mcap = the allowable bending stress of the member

This check will be done separately for bending about both the Z & Y axes.

The bending capacity of the section will be based on the maximum allowable bending stress, Fb. The maximum allowable stress in a member subject to bending shall not exceed the following:

1. The maximum allowable stress for the extreme tension fiber as given in Cl.6.1

 Fbt_allowable = F = 0.6 × Fy

where
 Fy = the minimum yield strength of the section
2. The maximum allowable stress in the extreme compression fiber as given in Cl.6.2

This will be calculated based on the w/t ratio of the compression element as per Cl.6.2(a), Cl.6.2(b), Cl.6.2(c), or Cl.6.2(d) as applicable. Note that these clauses will be applicable only for unstiffened elements in compression. For stiffened elements Fb will be taken as given in Cl.6.1

3. The maximum allowable lateral buckling stress as given in C.l6.3 (a) or Cl.6.3 (b) as appropriate for the section profile.

This clause will only be applicable for sections that are subject to bending about their major axis. For sections subject to minor axis bending this check will be ignored.

The moment of inertia terms, Iyc and the section modulus term Zxc in the equations will be based on the entire section. The value of the moment factor Cb, will be based on the end moments of the analytical member being designed. If the member is subject to axial loads along with the bending moment, the value of Cb will be taken as 1.0

4. The maximum allowable bending stress in the webs of a given section (I, C, Hat, Tube , Z), Fbw shall be calculated as per Cl6.4.2 of the code.

For pipe sections:

The maximum allowable compressive stress for pipes will be determined as per cl.6.8:

• For sections with D/t < 232000 / Fy, F = 0.6 × Fy
• For sections with 232000 / Fy < D/t < 914000 / Fy, F = 46540 / (D/t) + 0.399 Fy
• Sections with D/t > 914000 / Fy will not be designed.

## D.2.6 Members subject to shear

The applied shear stress will be calculated based on the calculated shear area of the given section profile. The shear area for the various shapes will be taken as follows:

• Angle with Lips
• For shear along the Y axis: (D-t)×t + 2.0×(Lip Length-t)×t
• For shear along the X axis: (B-t)×t
• Angle
• For shear along the Y axis: (D-t)×t
• For shear along the X axis: (B-t)×t
• Channel with Lips
• For shear along the Y axis: (D-2t)×t + 2.0×(Lip Length-t)×t
• For shear along the X axis: 2.0×B×t
• Channel or Eave Strut
• For shear along the Y axis: (D-2t)×t
• For shear along the X axis: 2.0×B×t
• Zee or Zee Purlin
• For shear along the Y axis: (D-2t)×t
• For shear along the X axis: 2.0×B×t
• Zee with Lips
• For shear along the Y axis: (D-2t)×t + 2.0×(Lip Length-t)×t
• For shear along the X axis: 2.0×B×t
• Hat
• For shear along the Y axis: 2.0 × (D-t)×t
• For shear along the X axis: B×t + 2.0×(Lip Length-t)×t
• Tube
• For shear along the Y axis: 2.0×(D-2t)×t
• For shear along the X axis: 2.0×(B-2t)×t
• Pipe
• For shear along the Y axis: 0.5 ×2×π×r×t
• For shear along the X axis: 0.5 ×2×π×r×t

For shear checks along the local Y-axis, the maximum allowable shear stress, Fv, in the web of a section (I, C, Hat, Tube, Z) will be calculated as per Cl.6.4.1 based on the h/t ratio of the web element.

The code does not explicitly mention about shear checks along the horizontal (Z-axis). Hence, the program takes the maximum allowable shear stress along Z as 0.4×Fy.

## D.2.7 Members subject to combined axial, bending, and shear

• Checks for members subject to combined axial compression and bending:

The combined stress checks will be based on whether the member is susceptible to torsional buckling mode or not. The implementation will consider all loads as being applied through the shear center.

• Members not susceptible to torsional buckling

For members that are not susceptible to torsional buckling, both the interaction equations as per Cl.6.7.1 will be checked as below:

 fa/ Fa1 + (Cmx × fbx) / [(1- fa /F’ex)×Fbx] + (Cmy × fby) / [(1- fa /F’ey)×Fby] ≤ 1.0

 fa/ Fa0 + fbx/ Fb1x + fby/ Fb1y ≤ 1.0

where fa = P/ Awith A = the full cross section area fbx = maximum applied bending stress about the x -axis. Note that fb for a section with stiffened compression element will be based on the effective width and the corresponding effective section modulus. fby = maximum applied bending stress about the y -axis. Note that fb for a section with stiffened compression element will be based on the effective width and the corresponding effective section modulus. Cm = a moment factor based on the ratio of the end moments and defined as 0.6- 0.4×M1/M2 ≥ 0.4. M1 & M2 are the smaller & larger end moments respectively, about the relevant axis. Fa1 = allowable compressive stress as per Cl.6.6.1.1 F’e = 12 × π2 × E / [23 × (KL/r)2] Note that F’e will be calculated for the respective axes. Fa0 = is the allowable compressive stress from Cl.6.6.1.1 using L = 0. Fb1 = maximum bending stress without any lateral buckling as per Cl.6.1 and Cl.6.2 as appropriate)
• Members susceptible to torsional buckling:
For members that are susceptible to torsional buckling, both the interaction equations as per Cl.6.7.2 (a) will be checked as below:
1. Sections that have the factor Q = 1.0:

The following two checks will be performed for all section profiles:

$f a F a 0 + f b 1 F b 1 ≤ 1.0$
where fa = P/ Awith A = the full cross section area fb1 = maximum applied bending stress about the relevant axis. Note that fb for a section with stiffened compression element will be based on the effective width and the corresponding effective section modulus. Cm = a moment factor based on the ratio of the end moments and defined as 0.6- 0.4×M1/M2 ≥ 0.4. M1 & M2 are the smaller & larger end moments respectively, about the relevant axis. Note that the end moments used will be the ones at the ends of the analytical member being designed. Fa1 = allowable compressive stress as per Cl.6.6.1.1 F’e = $12 π 2 E 23 ( K L / r ) 2$ Note that F’e will be calculated for the respective axes. Fa0 = the allowable compressive stress from Cl.6.6.1.1 using L = 0. Fb1 = maximum bending stress without any lateral buckling as per Cl.6.1 and Cl.6.2 as appropriate)

Since the loads are being taken as being applied through the shear centre, the checks as per Cl.6.7.2 (b), Cl.6.7.2 (c) & Cl.6.7.2 (d) will not be performed.

2. Sections that have the factor Q < 1.0:

For members with a Q factor less than 1.0, the interaction checks as per Cl.6.7.2 (a) will be performed, but with the term Fy being replaced with Q×Fy.

• Checks for members subject to combined shear and bending:

Only web elements of sections will be checked for the effects of combined bending & shear forces. The checks will be done as per Cl.6.4.3. The following check will be performed:

$f b w F b w 2 + f v F v 2 ≤ 1.0$
where fbw = the applied bending stress at junction of flange & web Fbw = 36560000 /(h/t)2 kgf/cm2 fv = the applied shear stress Fv = allowable shear stress as per Cl.6.4.1, but not limited to 0.4×Fy.