# D1.K.2.1 Design Process

The following Checks are to be performed on a Steel Member as per this AISC N690 – 1984 Code. When a design is performed, the output file the reports the maximum utilization from all of the checks.

## D1.K.2.1.1 Slenderness

The maximum allowable slenderness ratio in Compression (K·L/r_min), as per clause Q1.8.4 of the code shall not exceed 200. And the maximum allowable slenderness ratio in Tension (L/r_min) shall not exceed 240 for main members and 300 for bracing members and other secondary members.

This can be controlled by using the existing MAIN and TMAIN parameters respectively.

The default value of MAIN is 200 and for TMAIN is 240.

## D1.K.2.1.2 Check for Element Slenderness and Stress Reduction Factors

The permissible Width-to-Thickness Ratio of Un-stiffened Elements under Compression is determined as per section Q1.9.1 and that of Stiffened Elements under Compression is determined as per section Q1.9.2 of the code.

The permissible Width–Thickness Ratio of web is determined as per section Q1.10.2.

## D1.K.2.1.3 Tension

Allowable tensile stress on the Net section is calculated as 0.60·Fy , but not more than 0.5·Fu on the Effective Net area, as per section Q1.5.1.1.

The Net Area (An) shall be determined in accordance with Q1.14, and the NSF parameter can be utilized for that.

The Effective Net Area (Ae) of axially loaded tension members, where the load is transmitted by bolts through some but not all of the cross-sectional elements of the member, shall be computed from the formula (ref. Q1.14),

Ae = Ct·An

Unless otherwise specified, the default value of the CT parameter is set as 0.75.

The value of CT parameter for other conditions is described at section Q1.14.

The provisions for Pin-connected and Threaded tensile member are not implemented in STAAD.

## D1.K.2.1.4 Compression

The allowable compressive stress for columns which meet the provisions of section Q1.9, except those fabricated from austenitic stainless steel shall be as required by Q1.5.1.3. The allowable compressive stress for columns fabricated from austenitic stainless steel shall be in accordance to section Q1.5.9.

1. Gross Sections of Columns, except those fabricated of austenitic stainless steel:

1. On gross section of axially loaded compression members, when (Kl/r) ≤ Cc ,

Fa = [1 - (Kl/r)2/(2·Cc 2)]Fy / {5/3 + [3(Kl/r)/(8·Cc)] - [(Kl/r)3/(8·Cc 3)]}

Where:

Cc = [(2·π2E)/Fy]1/2

2. When (Kl/r) > Cc ,

Fa = 12·π2E/[23(kL/r)2]

2. Gross sections of columns fabricated from Austenitic Stainless steel:

1. When (Kl/r) ≤ 120,

Fa = Fy/2.15 - [(Fy/2.16 - 6)/120](kL/r)

2. When (Kl/r) > 120,

Fa = 12 - (KL/r)/20

If the provisions of the section Q1.9 are not satisfied,

1. For un-stiffened compression element, a reduction factor Qs is introduced. Detailed values of Qs for different shapes are given in Section QC2.

2. For stiffened compression element, a reduced effective width be is introduced.

1. For the flanges of square and rectangular sections of uniform thickness:

be = 253·t/√Fy{1 - (50.3/[(b/t)√Fy]} ≤ b

2. For other uniformly compressed elements:

be = 253·t/√Fy{1 - (44.3/[(b/t)√Fy]} ≤ b

Consequently, a reduction factor Qa is introduced and is equal to the effective area divided by the actual area. Combining both these factors, allowable stress for axially loaded compression members containing stiffened or unstiffened elements shall not exceed

Fa = QsQa[1 - (Kl/r)2/(2·Cc 2)]Fy / {5/3 + [3(Kl/r)/(8·Cc)] - [(Kl/r)3/(8·Cc 3)]}

Where:

C'c = [(2·π2E)/(QsQaFy)]1/2

## D1.K.2.1.5 Bending Stress

Allowable bending stress for tension and compression for a structural member, as given in section Q1.5.1.4 is:

1. Along Major Axis:

1. Tension and compression on extreme fibers of compact hot rolled or built-up members symmetrical about and loaded in the plane of their minor axes and meeting the requirements of Subsection Q1.5.1.4.1.1 to 7, shall result in a maximum bending stress:

Fb = 0.66·Fy

If meeting the requirements of this member of:

1. Width-thickness ratio of unstiffened projecting elements of the compression flange shall not exceed 65/√Fy .
2. Width-thickness ratio of stiffened elements of the compression flange shall not exceed 190/√Fy .
3. The depth-thickness ratio of the web shall not exceed

d/t = (640/√Fy)[1 – 3.74(fa/Fy)] when fa/Fy ≤0.16

d/t = 257/√Fy when fa/Fy > 0.16

4. The laterally unsupported length of the compression flange of members other than box-shaped members shall not exceed the value of 76bf/√Fy nor 20000/(d/Af)Fy .
2. For noncompact and slender elements, section Q1.5.1.4.2 is followed.
3. For box-type flexural members, maximum bending stress is:

Fb = 0.60·Fy

2. Along Minor Axis:

1. For doubly symmetrical members (I shaped) meeting the requirements of section Q1.5.1.4.1, maximum tensile and compressive bending stress shall not exceed the following value as per section Q1.5.1.4.3:

Fb = 0.75·Fy

2. For doubly symmetrical members (I shaped) meeting the requirements of section Q1.5.1.4.1, except where bf/2tf > 65/√Fy but is less than 95/√Fy , maximum tensile and compressive bending stress shall not exceed:

Fb = Fy[0.79 – 0.002(bf/2tf)√Fy]

## D1.K.2.1.6 Combined Interaction Check

Members subjected to both axial compression and bending stresses are proportioned to satisfy equation Q1.6-1a:

$f a SFC ⋅ F a + C m y f b y SMY ⋅ F b y ( 1 − f a F ′ e y ) + C m z f b z SMZ ⋅ F b z ( 1 − f a F ′ e z ) ≤ 1.0$

and Q1.6-1b

$f a SFC ⋅ 0.6 F y + f b y SMY ⋅ F b y + f b z SMZ ⋅ F b z ≤ 1.0$

when, fa/Fa > 0.15, as per section Q1.6.1 of the code.

Otherwise, equation Q1.6-2 must be satisfied:

$f a SFC ⋅ F a + f b y SMY ⋅ F b y + f b z SMZ ⋅ F b z ≤ 1.0$

It should be noted that during code checking or member selection, if fa/Fa exceeds unity, the program does not compute the second and third part of the formula, because this would result in a misleadingly liberal ratio. The value of the coefficient Cm is taken as 0.85 for side-sway and [0.6 - 0.4·(M1/M2)], but not less than 0.4 for no side-sway.

Members subjected to both axial tension and bending stress are proportioned to satisfy equation Q 1.6-1b:

$f a SFT ⋅ 0.6 F y + f b y SMY ⋅ F b y + f b z SMZ ⋅ F b z ≤ 1.0$

Where SFC, SFT, SMZ, and SMY are stress limit coefficient parameters used to control the components of the interaction equations. Refer to D1.K.2.3 Design Parameters for details.

## D1.K.2.1.7 Shear Stress

Allowable shear stress on the gross section [ref. section Q1.10.5.2] is calculated as

Fv = (Fy/2.89)Cv ≤ 0.4·Fy

Where:

• Cv = (45,000·k)/[Fy(h/t)2], when h/t ≤ 0.8
• Cv = [190/(h/t)]√(k/Fy), when h/t > 0.8
• k = 4.00 + [5.34/(a/h)2], when a/h ≤ 1.0
• k = 5.34 + [4.00/(a/h)2], when a/h > 1.0

For actual shear on the web, the gross section is taken as the product of the total depth and the web thickness. For shear on the flanges, the gross section is taken as the total flange areas.