Example E.2 Built-up column with a slender web

The results are generated with SDC Verifier 3.6 and calculated with FEMAP v11.0.0

Task:

Verify that a built-up, ASTM A572 Grade 50 column with PL1 in. × 8 in. flanges and PL¼× 15 in. The web is sufficient to carry a dead load of 70 kips and live load of 210 kips in axial compression. The column length is 15 ft and the ends are pinned in both axes.

Solution:

From AISC Manual Table 2-5, the material properties are as follows:

Built-up Column

ASTM A572 Grade 50

F_y = 50 ksi

F_u = 65 ksi

The geometric properties are as follows:

Built-up Column

d = 17.0 in.

b_f = 8.00 in.

t_f = 1.00 in.

h = 15.0 in.

t_w = ¼in.

From Chapter 2 of ASCE/SEI 7, the required compressive strength is:

Built-up Section Properties (ignoring fillet welds)

A = 2(8.00 in.)(1.00 in.) + 15.0 in.(¼ in.)

  = 19.8 in².

Elastic Flexural Buckling Stress

From AISC Specification Commentary Figure C-A-7.1, for a pinned-pinned condition, k = 1.0.

Because the unbraced length is the same for both axes, the y-y axis will govern by inspection.

Elastic Flexural Buckling stress

Note: Torsional buckling generally will not govern if KL_y ≥ KL_z; however, the check is included here to illustrate the calculation.

From the User Note in AISC Specification Section E4,

From AISC Design Guide 9, Equation 3.4,

Therefore, the flexural buckling limit state controls.

Use F_e = 38.3 ksi.

Slenderness

Check for slender flanges using AISC Specification Table B4.1a, then determine Q_s, the unstiffened element (flange) reduction factor using AISC Specification Section E7.1.

Calculate k_c using AISC Specification Table B4.1b note [a]

For the flanges,

Determine the flange limiting slenderness ratio, Λ_r, from AISC Specification Table B4.1a Case 2.

Λ < Λ_r therefore, the flange is not slender and Q_a = 1.0.

Check for slender web, then determine Q_s, the stiffened element (web) reduction factor using AISC Specification Section E7.2.

Determine the slender web limit from AISC Specification Table B4.1a Case 5.

Λ > Λ_r therefore, the web is slender

 where A_e = effective area based on the reduced effective width, b_e

From AISC Specification Equation E7-17, take ƒ as F_cr with F_cr calculated based on Q = 1.0.

Equations E7-2 and E7-3 based on KL/r_y.

KL/r = 86.5 as previously calculated

Flexural Buckling Stress

Determine whether AISC Specification Equation E7-2 or E7-3 applies.

KL/r = 86.5 as previously calculated

Therefore, AISC Specification Equation E7-2 applies.

Nominal Compressive Strength

From AISC Specification Section E1, the available compressive strength is:

Example from AISC Design Examples

Material summary

Properties Summary

Geometry Property	Value
Height	17.00
Width	8.00
h	17.00
a	8.00
b	8.00
c	1.00
d	0.25
t	1.00

FEM Loads and Constraint

1..Dead load 70 kips

2..Live load 210 kips

Constraint

1.. Pinned

Check 1..ANSI / AISC LRFD 360-10

Beam Characteristics

All (LS1, All Entities)

Axial check

All (LS1, 1 element(s))

Nominal Compressive Strength

From AISC Specification Section E1, the available compressive strength is:

Comparing results of calculation in SDC Verifier and in Example E.2 we can see that values completely match. The available compressive strength is 506 kips.  Example E2