# Example E.8 WT compression member with slender elements

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

**Task:**

Select an ASTM A992 WT-shape compression member with a length of 20 ft to support a dead load of 6 kips and live load of 18 kips in axial compression. The ends are pinned.

**Solution:**

From AISC Manual Table 2-4, the material properties are as follows:

ASTM A992

F_{y} = 50 ksi

F_{u} = 65 ksi

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

*Table Solution*

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

Therefore, (*KL*)_{x} = (*KL*)_{y} = 20.0 ft.

Select the lightest member from AISC Manual Table 4-7 with sufficient available strength about both the *x-x*axis (upper portion of the table) and the *y-y* axis (lower portion of the table) to support the required strength.

Try a WT7×15.

The available strength in axial compression from AISC Manual Table 4-7 is:

The available strength can be easily determined by using the tables of the AISC Manual. Available strength values can be verified by hand calculations, as follows

*Calculation Solution*

From AISC Manual Table 1-8, the geometric properties are as follows:

WT7×15.

A_{g} = 4.42 in^{2}.

r_{x} = 2.07 in.

r_{y} = 1.49 in.

J = 0.190 in^{4}.

Q_{s} = 0.611

γ^{‾} = 1.58 in.

I _{x} = 19.0 in^{4}.

I _{y} = 9.79 in^{4}.

d = 6.92 in.

t_{w} = 0.270 in.

b_{f} = 6.73 in.

t_{f} = 0.385 in.

*Stem Slenderness Check*

Determine the stem limiting slenderness ratio, Λ_{r}, from AISC Specification Table B4.1a Case 4.

Λ > Λ_{r} therefore, the web is slender

*Flange Slenderness Check*

Determine the flange limiting slenderness ratio, Λ_{r}, from AISC Specification Table B4.1a Case 1.

Λ < Λ_{r} therefore, the flange is not slender

Because this WT×15 has a slender web, AISC Specification Section E7 is applicable. The nominal compressive strength, P_{n} shall be determined based on the limit states of flexural, torsional and flexural-torsional buckling.

*x-x* Axis Critical Elastic Flexural Buckling Stress

Critical Elastic Torsional and Flexural-Torsional Buckling Stress

*Torsional Parameters*

The shear center for a T-shaped section is located on the axis of symmetry at the mid-depth of the flange

Omit term with C_{w} per User Note at end of AISC Specification Section E4.

Check limit for the applicable equation.

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

#### Example from AISC Design Examples

**Material summary**

**Properties Summary**

**1..WT7×15**

Geometry Property | Value |
---|---|

Height | 6.92 |

Width | 6.73 |

h | 6.92 |

b | 6.73 |

d | 0.27 |

t | 0.39 |

### FEM Loads and Constraint

#### 1..Dead load 6 kips

#### 2..Live load 18 kips

### Constraint

#### 1.. Pinned

### Check 1..ANSI / AISC LRFD 360-10

#### Beam Characteristics

**All (LS1, All Entities)**

#### Axial check

**All (LS1, All Entities)**

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

Comparing results of calculation in SDC Verifier and in Example E.8 we can see that values completely match. The available compressive strength is 38.4 kips.

Download SDC Verifier project file, model and report of Example E.8