# 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 in^{2}.

*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*; however, the check is included here to illustrate the calculation.

_{z}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