# Example E.3 Built-Up column with slender flanges

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

**Task:**

Determine if a built-up, ASTM A572 Grade 50 column with PL? in. × 10½ in flanges and a PL¼ in. × 7¼ in. The web has sufficient available strength to carry a dead load of 40 kips and a live load of 120 kips in axial compression. The column’s unbraced length is 15 ft in both axes and the ends are pinned.

**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* = 8.00 in.

*b _{ƒ}* = 10½ in.

*t _{ƒ}* = ? in.

*h* = 7¼ in.

*t _{w}* = ¼ in.

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

*Built-Up Section Properties (ignoring fillet welds)*

A_{g} = 2(10½ in.)(? in.) + 7¼ in.(¼ in.)

=9.69 in.^{2}

Because the unbraced length is the same for both axes, the weak axis will govern.

*Weld Slenderness*

Determine the limiting slenderness ratio, Λ_{r}, from AISC Specification Table B4.1 a case 5:

Λ < Λ_{r}; therefore, the web is not slender.

Note that the fillet welds are ignored in the calculation of *h* built up sections.

*Flange Slenderness*

Calculate K_{c–}

Use k_{c} = 0.743

Determine the limiting slenderness ratio, Λ_{r}, From AISC Specification Table B4.1a case 2.

Λ > Λ_{r}; therefore, the flanges are slender.

For compression members with slender elements, Section E7 of the AISC Specification applies. The nominal compressive strength, P_{n}, shall be determined based on the limit states of flexural, torsional and flexural-torsional buckling. Depending on the slenderness of the column, AISC Specification Equation E7-2 or E7-3 applies. Fe_{e} is used in both equation and is calculated as the lesser of AISC Specification Equation E3-4 or E4-4.

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

Because the unbraced length is the same for both axes, the weak axis will govern.

*Elastic Critical Stress, F _{e}, for Flexural Buckling*

*Elastic Critical Stress, F _{e}, for Torsional Buckling*

Note: This limit state is not likely to govern, but the check is included here for completeness.

From the User Note in AISC Specification Section E4,

From AISC Design Guide 9, Equation 3.4,

Therefore, use F_{e} = 65.9 ksi.

*Slenderness Reduction Factor Q*

Q = Q_{s}Q_{a} from AISC Specification Section E7, where Q_{a} = 1.0 because the web is not slender.

Calculate Q_{s}, the unstiffened element (flange) reduction factor from AISC Specification Section E7.1(b).

Determine the proper equation for Q_{s} by checking limits for AISC Specification Equation E7-7 to E7-9.

*Nominal Compressive Strength*

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

Note: Built-up sections are generally more expensive than standard rolled shapes; therefore, a standard compact shape, such as a W8×35 might be a better choice even if the weight is somewhat higher. This selection could be taken directly from AISC Manual Table 4-1.

#### Example from AISC Design Examples

**Material summary**

**Properties Summary**

Area, moment Izz, moment Iyy and other shape parameters are corrected because in FEMAP it calculated without taken into account fillets and chamfers.

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

Height | 8.00 |

Width | 10.50 |

h | 8.00 |

a | 10.50 |

b | 10.50 |

c | 0.38 |

d | 0.25 |

t | 0.38 |

#### FEM Loads and Constraint

#### 1..Dead load 40 kips

#### 2..Live load 120 kips

#### Constraint

#### 1..Pinned

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

#### Beam Characteristics

**All (LS1, All Entities)**

**All (LS1, All Entities)**

*Web Slenderness*

Determine the limiting slenderness ratioΛ_{r}, from AISC Specification Table B4.1a case 5:

Λ < Λ therefore, the web is not slender

Calculate k_{c–}

Determine the limiting slenderness ratio,Λ_{r}, from AISC Specification Table B4.1a case 2:

Λ > Λ; therefore, the flanges are slender

#### 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.2 we can see that values completely match. The available compressive strength is 312 kips.