# Example F.7A HSS flexural member with noncompact flanges

The results are generated with SDC Verifier 3.7.1 and calculated with FEMAP v11.0.0. The Example was calculated in American unit system.

**Task:**

Select a rectangular ASTM A500 Grade B HSS beam with the span of 21 ft. The loads include a uniform dead load of 0.15 kip/ft and a uniform live load of 0.4 kip/ft. Limit the live load deflection to L/240. The beam is braced at the end points only. A noncompact member was selected here to illustrate the relative ease of selecting noncompact shaped from the AISC Manual, as compared to designing a similar shape by applying the AISC Specification requirements directly, as shown in Example F.7B.

**Solution:**

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

ASTM A500 Grade B

F_{y} = 46 ksi

F_{u} = 58 ksi

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

*Minimum Required Moment of inertia*

The maximum live load deflection permitted is:

The maximum calculated deflection is:

Rearranging and substituting Δ_{max} = 1.05 in.,

*Beam Selection*

Select rectangular HSS with a minimum l_{x} of 57.5 in^{4}.,using AISC Manual Table 1-11, and having adequate available strength, using AISC Manual Table 3-12.

Try an HSS 10×6× ^{3}/_{16} oriented in the strong direction. This rectangular HSS section was purposely selected for illustration purposes because it has a noncompact flange. See AISC Manual Table 1-12A for compactness criteria.

l_{x} = 74.6 in^{4}. > 57.5 in^{4}. **o.k.**

From AISC Manual Table 3-12, the available flexural strength is:

# Example F.7B HSS flexural member with noncompact flanges

**Task:**

Notice that in Example F.7A the required information was easily determined by consulting the tables of the AISC Manual. The purpose of the following calculation is to demonstrate the use of the AISC Specification equations to calculate the flexural strength of an HSS member with a noncompact compression flange.

**Solution:**

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

ASTM A500 Grade B

F_{y} = 46 ksi

F_{u} = 58 ksi

From AISC Manual Table 1-11, the geometric properties are as follows:

HSS 10×6× ^{3}/_{16}

Z_{x} = 18.0 in.^{3}

S_{x} = 14.9 in.^{3}

*Flange Compactness*

= 31.5 from AISC Manual Table 1-11

Determine the limiting ratio for a compact HSS flange in flexure from AISC Specification Table B4.1b Case 17.

*Flange Slenderness*

Determine the limiting ratio for a slender HSS flange in flexure from AISC Specification Table B4.1b Case 17.

flexure from AISC Specification Table B4.1b Case 17.

Λ_{p}<Λ<Λ_{r} therefore the flange is noncompact. For this situation, AISC Specification Equation F7-2 applies

*Web Slenderness*

= 54.5 from AISC Manual Table 1-11

Determine the limiting ratio for a compact HSS web in flexure from AISC Specification Table B4.1b Case 19.

Λ < Λ_{p} therefore, the web is compact

For HSS with noncompact flanges and compact webs, AISC Specification Section F7.2(b) applies.

From AISC Specification Section F1, the available flexural strength is:

Units which were used in calculation:

1 kip = 1000lb

1 ft = 12 in

1 ksi = 1000 psi (lb/in^2)

#### Example from AISC Design Examples

**Material summary**

**Properties Summary**

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

Height | 10.00 |

Width | 6.00 |

h | 10.00 |

b | 6.00 |

D | 0.174 |

### FEM Loads and Constraint

#### 1..Loads

### Constraint

#### Individual Load ‘1..Loads.Constraint’

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

Convert values: 363.80e+03 lb-in = 30.31 kip-ft

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

#### 1..HSS (square and rectangular)

#### 2..Bending

From AISC Specification Section F1, the available flexural strength is:

Utilization factor

777.51 kip-in = 64.79 kip-ft;

363.8 kip-in = 30.31 kip-ft;

64.79 kip-ft/1.67 =38.79 kip-ft

30.31/38.79 = **0.78**

Comparing results of calculation with SDC Verifier and Example F.7 can be seen that values coincide. Slight difference is explained by converting units from one to another and using conservative shape of the beam in Femap.

The required flexural strength is 30.31 kip-ft.

The available flexural strength is 38.79 kip-ft.

Download SDC Verifier project file, model and report of Example F.7