# Example F.3A W-shape flexural member with noncompact flanges in strong axis bending

The results are generated with SDC Verifier 3.7 and calculated with FEMAP v11

**Task:**

Select an ASTM A992 W-shape beam with a simple span of 40 ft. The nominal loads are a uniform dead load of 0.05 kip/ft and two equal 18 kip concentrated live loads acting at the third points of the beam. The beam is continuously braced. Also, calculate the deflection.

Beam Loading & Bracing Diagram (continuous bracing)

Note: A beam with noncompact flanges will be selected to demonstrate that the tabulated values of the AISC Manual account for flange compactness.

**Solution:**

From A Manual 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 flexural strength at midspan is:

*Beam Selection*

For a continuously braced W-shape, the available flexural strength equals the available plastic flexural strength. Select the lightest section providing the required strength from the bold entries in AISC Manual Table 3-2.

Try a W21×48

This beam has a noncompact compression flange at F_{y} = 50 ksi as indicated by footnote “f” in AISC Manual Table 3-2. This shape is also footnoted in AISC Manual Table 1-1.

From AISC Manual Table 3-2, the available flexural strength is:

Note: The value M_{px} in AISC Manual Table 3-2 includes the strength reductions due to the noncompact nature of the shape.

*Deflection*

l_{x} = 959 in.^{4} from AISC Manual Table 1-1

The maximum deflection occurs at the center of the beam.

from AISC Manual Table 3-23 cases 1 and 9

This deflection can be compared with the appropriate deflection limit for the application. Deflection will often be more critical than strength in beam design.

# Example F.3B W-shape flexural member with noncompact flanges in strong axis bending

**Task:**

Verify the results from Example F.3A by calculation using the provisions of the AISC Specification.

**Solution:**

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

ASTM A992

F_{y} = 50 ksi

F_{u} = 65 ksi

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

W21×48

S_{x} = 93.0 in.^{3}

Z_{x} = 107 in.^{3}

The required flexural strength from Example F.3A is:

*Flange Slenderness*

The limiting width-to-thickness ratios for the compression flange are:

from AISC Specification Table B4.1b Case 10

from AISC Specification Table B4.1b Case 10

λ_{rf} > λ > λ_{pf}, therefore, the compression flange is noncompact. This could also be determined from the footnote “f” in AISC Manual Table 1-1.

*Nominal Flexural Strength, M _{n}*

*Because the beam is continuously braced, and therefore not subject to lateral-torsional buckling, the available strength is governed by AISC Specification Section F3.2, Compression Flange Local Buckling.*

*M _{p} = F_{y}Z_{x}*

*= 50 ksi(107 in. ^{3}*

*= 5.350 kip-in. or 446 kip-ft*

*from AISC Specification*

*From AISC Specification Section G1, the available shear strength is:*

*Example from AISC Design Examples*

**Material summary**

**Material summary**

**Properties Summary**

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

Height |
9.00 |

Width |
2.65 |

h |
9.00 |

a |
2.65 |

b |
2.65 |

c |
0.41 |

d |
0.45 |

t |
0.41 |

*FEM Loads and Constraint*

*1..Dead load 10 kips*

*2..Live load 30 kips*

*Constraint*

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

*Shear*

**All (LS1, 17 Property Shape(s))**

*From Chapter 2 ASCE/SEI 7, the required shear strength is:*

*From AISC Specification Section G1, the available shear strength is*

*Comparing results of calculation in SDC Verifier and in Example G.7 we can see that values completely match.*

*The required shear strength is 30 kips.*

*The available shear strength is 42.55 kips.*