# Example G.6 Doubly symmetric shape in weak axis shear

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

**Task:**

Verify the available shear strength and adequacy of W21×48 ASTM A992 beam with end shears of 20.0 kips from dead load and 60.0 kips from live load in weak direction.

**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 1-11, the geometric properties are as follows:

W21×48

*b _{ƒ}* = 8.14 in.

*t _{ƒ}* = 0.430 in.

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

From AISC Specification Section G7, for weak axis shear, use AISC Specification Equation G2-1 and AISC Specification Section G2.1(b) with *A _{w}* =

*b*for each flange,

_{ƒ}t_{ƒ}*h/t*=

_{w}*b/t*,

_{ƒ}*b = b*/2 and

_{ƒ}*k*= 1.2.

_{v}Calculate * _{w}* (Multiply by 2 for both shear resisting elements)

Calculate *C _{v}*.

Note: For all ASTM A6 W-, S-, M- and HP shapes when *F _{y}* ≤ 50 ksi,

*C*= 1.0, except some M-shape noted in the User Note at the end of AISC Specification Section G2.1.

_{v}Calculate *V _{n}*.

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

#### Example from AISC Design Examples

**Material summary**

**Properties Summary**

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

Height | 20.60 |

Width | 8.14 |

h | 20.60 |

a | 8.14 |

b | 8.14 |

c | 0.43 |

d | 0.35 |

t | 0.43 |

### FEM Loads and Constraint

#### 1..Dead load 20 kips

#### 2..Live load 60 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:

Calculate *A _{w}*. (Multiply by 2 for both shear resisting elements.)

From AISC Specification Section G1, the available shear strength is

Comparing results of calculation in SDC Verifier and in Example G.6 we can see that values completely match.

The required shear strength is 120 kips.

The available shear strength is 189.01 kips.