# Example G.4 Rectangular HSS in shear

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

Determine the available shear strength and adequacy of HSS6×4×¾ ASTM A500 Grade B member with end shears of 11.0 kips from dead load and 33.0 kips from >live load. The beam is oriented with the shear parallel to the 6 in. dimension

Solution:

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

Fy = 46 ksi

Fu = 58 ksi

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

HSS6×4×?

H = 6.00 in.

B = 4.00 in.

t = 0.349 in.

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

Note: There are no AISC Manual Tables for shear in HSS shapes, but the available shear strength can be determined from AISC Specification Section G5, as follows.

Nominal Shear Strength

For rectangular HSS in shear, use AISC Specification Section G2.1 with Aw = 2ht (per AISC Specification Section G5) and kv = 5.

From AISC Specification Section G5, if the exact radius is unknown, h shall be taken as the corresponding outside dimension minus three times the design thickness.

Note:Most standard HSS sections listed in the AISC Manual have Cv = 1.0 at Fy ≤ 46 ksi.

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

#### Example from AISC Design Examples

Material summary

Properties Summary

Geometry Property Value
Height 6.00
Width 4.00
h 6.00
b 4.00
d 0.35

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

#### Shear

All (LS1, All Entities)

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

From AISC Specification Section G5, if the exact radius is unknown, h shall be taken as the corresponding outside dimension minus three times the design thickness

From AISC Specification Section G1, the available shear strength is

Comparing results of calculation in SDC Verifier and in Example G.4 we can see that values completely match.

The required shear strength is 66 kips.

The available shear strength is 85.87 kips.