Design the strut:

Design the strut in Example if the two angles are placed on the same side of the 10 mm gusset plate.

Figure

Solution

(a) Try two ISA angles 75 × 75 × 8 placed on the same side of the gusset plate as shown in Figure 6. The properties of the section are:

Area = 11.4 cm², r_xx= r_yy = 2.28 cm, C_x= C_y = 2.14 cm.

The radius of gyration about axis xx

The radius of gyration about axis yy

As r_xx = r_yy for the equal angles, the second case will give smaller value of radius of gyration (about y-y axis).

∴          r_xx of the double angle section = 2.28 cm = 22.8 mm.

∴ As each angle is connected to the gusset plate by one rivet only the effective length is equal to actual length, i.e. l_eff = 2800 mm.

∴ Slenderness ratio, λ = 2800/22.8= 123 , for which corresponding

σ_ac = 62 MPa.

Here the allowable stress will be 80% of σ_ac.

∴ P_allowable = (0.8 × 62) × (2 × 1140) N =113 kN < 120kN ∴ rejected.

(b)       Next try two ISA 80 × 80 × 8 sections similarly placed

Area = 2 × 12.2 cm² = 2440 mm², r_xx = r_yy = 2.44 cm

∴ λ = 2800/24.4 = 115, for which corresponding σ_ac= 68 MPa.

∴ P_allowable = 0.8 × 68 × 2440 N = 132.7 kN.

As this is larger than the required 120 kN load, we have to accept it, as the standard section (IS angles) of next lower size (i.e. 2 nos ISA 75 × 75 × 8) was found to be insufficient.