Question

Two prismatic bars are rigidly fastened together and support a vertical load of 45kN as shown in Fig. The upper bar is steel having mass density 7750 kg/m³, length 10 m and crosssectional area 65 cm². The lower bar is brass having mass density 9000 kg/m³, length 6 m and cross-sectional area 50 cm². Determine the maximum stress in each material. For steel E_S = 200 GN/m² and for brass E_b =100 GN/m².

Answer 1

 Fig The maximum stress in the brass bar occurs at junction BB, and this stress is caused by the combined effect of 45kN load together with the weight of brass bar.

Weight of brass bar, W_b = ρ_bgV_h = 9000 × 9.81 × (6 × 50 × 10^–4) = 2648.7 N

Stress at section BB, σ_b = (P + W_b)/A_b

= (45000 + 4648.7)/50 × 10^–4 = 9529740 N/m² = 9.53 MN/m²

The maximum stress in the steel bar occurs at section A–A. Here the entire weight of steel and brass bars and 45kN load gives rise to normal stress. 

Weight of steel bar, W_S = p_sgV_s =7750 × 9.81 × (10 × 65 × 10^–4) = 4941.79 N

Stress at section AA ; σ_s = (P + W_h + W_s )/A_s

= (45000 + 2648.7 + 4941.79)/ 65 × 10^–4

= 8090845 = 8.09 MN/m².