Question

A rigid beam BCD is supported on a roller support at C (4m from B) and has two bars AB and DE attached at each end. The bars can carry either tension or compressive forces. The rigid beam carries a UDL of I kN/m across BC and a point load of P at D as shown in the figure above. The length of the two bars is 3000 mm. The elastic modulus of both bars is 200 GPa and the yield stress is ± 250 MPa. The cross-sectional area of bar AB is 100 mm² while bar DE has an area of 200 mm2. The coefficient of thermal expansion a for bar AB is 13x10^-6 per C and that for bar DE is 24x10^-6 per °C. 

1 Write down the equation of compatibility for the elongations in the bars (assume both are in tension). 

2 Write down the equilibrium equations involving the axial forces in the bars and the loads. (4 marks) 

3. If there are no temperature changes and P=75kN, find the forces and stresses in each bar and the 

4. If there is a temperature change in bar AB of ΔT_AB =+20℃ and bar DE of ΔT_DE =+40℃ combined  with the UDL and P 75kN, find the forces and stresses in each bar. 

5. If there is no temperature change in the bars (assume they remain in tension) and the beam carries the UDL plus the unknown point load P, what is the maximum load P that can be carried? 

6. If there is a temperature change in the bar DE ΔT_DE = -50° C combined with the UDL and the unknown point load P, what is the maximum load P that can be carried? 

Answer 1