b) Calculate the maximum height from which the 95-kg mass can be dropped to not exceed the 253 MPa maximum normal stress design condition.

c) Calculate the end point deflection of the beam, at point C, when the 95-kg mass is dropped from a height h that results in a maximum normal stress in the beam of 253 MPa. 

A downwards deflection is negative.

Question 1

A simply-supported overhanging steel beam (E = 200 GPa) is shown below. A 95-kg mass is dropped from a state of rest, from height h onto the end of the beam.

a) If the maximum normal stress due to bending in the beam is 253 MPa, calculate the maximum equivalent static load that can be applied to the end of the beam.

Calculate the vertical displacement of the end point of the curved bar due to the applied load P. Consider the strain energy due to both bending and torsion.

Provide your answer in terms of the elastic constants E and G, and the moment of inertia I and polar moment of inertia J of the bar.

Select the correct answer from the options below.

b) Calculate the vertical displacement of joint B if P = 27 kN. A positive value indicates a displacement in the same direction as the load P application, i.e. downwards positive. Give your answer to 3 significant figures.

b) Calculate the displacement of the end point C in the direction of the applied load, due to the applied load at C. A negative value would indicate displacement in the opposite direction to the applied load.

Question 1

A torsion bar (𝐿_𝐴𝐵=0.16 m) is fixed at end A; a lever arm (𝐿_𝐵𝐶=0.20 m) is welded rigidly onto the other end at B. A force, 𝐹 = 5.9 kN, is applied vertically at the end of the lever arm at point C. 

Torsion bar: kN.m²;  kN.m²

Lever arm: kN.m²

a) Solve the strain energy in the system, considering the energy due to bending moments and torsion only.

c) Determine the shear stress at section , a distance {l2} from the first pulley, at position A on the cross-section.

(positive shear stress vectors meet at the top right corner of a stress element, report to 3 significant figures)

b) Determine the shear stress at section , a distance 0.22 from the first pulley, at position A on the cross-section.

(positive shear stress vectors meet at the top right corner of a stress element, report to 3 significant figures)