Hello, if you have any need, please feel free to consult us, this is my wechat: wx91due
ENGG2400 – Mechanics of Solids 1
T2 2020 Block Test 3
Question 1: Stress and Strain Transformation (3 Marks)
A circular rod with radius r = 25mm is fixed at point A. The rod is loaded with a combination of two forces F1, F2 and a torque T. The two forces are applied at the end of the rod which is a distance d = 0.2m away from point P.
Take F1 = 10kN, F2 = 4kN and T = 0.75kNm. Use the coordinate system given in the figures.
The point P is located on the surface of the rod.
a) Calculate the normal stress at point P caused by the axial load.
b) Calculate the normal stress at point P caused by the bending load.
c) Calculate the shear stress at point P caused by the torsional load.
d) Select the correct orientation of stresses on the material element at point P. Use the coordinate system given in the figures.
e) Add appropriate axes to the given diagram and use it to construct Mohr’s circle. Use Mohr’s circle to calculate the principal stresses and rotation angle/s to the principal orientation. Include signs in all calculated values. Label all important points used for the construction of Mohr’s circle and all calculated features.
f) What is the value of the shear stress on the material element rotated to the principal orientation?
Question 2: Beam Deflection (3 Marks)
The beam ABC is supported by a roller at B and a pin joint at C.
A uniformly distributed load with magnitude W = 1500 N/m is applied as shown in the figure.
Take EI = 120,000 Nm2 and L = 1.2 m.
a) Calculate the support reactions at B and C
b) Select the correct boundary condition at point B
c) Select the correct boundary condition at point C
The bending moment function using discontinutity functions is given as:
M(x) = − 2/W < x − L >2 + RB < x − 2L >1
Integrate the bending moment function twice to get the beam deflection function in the following form:
EIU(x) = ∫ ∫ M(x) dx dx + C1x + C2
d) Calculate the constant of integration C1
e) Calculate the constant of integration C2
f) Calculate the deflection at the left end A
g) If section AB was constructed using aluminium and section BC was constructed using steel. How would you alter the procedure for calculating the beam deflection? You do not have to do any calculations.
Question 3: Energy Methods (3 Marks)
A steel beam AB (E = 200 GPa, G = 75 GPa) is supported at A by a pin support and at B by a pin connection to a supporting
aluminium rod BC (E = 70 GPa). The steel beam has a square cross-section with width 50mm and the aluminium rod has a circular
cross-section with radius 12mm.
Take F = 12 kN and L = 4 m
a) Draw and upload a Free Body Diagram of the beam.
b) Calculate the elastic strain energy due to the axial load on the aluminium rod BC.
c) Calculate the elastic strain energy due to shearing of the steel beam AB. The shear form factor for a rectangular cross-section is 1.2.
d) Calculate the elastic strain energy due to bending of the steel beam AB.