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ENGG2400 – Mechanics of Solids 1
T2 2021 Block Test 3
Question 1: Stress and Strain Transformation (3 Marks)
A bent pole is loaded with two forces F1 and F2 at its end. F1 is parallel to the z-axis and F2is parallel to the x-axis. The pole has a radius r and the bend is 90 degrees.
Point A is located at the top surface of the pole and the stress state at this point is to be calculated.
Take the following values:
F1 = 1200 N, F2 = 9000 N
L1 = 1.6 m, L2 = 1.8 m
r = 0.04 m
a) Draw one or more Free Body Diagrams showing the internal loadings at a section cut through point A. Make sure to include all axial forces, shear forces, moments and torque.
b) Calculate the normal stress magnitude at A due to axial loading only.
c) Calculate the normal stress magnitude at A due to bending only.
d) Calculate the shear stress magnitude at A due to torsion only.
e) Construct Mohr’s circle for stresses in the x-y plane. Use Mohr’s circle to calculate the principal stresses at point A. Label all important features used for the construction of Mohr’s circle and all calculated features. Ensure signs are included in all calculated values.
f) Complete the stress element at A by drawing arrows representing the stress state of the element. Use the coordinate system given. This is NOT the principal orientation.
g) Which of these statements best describes the shortest rotation required to transform the x,y,z axes to the principal axes?
Question 2: Beam Deflection (3 Marks)
The beam in the figure is fixed at end A and is supported by a roller at B. At the right most end a point load with magnitude P is applied in the downwards direction. The flexural rigidity of the beam is EI.
Take the following values:
L = 0.8 m
P = 4000 N
EI = 60000 Nm2
a) Write down the bending moment function in terms of the unknown support reactions at A and B.
b) Select the correct boundary conditions at A
c) Select the correct boundary conditions at B
d) Use the equilibrium equations for the beam and information gained from the boundary conditions to calculate the magnitude of the support reactions at A and B.
e) Calculate the signed deflection of the beam at a point halfway between A and B. Use positive to represent upwards an upwards deflection.
Question 3: Energy Methods (3 Marks)
The five-member truss ABCD is loaded with a horizontal force at joint A. The truss members have the same rectangular cross-section with side lengths a and b.
Take the following values:
L1 = 2.4 m, L2 = 1.8 m
a = 12 mm, b = 40 mm, E = 200GPa
P = 20000N
a) Calculate the axial force magnitude in each member of the truss.
b) Determine the total axial strain energy stored by the structure
c) Calculate the horizontal deflection of point A.