代写ENGG2400 - Mechanics of Solids 1 T2 2022 Block Test 3代写C/C++编程

ENGG2400 - Mechanics of Solids 1

T2 2022 Block Test 3

Question 1: Beam Bending                                                             (3 Marks)

The beam AB is loaded with a uniformly distributed load as well as a point load at its midpoint, as shown. The beam has an I-section with dimensions shown.

Use the following values in your working out:

L = L

b = b

h = h

F = F

w = w

a)   Draw the Free Body, Shear Force and Bending Moment diagrams on your response sheet using the axes provided. Label any important points—such as maxima and minima—on your diagrams. (1.5 marks)

b)   What is the maximum bending stress experienced in the beam? What is its nature (tensile or compressive)?   (1 mark)

c)   What would be the effect of rotating the beam by 90 degrees about its longitudinal axis? (ie. “b” would become the vertical distance as seen in the loading diagram) (0.5 marks)

Question 2: stress and strain Transformation                     (3 Marks)

A car rapidly accelerates, subjecting one of its wheels to the loading shown.

Use the following values in your working out:

l = l

d1  = d1

d2  = d2

P = P

F = F

a)    Draw the stresses acting on an element located at A, at the top of the axle connected to the wheel, in the X–Y plane. Label these stresses with their appropriate magnitudes. (1 mark)

If you are using the response sheet from your PSS Booklet, please disregard the template stress elements and only consider a 2D element in the X–Yplane.

b)   By drawing a Mohr’s circle, find the three principal stresses and maximum in-plane shear stress at A (1.5 marks)

c)   If the axle is made from a material with Young’s Modulus and Poisson’s ratio as shown below, determine the in- plane principal strains at A. (0.5 marks)

E = E

v = ν

Question 3: Beam Deflection                                                      (3 Marks)

The beam ABC is loaded as shown.

Use the following values in your working out:

L = L

F = F

w = w

a)   Using discontinuity functions/Macauley brackets, write the bending moment equation as a function of x in terms of the unknown reaction forces at A and C. Clearly state what your chosen sign convention is for x. (0.75 marks)

b)   Which elastic curve diagram best represents the shape of the resulting deflection of the beam? (0.5 marks)

c)   Using the double integration method, determine the magnitude of the reaction forces at A and C. (1.75 marks)