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CIVE 2005

Sample exam to Mechanics of Materials

Question 1: Complete parts a) to e) (20 marks)

a) Please calculate the centroidal second moment of area Ix-x for the following section              4 Marks

(unit: mm)

b) A shaft with diameter of 100mm is subjected to a torque 15kN-m, please calculate the maximum shear stress due to torque. Hint: τ=Tr/J; J=π*d4 /32                    4 Marks

c) A simply supported beam is subjected to a concentrate load of 20kN at the middle point as shown in the following figure. If the basic parameters for the beam are E=200GPa, I=15*106mm4 , please calculate the maximum deflection.

Hint: Δ=PL3 /(48EI)       4 Marks

Figure for question 1(c)

d) Please give the K values for columns with different end conditions, when calculating the effective length Le=K*L in a buckling analysis.      4 Marks

e) If one point is subjected to two direction normal stresses and shear stress as shown in the figure below, please calculate the principle stresses for the point.

Hint:              4 marks

Stress state for one point

Question 2. (36 Marks)

The simply supported beam “ABCD” with overhanging end is subjected to one point load P=10kN and uniformly distributed load q=5kN/m as shown in Figure 2a.

Figure 2a : Beam ABCD (unit: kN, m)

Figure 2b : Cross section for beam ABCD (unit: mm)

(1) Please draw shear force diagram (SFD) and bending moment diagram (BMD) for beam “ABCD”.        16 marks

(2) The cross section of the beam is a T section as shown in figure 2b, where x-x axis is the neutral axis (centroidal axis), Ix-x=2.34*106 mm4 . Please calculate the maximum compressive stress and maximum tensile stress in the beam. (Hint: you need do the calculation for both B and C sections; σ=M*y/I).         12 marks

(3) Please calculate the maximum shear stress in the beam and indicate the maximum shear stress points. (hint: τ=V*Q/(I*t) where Q =A’*y’ )            8marks

Question 3. (26 marks)

A truss structure ABC is supported at “A” and “C” points by pinned supporters. Rod AB and BC have the same diameter of 60mm. The material parameters for the steel rods are: E=200 000MPa, allowable compressive/tensile stress σallow=200MPa. A concentrated load P in horizontal direction is acting at B point.

(1) Please determine the normal forces in rods AB and BC in terms of P. And indicate which member in tension, which member in compression.          10 marks

(2) Considering rod ends A, B, C as pin joints, please calculate the critical load for the compressive member in the truss structure (Hint: Pcr=π2*E*I/Le 2 , Le=k*L, I=π*d4 /64. If you are not sure which member is in compression, you can do the critical load calculation for both members “AB” and “BC” without losing marks in this part)        10 marks

(3) Please determine the maximum load P can be applied on the structure.       6 marks

Figure for Question 3

Question 4. (18 marks)

A steel post is subjected to a concentrated load P=60 kN acting at the middle point of the right edge as shown in the following figure.

Figure for question 4

Ignoring the self weight of the steel post

(1) Please calculate bending moments and axial force acting at section “A” (the fixed end) of the steel post.      8 Marks

(2) If the post has a square hollow section (SHS 200*200*5) with width 200mm and thickness 5mm, please calculate the maximum compressive stress at section “A”.             10 marks