48331-Mo S-Assignment-3 2017-Summer-Solution-Assignment-rev PDF

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Assignment 3 – 48331 – Summer 2017 Question 1 (30 marks) The composite beam is made of steel (A) bonded to brass (B) and has the cross section shown in Figure 1. If the composite beam is subjected to a moment of M = 6 kN m, determine the maximum bending stress in the brass and steel. Also, what is t...

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Assignment 3 – 48331 – Summer 2017

Question 1

(30 marks)

The composite beam is made of steel (A) bonded to brass (B) and has the cross section shown in Figure 1. If the composite beam is subjected to a moment of M = 6.5 kN m, determine the maximum bending stress in the brass and steel. Also, what is the stress in each material at the seam where they are bonded together? The modulus of elasticity for steel, Est is 210 GPa. The modulus of elasticity for brass, Ebr is 105 GPa.

Figure 1 Question 2

(20 marks)

A simply supported beam of span length 3.2 m carries a uniform load of intensity 48 kN/m. The cross section of the beam is hollow box with wood flanges and steel side plates, as shown in Figure 2. The wood flange is are 75 mm by 100 mm in cross section, and the steel plates are 300 mm deep. Assume the moduli of elasticity for steel and wood are 210 GPa and 10 GPa, respectively, and disregard the weight of the beam. Determine the allowable required thickness t of the steel plates if the allowable stresses are 120 MPa for the steel and 6.5 MPa for the wood.

1

Figure 2 Question 3

(30 marks)

The beam is fabricated using a mild-strength steel which is assumed to be elastic-perfectly plastic. The beam is subjected to distributed load as shown in Figure 3(a). The cross section of beam is shown in Figure 3(b). Consider yield stress σy = 175 MPa. Determine the maximum intensity of the distributed load that can be applied to the beam when (i) yield first occurs. and (ii) top and bottom flanges have just become fully plastic.

Figure 3(a)

Figure 3(b) 2

Question 4

(20 marks)

A simply supported beam is subjected to uniformly distributed load (Figure 4a). The measured extreme fibre strains at the centre section a-a of beam are: -2800  10-6 at top and +2800  10-6 at bottom. The cross section of beam is shown in Figure 4(b). The beam is made of elasticperfectly plastic stress-strain curve as shown in Figure 4(c). Assume that the stress-strain diagram is same for both tension and compression. Determine the bending moment on the centre section a-a of beam.

Figure 4(a)

Figure 4(b)

σ 210 MPa

ε 0.0015 Figure 4(c) 3

Question 1 (30 out of 100)

Question 2 (20 out of 100)

Question 3 (30 marks out of 100)

Question 4 (20 out of 100)...