Consider a square-faced beam | supporting a section of a building. a) d b) c) m2 lo lo d+Ad (a) Before installati the length the beam is found to be l, = 15.01 m (figure a). After installation and construction, the length is remeasured and found to be i = 14.92 m (figure b). Determine Young's Modulus Y in N/m2 for the beam if it supports a mass m = 31000 kg and has a side |length d= 1.1 m. Part (b) If we were to double the dimensions (length and width) of the beam, which of the following are correct. Part (c) Suppose that after the beam is installed it needs to be repaired. The weight it supports is removed and replaced with a new mass m2 (figure c). After the new mass is supported, the side length is remeasured and found to be larger with a difference of Ad. Assuming that this side length deformation is uniform and small, write an expression for determining Poisson's ratio v for this beam if its Young's modulus Y is known.

Calculate the bending moment at C to one decimal place (e.g. 35.0) Mc = Blank 1 kNm 20 KN + A B form 3.000 m с 2.000 m 25 kN/m 3.000 m 10 KN 11.000] E

A simply supported beam hinged at A and supported at C, is carrying a distributed load and a point load (see Fig. 1). The beam has a Young Modulus E = 80 GPa and a constant depth of 400 mm. The moment of inertia of the beam is limited to be I = 255 x 10-4 m*. 1. P- 120 KN 9 15 KN/m 4 (m) 2 (m) Figure 1 (a) (i) Write the bending moment expression using Macauley's method. (ii) Determine the bending moment at A. (ii) Determine the bending moment at B. (iv) Determine the bending moment at C. (v) Derive the deflection equation and find the value of the integration constants. (vi) Find the deflection at

3. The simply-supported beam shown below has the cross-sectional area shown in on the right. Draw shear and moment diagrams. Determine the max bending stress and max transverse shear in the beam. 6 m a) b) Tmax-bending= Tmax-transverse = 5kN/m 20 mm N 20 mm MPa MPa B 20 mm- C 250 mm 150 mm 150 mm D A

Consider the beam in the picture below: 7kN/m 5kN/m P N/m Section 1 Section 2 Section 3 - L/3 L/3 L/3 %3D Take P = the last four digits of your student number in N/m. If P<250 N/m then take P = 30OON/m instead. Take L = the third digit of your student number, reading left to reight. If this value is zero then take L = 2 Assume: The reaction at the Pin = V pin 47000L+9PL )N 54 The reaction at the Roller = Vroller = 61000L+9PL 54 and that both reactions act vertically upwards. a) Find an expression for the internal moment for Section 1. Show all working and any relevant free body diagrams. b) What is the maximum magnitude of the internal moment for Section 1? Mark sure you prove that the value you calculate is the maximum. c) Find an expression for the internal moment for Section 2. Show all working and any relevant free body diagrams. d) What is the maximum magnitude of the internal moment for Section 2? Mark sure you prove that the value you calculate is the maximum. e) Find an…

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The 10-ft long beam shown below is subjected to a uniformly-distributed load of w = 5 kip/ft. W L B a) What is the total magnitude of the force applied to the beam? b) If the distributed load were replaced with a single point force, where on the beam would it need to act in order for the beam supports to experience the same effect?

Draw bending moment diagram for the loading shown in Figure Q15

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