2000 Final Exam

# A draw the distribution of the internal torque along

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Unformatted text preview: ameter is 40 mm. (a) Draw the distribution of the internal torque along the length of the bar from A to D. (b) Obtain the maximum shear stress, τ max , and the maximum angle of twist, φ max , and indicate where they occur along the bar. 500 Nm A B 1m 1m 1000 Nm C Figure 2 1m 40 mm D Name: Signature: Student Number: Marks (%) (25) 3. A simply-supported beam ABCD with overhangs is subjected to a uniformly distributed load as shown in Figure 3. The cross-section of the beam has a box-shape made up of four wooden planks with dimensions: h × b nailed together as shown to form a built-up beam. (a) Draw the shear force and bending moment distribution diagrams for the beam (in terms of q and L), labeling all critical values including the maximum bending moment and maximum shear force. (b) Determine the maximum tensile and compressive bending stresses, σ tmax and σ c and the max maximum shear stress, τ max in the beam and indicate the coordinates of the points (i.e. x and y) where they occur. (c) Given that q = 2 kN/m , L = 1m , h = 200 mm, b = 20 mm and each nail has an allowable shear force of 750 N, calculate the maximum permissible longitudinal spacing smax of the nails. y q A C B L 4L D L Figure 3 y nail x z h b b h b Name: Signature: Student Number: Marks (%) (25) 4. A cantilever beam, ABC, has a fully fixed support at A and an elastic spring support at B. A concentrated force P acts at the free end C. Assume that the beam has a modulus of elasticity E, cross-sectional second moment of area I, and that the spring stiffness, k = EI /L3. (a) Using the method of superposition, determine the displacements and angles of rotation at B and C. (b)...
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## This document was uploaded on 04/09/2014.

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