The beam shown in the figure has a roller support at A, a fixed support at C and an internal hinge at B. The lengths of segments AB and BC are a and b respectively. A uniformly distributed load, q, is applied between points B and C, and a concentrated load P acts at a distance a/2 from the support A. EI is constant. ←a/2. P Jag quly A B Figure 2: Beam with internal hinge Determine the expression for the elastic curve (v(x)) for segment BC using the method of superposition.

The figure shows an aluminum beam OB with rectangular cross section, pinned to the ground at one end and supported by a round steel rod with hooks formed on the ends. A load is applied as shown. Use superposition to determine the vertical deflection at point A. 2 in 6 in. where F-104 lbf -in dia. F -in thick 12 in -A 12 in B The vertical deflection at point A is .0706 × 10-3 in.

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A flanged wooden shape is used to support the loads shown on the beam. The dimensions of the shape are shown in the second figure. Assume LAB = 9 ft, LBc = 2 ft, LcD = 3 ft, LoE = 2 ft, Pc = 1920 Ib, PE = 2070 Ib, wAB = 810 Ib/ft, b1 = 8 in., b2= 2 in., b3= 6 in., dz = 2 in., d2= 11 in., d3= 2 in. Consider the entire 16-ft length of the beam and determine: (a) the maximum tension bending stress or at any location along the beam, and (b) the maximum compression bending stress oc at any location along the beam. PC PE WAB B |C D E LAB LBC LCD LDE b1 d |d2 - bz dz bz Answers: (a) or = i psi. (b) oc psi.

A built-in cantilever beam with a hollow rectangular cross-section is subjected to a uniformly distributed load as shown in Figure Q1 below. Which of the following statements best describes the shear force variation along the length, in the x direction, using the sign conventions provided in lectures? Figure Q1 O a ltis constant and positive throughout the length. Ob.it is constant and negative throughout the length. Ocit begins as a negative value and increases linearly to reach a positive value of the same magnitude. Od. None of the provided answers are correct. Oelt begins with a positive constant value for half the length, then suddenly decreases to a negative value, remaining constant for the remaining length. Of. It increases linearly from zero, then continues at a constant value before decreasing linearly to reach a value of zero again. Og It begins as a positive value and decreases linearly to reach a value of zero at the end of the length of the beam.

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Figure 2 shows a horizontal beam AB. It is pin-supported at end A and carrying a load Q at end B. The beam is supported at C by a pinned-end column. The column is a solid steel bar of square cross-section having length L and side dimension b = 60 mm. Based upon the critical load of the column, if the allowable load Q is given by 109 KN with the factor of safety n = 2.0 with respect to buckling, determine the length of the column. E = 200 GPa 2d Q Figure 2 (201

The frame shown in Figure 3.1 has internal pins at points B, C and D and is supported by a pin at point A and a roller at point E. The loading consists of two concentrated loads and a point moment, as shown in the figure. a) Calculate the support reactions at points A and E. A 6 in. B -9 -9 in. →✦9 in. →✦9 in. →| 500 lb 700 lb ←9 in. D E Figure 3.1 - Compound Frame 2 kip-in 12 in. 12 in.

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