Member BC is joined to the horizontal beam by a pin at B. Use the Castigliano's 2nd Theorem and f...
Q1. (45p) Use Castigliano's Theorem to find the vertical deflection at point B for the given member under the load of P. The member is fixed at A and free at the other end. 450 Divide the member in two sections AB and BC. Use the figures below if necessary BF a=45° Use the values below to compare the contribution of each component to total deflection. R = 75 mm, h = 30 mm, b = 15 mm. P =...
A beam ABC is loaded as shown in the fique and is supported by a pin at A and roller at B. The overnarding part of the beam is BC. find: a) egin of deflection curve between A and, B. and between B and C using and order integration method b) from part a, determine the value of deflection and slope at the roller. 'Hint (express in terms of E, I, Woor] c) construct a shear force and bending moment...
Question 1 (25 points) Determine the horizontal displacement of point C. Assume the members are pin connected at their ends. Take A = 400 mm? and E = 200 GPa for each member. 5 kN C 2 m 1.5 m 10 kN Member Foron N: Member forces due to external force P and external applied forces are shown on the figurt. Castigliano's Second Theorem : Applying Eq. 9-27, we have
A beam is supported by a pin at A and a roller B. It is loaded as shown. Determine the deflection at the midpoint (1/2) of the beam given the following: L = 17 ft M1 = 12 kip-ft M2 = 16 kip-ft E = 29,000 ksi 1 = 25 in i n Deflection at the midpoint (L/2) = Number Round answer to the nearest hundredth. Answer must include the proper sign (+/-).
Can someone help solve this using the unit load method. I am unsure how to do this for members that are not all the same AE, nor how to resolve the angles. Problem 2 The members AB and BC have the same cross-sectional area A and length L. They are pinned to rigid supports B and C. Find the horizontal and vertical deflection of A due to a horizontal load W then the moduli of elasticity are: i) E for...
The figure shows a rectangular member OB, made from ¼-in-thick aluminum plate, pinned to the ground at one end and supported by a 1/3-in-diameter round steel rod with hooks formed on the ends. A load of 80 lbf is applied as shown. Use Castigliano's Theorem to determine the vertical deflection at point C, midway between points A and B. Aluminum: E 10 Mpsi, Steel: E 30 Mpsi. L-in dia. lbf 12 in L-in thick 2 in -A 6 in 12...
Calculate the deflection and slope at B and the deflection at D for the uniform beam (Stiffness - EI). W kN/m V V V V V V V V V V L/2 Calculate the horizontal deflection of B and the relative rotation of the hinge at B in the frame ABC (member stiffness's shown). W = 2P/L kN/m 2L 4EI L/2 PKN
AB length is 4000mm AD length is 3000mm A pin jointed frame ABCD is supported by a pinned support at A, a roller at B and is subjected to the loading indicated in Figure Q1. All members have circular cross-section and all are made of steel materials with same cross-section. Determine the support reactions at A and B Determine all the member forces Find out the horizontal displacement at point C using a table template as shown in Table Q1....
2. Determine the vertical displacement at joint B and horizontal displacement at joint D using Castigliano's Second Theorem. The truss is pinned and roller at A and C, respectively. Use, E = 200 GPa and A = 2400 mm. E = 200 x 10°N/m². 20 KN 60 CAB 4 m 3m 3m
Young's modulus is E the expressions for deflections of points A and B due to the force F applied at the end of the step shaft that the I values for the 2 segments differ by a factor of -2.0), l-25 in, and F12 kip, evaluate the (2) The second area moments for sections AB and BC are hand 2/1, respectively. The material's (a) Treating all the symbols listed in the figure as knowns, use the Castigliano's method to determine...