A rectangular element as shown in the figure is used to represent a pure bending problem. Due to the bending moment M, the element is deformed as shown in the figure with displacement {d} = {u1, v1, U2, V2, U3, V3, U4, V4} = {−1, 0, 1, 0, -1, 0, 1, 037. (a) Derive expressions of strain component Exx, Ɛyy, and xy, as functions of x and y based on the shape functions. (b) Does the element satisfy pure bending condition? Explain your answer. y M | A UA Из 4 (0,2) 3 (3,2) 1 (0,0) 2 (3,0) x B 12 UI

Nilo

Find the shear force and bending moment at points C and D. 500 lb 200 lb A Answer: Vc = -386 lbf Mc = -857 lbf.ft VD = 300 lbf Mp = -600 lbf.ft C² 6 ft4 ft 4 ft B 6 ft D 300 lb 2 ft E

The bending moment in a horizontally placed beam at distance x from one of the ends is given by the expression M = 13x - 3x - 12 . The shear force in the beam is zero at, O a. x = 7.12 O b.x = 3 and x = 1.33 O C. X = 2.16 O d. Need more data and a figure to solve the problem.

Q4

Determination of vertical displacement of Mid-Term Project pipe assembly Find the vertical displacement at position C in the figure. 800 mm Pipe inner diameter: 40 mm, Pipe outer diameter: 60 mm Material: A-36 Steel 600 N B. -By the force 600N, the AB part of the pipe is subjected to bending and torsional loads. BC part is subjected to bending load. -The energy equation by this load is as follows. Energy equation by torsional load: 400 mm T²dx (U), = 2GJ Problem: Energy equation by bending load a) First, draw a free body diagram and the AB part Of the bending/torsional load of the BC and Derive the bending load equation. So M²dx (U) = 2EI By applying it to the high energy formula, Save energy and make it the same as external energy Release to find the vertical displacement. -The sum of the internal energy of 2 energy is as follows. U=U: +Ub b) Creo modeling and structural analysis -Due to energy conservation, the sum of the internal energy U is the external due to the load 600 NGet the…

Problem: I+12 For the given compound curve (see figure): a. Determine R, and R2. b. Determine T, and T2. c. Determine C, and C2. d. Determine L, and L2. e. If the stationing of PC is at 10 + 304.62 m, determine the stationing of PCC and PT. T+T2 РСС Pl, I = 12° I = 15° Pl2 L2 T, PC6 (Sta PC = 10 + 304.62) PT Long chord = 300m I = 15° R2 R1 'O2 I = 12° R,

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Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W1 L/2 W2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 Axial force at point A (kN, tension positive): Displacement at point B (mm, positive to right): L/2 P1 P2 (type in your multiple choice answer, e.g. a, b, c or d) (type in your multiple choice answer, e.g. a, b, c or d)

Plot the Shear and Bending moment diagrams for the following. Use Singularity Functions to Solve the problem y 400 lbf Hinge | A B₁ AC R₂ R₁ 4 in 4 in 2 in 40 lbf/in 10 in D R3 X