1) Determine the position a of the roller support B in terms of L so that the deflection at end C is the same as the maximum deflection of region AB of the overhang beam. EI is constant. Use the Moment Area method. A a Mo B 2) A propped cantilever beam of length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Let k = 6EI/L³. 90 -x A B L L

1) Determine the position a of the roller support B in terms of L so that the deflection at end C is the same as the maximum deflection of region AB of the overhang beam. EI is constant. Use the Moment Area method. A a Mo B 2) A propped cantilever beam of length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Let k = 6EI/L³. 90 -x A B L L

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.5.15P: Use the method of superposition to find the angles of rotation 9Aand SBat the supports, and the...

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-22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity q0acting over the left-hand half of the span (see figure). Also, determine the deflection cat the midpoint of the beam. Use the second-order differential equation of the deflection curve.
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that El is constant for the beam. Let Mo = 50KN-m, L= 4.5 m, E= 180 GPa, and I = 115x 106 mm4. Mo B Answer: (b) 0A = i rad (c) Og = i rad (d) vmid = i mm
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, and (c) the slope at the free end. Assume that EI is constant for the beam. Let w0 = 6 kN/m, L = 5.5 m, E = 195 GPa, and I = 140 x 106 mm4.
Learning Goal: To determine the support reactions in a statically indeterminate beam using the moment- area method. Part A - Support reaction force at B The beam shown has length L = 15.0 ft and is loaded with the applied moment M = 210 kip - ft at B. Assume EI is constant. (Figure 1) Using the moment-area method, determine the magnitude of the unknown support reaction at B due to the applied moment. Express your answer to three significant figures and include appropriate units. > View Available Hint(s) ? |By| = |10.5 kip Submit Previous Answers
4
Part A is already answered and correct please solve part B
A fixed-end beam of length Lis loaded by adistributed load in the form of a cosine curve with maximumintensity q0 at A. a)Use the fourth-order differential equation of the deflectioncurve to solve for reactions at A and B and also theequation of the deflection curve. b)Evaluatethe rotation at L/3 for L=2 m and q0=20 kN/m
Problem 2 (30 points): The formula for the deflection of the beam shown is: Wo y(x) = (-x5 + 5Lx-10L?x3 + 10L³x²) 120LEI Wo 15 x 107 N L = 2m %3D max m E = 7 × 1011 N m2 I = 6 x 10-4m Use the Newton-Raphson Method to determine the x location along the beam where the deflection is y(x) = 0.14 m. Use a starting guess of xo 1.2 m. Be sure to show your %3D calculation for the derivative of the function and your calculations you use to fill out the table. You only need to perform two iterations of the method, which means you should fill out the table below. Notice that y is defined as positive in the downward direction, which means that both the function and the target deflection are positive values in the coordinate system. y(xn) y'(xn) Xn+1 Step Xn 2.
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For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, and (c) the slope at the free end. Assume that El is constant for the beam. Let wo = 9 kN/m, L = 5.5 m, E = 220 GPa, and I = 100 x 10° mm“. |B L Part 1 Incorrect Cut a cross-section through the beam at any point and draw a free body diagram to the right of your cut. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for M at x = 2.8 m. Wo M(x) |B L-x Answer: M(x = 2.8 m) = i ! kN-m
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