A frame consisting of a simple span BD, an overhang AB, and a bracket CEF, is supported by a pin at B and a roller at D (see Figure 2). The beam ABCD has a uniform cross section with a moment of inertia I = 0.00025 ft¼. The frame is subjected to a concentrated load P at point F as shown in the figure. Take E 32,000 ksi, L 12 ft, a = 6 ft, and P = 900 lb. = = a) Draw the shear force and bending moment diagrams of the horizontal section ABCD using the graphical method. (Hint: use the method of sections to study CEF first) b) Using the method of superposition, find an expression for the elastic curve v(x) of the segment BC. x is a horizontal coordinate measured from point of A. (Hint: select appropriate cases from the table shown below and use superposition to find v(x') for 0 ≤ L x' ≤½, then translate the origin of the coordinate system to point A to get the final expression 3' in terms of x). c) Using the method of integration, find expressions for the elastic curve v(x) of the segments AB and CD. x is a horizontal coordinate measure from point of A. d) Plot the elastic curve for the horizontal section ABCD using appropriate computer software. L L 2 3 A B C E F P 17 Figure 2 2L 3 D

A frame consisting of a simple span BD, an overhang AB, and a bracket CEF, is supported by a pin at B and a roller at D (see Figure 2). The beam ABCD has a uniform cross section with a moment of inertia I = 0.00025 ft¼. The frame is subjected to a concentrated load P at point F as shown in the figure. Take E 32,000 ksi, L 12 ft, a = 6 ft, and P = 900 lb. = = a) Draw the shear force and bending moment diagrams of the horizontal section ABCD using the graphical method. (Hint: use the method of sections to study CEF first) b) Using the method of superposition, find an expression for the elastic curve v(x) of the segment BC. x is a horizontal coordinate measured from point of A. (Hint: select appropriate cases from the table shown below and use superposition to find v(x') for 0 ≤ L x' ≤½, then translate the origin of the coordinate system to point A to get the final expression 3' in terms of x). c) Using the method of integration, find expressions for the elastic curve v(x) of the segments AB and CD. x is a horizontal coordinate measure from point of A. d) Plot the elastic curve for the horizontal section ABCD using appropriate computer software. L L 2 3 A B C E F P 17 Figure 2 2L 3 D

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.3.9P: A simple beam thai is IS ft long supports a uni¬form load of intensity a. The beam is constructed of...

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