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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

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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
Transcribed Image Text: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
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