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 ft. The frame is subjected to a concentrated load P at point Fas 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≤ x' ≤3, then translate the origin of the coordinate system to point A to get the final expression 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 2L 2 3 3 D A B C 080 F E Figure 2
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 ft. The frame is subjected to a concentrated load P at point Fas 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≤ x' ≤3, then translate the origin of the coordinate system to point A to get the final expression 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 2L 2 3 3 D A B C 080 F E Figure 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 ft. The frame is subjected to a concentrated load P at point Fas
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≤
x' ≤3, then translate the origin of the coordinate system to point A to get the final expression
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
2L
2
3
3
D
A
B
C
080
F
E
Figure 2
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