a) Draw the approximate deflected shape from the bending moment diagram. b) Develop the piecewise functions of θ(x) and v(x) using double integration. Assume EI is constant. Take x to be references from the farthest left point on the beam similar to the method used in class. c) If w = 2 k/ft and L = 5 ft, locate the point of maximum deflection between supports A and B. d) Develop a variable based excel program that allows you to plot both the slope and displacement functions with x. In other words, your program should be able to take any value of w, L, E, I and x and automatically calculate deflection and slope. Print x-y scatter plots connected by smooth lines for both the deflection and slope using values of x ranging from 0 to 2L in increments of 0.5 ft. Plot the displacement in inches and slope in radians for the following cases using your program: i) w = 2 k/ft, L = 5 ft, E = 4,176,000 ksf, I = 0.073784 ft4 ii) w = 10 k/ft, L = 6 ft, E = 4,176,000 ksf, I = 0.073784 ft4 Along with the two plots for each case, output the displacements and slopes for each value of x similar to the table shown.
a) Draw the approximate deflected shape from the bending moment diagram. b) Develop the piecewise functions of θ(x) and v(x) using double integration. Assume EI is constant. Take x to be references from the farthest left point on the beam similar to the method used in class. c) If w = 2 k/ft and L = 5 ft, locate the point of maximum deflection between supports A and B. d) Develop a variable based excel program that allows you to plot both the slope and displacement functions with x. In other words, your program should be able to take any value of w, L, E, I and x and automatically calculate deflection and slope. Print x-y scatter plots connected by smooth lines for both the deflection and slope using values of x ranging from 0 to 2L in increments of 0.5 ft. Plot the displacement in inches and slope in radians for the following cases using your program: i) w = 2 k/ft, L = 5 ft, E = 4,176,000 ksf, I = 0.073784 ft4 ii) w = 10 k/ft, L = 6 ft, E = 4,176,000 ksf, I = 0.073784 ft4 Along with the two plots for each case, output the displacements and slopes for each value of x similar to the table shown.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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a) Draw the approximate deflected shape from the bending moment diagram.
b) Develop the piecewise functions of θ(x) and v(x) using double integration. Assume EI is constant. Take x to be references from the farthest left point on the beam similar to the method used in class.
c) If w = 2 k/ft and L = 5 ft, locate the point of maximum deflection between supports A and B.
d) Develop a variable based excel program that allows you to plot both the slope and displacement functions with x. In other words, your program should be able to take any value of w, L, E, I and x and automatically calculate deflection and slope. Print x-y scatter plots connected by smooth lines for both the deflection and slope using values of x ranging from 0 to
2L in increments of 0.5 ft. Plot the displacement in inches and slope in
radians for the following cases using your program:
i) w = 2 k/ft, L = 5 ft, E = 4,176,000 ksf, I = 0.073784 ft4
ii) w = 10 k/ft, L = 6 ft, E = 4,176,000 ksf, I = 0.073784 ft4
Along with the two plots for each case, output the displacements and slopes for each value of x similar to the table shown.
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