(a) A beam is simply supported at its end supports A and B, and is subject to a mid-span point load F. Using the method of successive integration, determine an expression for the deflection of this beam. Calculate the maximum deflection. (b) The beam shown in Figure Q3b is simply supported at A and C, and is subject to the loading shown. Determine and plot the Shear Force Diagram and the Bending Moment Diagram for this beam. 25 kN/m UDL B 8m 8m Figure Q3b

(a) A beam is simply supported at its end supports A and B, and is subject to a mid-span point load F. Using the method of successive integration, determine an expression for the deflection of this beam. Calculate the maximum deflection. (b) The beam shown in Figure Q3b is simply supported at A and C, and is subject to the loading shown. Determine and plot the Shear Force Diagram and the Bending Moment Diagram for this beam. 25 kN/m UDL B 8m 8m Figure Q3b

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

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 maximum deflection, and (c) the slope at A. Assume that EI is constant for the beam. Let w = 14 kN/m, L = 4.5 m, E = 180 GPa, and I = 130 x 106 mm4. Part 1 Draw a free body diagram of the beam and solve the reaction forces Ay and By. Forces are positive upwards. Answer:Ay = kNBy = kN Part 2 Cut a cross-section through the beam at any point and draw a free body diagram. 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 = 2.3 m.Answer:M(x = 2.3 m) = kN·m
A cantilever beam AB is loaded as shown in Figure 1. EI is constant for the beam. L = 2.7 m and P = 8.9 kN. Write down your L and P values and answer parts a to c below. (a) Using the moment area method, determine the slope of the beam at B. (b) Using the conjugate beam method, determine vertical deflection at B. (c) Draw the free body diagram (FBD) of the virtual force system for the virtual work method to determine the vertical deflection at the mid-span of the beam. (Note: No calculations are required and show only the FBD).
A simply supported beam is consisting of two segments, segment AB is 5 m long while segment BC is 3 m long. If 20 kN/m uniformly distributed load is applied to the entire span of segment AB, determine the following: a. Maximum Slope of the beam using double integration method. b. Deflection at point B using moment area method. c. Maximum deflection of the beam using conjugate method.
Moment-Area Method A simply supported beam is loaded with a concentrated load and a uniformly distributed load as shown in the figure. Assume EI =90 x 10^6 lb-in^2. Please draw the moment diagram. Assume the fixed support is at B. a. Find the tangential deviation of B with respect to D b. Find the deflection of the beam at B.
For the beam and loading shown, integrate the load distribution to determine (a) the equation of the elastic curve, (b) the deflection at the left end of the beam, and (c) the support reactions By and MB. Assume that EI is constant for the beam. Let w0 = 11 kN/m, L = 3.5 m, E = 195 GPa, and I = 125 x 106 mm4.
EI is constant (Assume EI = 1 kN-m2). Solve using the conjugate-beam method. Determine the (a) maximum upward deflection and the (b) maximum downward deflection If moment diagrams are referred at A, what is the total upward load for the equivalent conjugate beam If moment diagrams are referred at B, what is the total upward load for the equivalent conjugate beam
For the loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, and (c) the slope at the free end. Assume that EI is constant for the beam. Let w = 8 kN/m, L = 3.0 m, E = 205 GPa, and I = 100 x 106 mm4. Cut a cross-section through the beam at any point and draw a free body diagram. 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 = 1.5 m.Answer:M(x = 1.5 m) = kN·m
The simply supported beam in the figure is loaded by the clockwise moment 10 kN-m at B. Draw the shear force and bending moment diagrams by area method. Neglect the weight of the beam.Show complete solution with FBD
1.) Assume that A is pin and C is roller. Determine the support reaction.2.) Use conjugate beam method and determine the deflection at B. Let w=1and L=9. Assume EI is constant.3.) Use conjugate beam method and determine the slope at A. Let w=1and L=9. Assume EI is constant.
Given the figure below. Use UNIT LOAD METHOD in determining the maximum deflection at midspan. E and I are constant. 1. What is the reaction at A of the real beam? 2. In constructing the virtual beam and determining the maximum deflection, where must be the 1-unit load be placed? 3. What is the reaction at the support of the virtual beam? 4. In solving the maximum deflection at midspan, how many portions or segments must the beam be divided so that the real and virtual loadings are continuous in each segment? 5. Consider segment AB of the real beam, with x measured from A, what is the moment equation M_(AB ) ? 6. In question 4, what are the limiting values of x? 7. Consider segment AB of the virtual beam, with x measured from A, what is the moment equation? 8. Analyzing segment BC of the real beam, with x measured from A, what is the moment equation M_BC? 9. In the given beam, if the 50 KN load is moved 2m closer to A and deflection at midspan is desired, how many segments must the…
Solve the following problem: The beam AB is subjected to the uniformly distributed load shown in the figure and to two unknown forces P and Q. If it is known that the experimental calculation of the value of the bending moment is 4.5 kip * ft at point D and 3.5 kip * ft at point E. a) Determine P and Q b) Draw the shear force and bending moment diagrams for the beam.
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, and (b) the deflection at B. Assume that EI is constant for the beam. Let w = 14 kN/m, L = 4.5 m, E = 215 GPa, and I = 125 x 106 mm4