Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Textbook Question
Chapter 5, Problem 54P
For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.
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The beam is supported by a roller at B and a pin at C and is subjected to the distributed load shown with
intensity w = 180 N/m. The maximum positive and negative internal bending moments are critical factors
in the design of the beam material and geometry. Determine the largest positive and negative internal
bending moments that occur in the beam and the points along the length where each occurs. Take z = 0
to be at point A at the left edge of the beam.
cc 1❀0
BY NC SA
2016 Eric Davishahl
a
X
b
-a-
4.00 m
5.20 m
B
Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.
Variable Value
The maximum negative internal bending moment is
and occurs at z =|
m to the right of A.
The maximum positive internal bending moment is
and occurs at x =
W
m to the right of A.
·b-
N-m
N-m
The bending moment diagram is constant for an interval of a beam then the crossponding shear force diagram
is an inclined straight line.
A curved line.
A line parallel to the axis.
A zero line
Start with the shear diagram. To use a segment of the left end of the beam to develop the expression for the shear, the vertical reaction at A must be known. Calculate the vertical reaction at A. Let a positive force act up.
Write an expression for the internal shear for an arbitrary point between A and B.
Write an expression for the internal shear for an arbitrary point between B and C.
Draw the shear diagram for the beam.
Write an expression for the bending moment at an arbitrary point between A and B. Use the standard sign convention for the internal moment for a beam.
Write an expression for the bending moment at an arbitrary point between B and C.
Draw the moment diagram for the beam.
Chapter 5 Solutions
Structural Analysis
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Draw the shear and bending moment diagrams for the...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71P
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- be L.A prismatic beam fixed at both ends carries a uniformly distributed load. The ratio of bending moment at supports to bending moment at midspan isarrow_forwardIn the structures shown below all members have the same Young's Modulus, E, second moment of area, I, and cross sectional area, A. (a) Calculate the vertical deflection of the point load in the structure shown below. L A L (b) Using the principle of virtual work, calculate the internal forces in all the members in the structure shown below L A в (c) State all the assumptions. Barrow_forwardNonearrow_forward
- Figure Q2(a) shows a cantilever beam that is subjected to a pure bending moment M = 3kN.m about the neutral axis (N.A) and the cross-section of a beam is shown in Figure Q2(b). Determine: (a) The moment of inertia about the neutral axis, InA. (b) The bending stress acting at point B and state whether it is in tension or compression. (c) The bending stress acting at point C (d) The maximum bending stress in the beam. M Figure Q2 (a) 20 mm B 150 mm C N 20 mm 150 mm 20 mm 250 mm Figure Q2 (b)arrow_forwardFor the beam shown, how does the shear change as you move from A to B? L- Select the correct response: There is not enough information to tell. It stays constant. It decreases linearly. It increases linearlyarrow_forwardfind the bearing reaction forces of the beam in the figure by the singularity methodarrow_forward
- Problem 2: For the beam given below: (a) Calculate all support reactions. (b) Draw the shear diagram. Show all important values of shear. Show the sign convention within each region. (c) Draw the moment diagram. Show all important values of moment. Show the sign conventions within each region (concavity: smiley face, sad face, etc.) (d) Sketch the deflected shape. Show supports in your sketch. For your solution, let w = 2 kips/ft and L = 20 ft. A L 22 B L W Carrow_forwardIn the restrained beam shown, solve for the following a. end moments b. max deflection 15KN imarrow_forwardDetermine all the reactions at the support of the three-span continuous beam shown in the figure. Take flexural rigidity EI as constant. Horizontal Reaction at fixed support A, Ax, is zero. Draw the shear force and bending moment diagrams. Using the Method of Consistent Deformations. Solve the moment reaction at A (MA in kN-m), vertical reaction at A (Ay), B (By), C (Cy), D (Dy) (in kN)arrow_forward
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