21.21 An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x² where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M is the bending moment. Integration yields the relationship M = M, + V dx If M, is zero and x = 11, calculate M using (a) analytical integration, (b) multiple-application trapezoidal rule, and (c) multiple-application Simpson's rules. For (b) and (c) use 1-m increments.

21.21 An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x² where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M is the bending moment. Integration yields the relationship M = M, + V dx If M, is zero and x = 11, calculate M using (a) analytical integration, (b) multiple-application trapezoidal rule, and (c) multiple-application Simpson's rules. For (b) and (c) use 1-m increments.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Matrix Algebra for Structural analysis

Structural analysis is a process in which the effects of different loads and internal forces, acting on structures and their elements are determined. This method of analysis is effective in detecting the failure loads of the structural elements and the design can be altered before commencing the construction process, which ensures proper strength and safety of the structures.

Question

21.21 An 11-m beam is subjected to a load, and the shear force
follows the equation
V(x) = 5 + 0.25x²
where V is the shear force and x is length in distance along the
beam. We know that V = dM/dx, and M is the bending moment.
Integration yields the relationship
M = M, +
V dx
If M, is zero and x = 11, calculate M using (a) analytical integration,
(b) multiple-application trapezoidal rule, and (c) multiple-application
Simpson's rules. For (b) and (c) use 1-m increments.

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Use discontinuity functions to develop the load function w(x) for the beam shown. Include the beam reactions in this expression. Integrate w(x) twice to determine V(x) and M(x), and use these functions to plot the shear-force and bending-moment diagrams on paper. Use these plots to answer the questions in the subsequent parts of this GO exercise. Let a = 2.75 m, b = 4.00 m, c=1.75 m, Wg = 20 kN/m and wc = 55 kN/m. WC WR b Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since A, = 0, it has been omitted from the free-body diagram.) WC y A B C A D |Dy Incorrect Use your shear-force equation V(x) to find the location where V= 0 between points B and C. Alternatively, note that the shear force at B in this case is known from Part 3. Recall that the change in the shear force between any two locations is equal to the area under the distributed-load curve…
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.250 m, b=6.50 m, PA = 60kN, and PC = 70kN. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise.
1)
Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN
For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at B and (b) the deflection of the beam at A. Assume a constant value of EI = 106000 kip·ft2 for the beam; w0 = 3.8 kips/ft, LAB = 6 ft, LBC = 3 ft.
AE = 2000 p= 7
ILLUSTRATE FREE BODY DIAGRAM. and show your complete solutions for better understanding.