Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 4.3.17P
Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0 and beam length variable L. Repeat for beam (b).
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A
16 kN/m
80 kN.m
C
75 kN
B
2 m
2m 1 m 2 m
5 m
El is constant all across the structure.
D
Use the Force Method to analyse the beam shown in the Figure
by introducing hinges and corresponding redundant bending
moments at points A, B, C. Plot the bending moment (M) and
shear force (V) diagrams for the loading shown.
A) Find X1 (see the similar example(s) of the note if you do not know what X1, X2 and X3 are) - XI is
associated with the unit moment at A.
B) Find X2. Note: X2 is associated with the unit moment at B.
C) Find X3. Note: X3 is associated with the unit moment at C.
D) Based on X1, X2, and X3: Find Ray (Vertical reaction at A).
E) Based on X1, X2, and X3: Find Roy (Vertical reaction at D)
and y vs. y (phase plot)
4. Consider the deflection v of the beam to the right. The beam is supported at each end and sags due to its own
weight (a distributed load q = 50 kN/m). The equation describing the deflection is
d'u
qx (x- L)
dx
2EI
where L=5.0 m, I = 0.0052 m* and E = 1.0x1010 Pa. Use the method
of your choosing (shooting or finite differences) to solve for: 1) the
slope at each end of the beam; 2) the maximum deflection; and
3) the location of maximum deflection.
using MATLAB
Chapter 4 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 4 - Calculate the shear force V and bending moment...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Calculate the shear force V and bending moment M...Ch. 4 - Consider the beam with an overhang shown in the...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - The beam ABCD shown in the figure has overhangs at...Ch. 4 - At a full d raw, an archer applies a pull of 130 N...Ch. 4 - A curved bar ABC is subjected to loads in the form...Ch. 4 - Under cruising conditions, the distributed load...
Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - A simply supported beam AB supports a trapezoid...Ch. 4 - Beam ABCD represents a reinforced-concrete...Ch. 4 - Find shear (V) and moment (M) at x = 3L/4 for the...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at A...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at D...Ch. 4 - Frame ABCD carries two concentrated loads (2P at T...Ch. 4 - Frame ABC has a moment release just left of joint...Ch. 4 - The simply supported beam ABCD is loaded by a...Ch. 4 - The centrifuge shown in the figure rotates in a...Ch. 4 - Draw the shear-Force and bending-moment diagrams...Ch. 4 - A simple beam AB is subjected to a counter...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The cantilever beam AB shown in the figure is...Ch. 4 - Cantilever beam AB carries an upward uniform load...Ch. 4 - The simple beam AB shown in the figure is...Ch. 4 - A simple beam AB subjected to couples M1and 3M2...Ch. 4 - A simply supported beam ABC is loaded by a...Ch. 4 - A simply supported beam ABC is loaded at the end...Ch. 4 - A beam ABC is simply supported at A and B and has...Ch. 4 - Beam ABCD is simply supported at B and C and has...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The simple beam AB supports a triangular load of...Ch. 4 - The beam AB shown in the figure supports a uniform...Ch. 4 - A cantilever beam AB supports a couple and a...Ch. 4 - The cantilever beam A B shown in the figure is...Ch. 4 - Beam ABC has simple supports at .A and B. an...Ch. 4 - Beam ABC with an overhang at one end supports a...Ch. 4 - Consider the two beams shown in the figures. Which...Ch. 4 - The three beams in the figure have the same...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - A simple beam AB is loaded by two segments of...Ch. 4 - Two beams (see figure) are loaded the same and...Ch. 4 - The beam A BCD shown in the figure has overhangs...Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - Beams ABC and CD are supported at A,C, and D and...Ch. 4 - The simple beam ACE shown in the figure is...Ch. 4 - A beam with simple supports is subjected to a...Ch. 4 - A beam of length L is designed to support a...Ch. 4 - The compound beam ABCDE shown in the figure...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The shear-force diagram for a simple beam is shown...Ch. 4 - The shear-force diagram for a beam is shown in the...Ch. 4 - A compound beam (see figure) has an internal...Ch. 4 - A compound beam (see figure) has an shear release...Ch. 4 - A simple beam AB supports two connected wheel...Ch. 4 - The inclined beam represents a ladder with the...Ch. 4 - Beam ABC is supported by a tie rod CD as shown....Ch. 4 - A plane frame (see figure) consists of column AB...Ch. 4 - The plane frame shown in the figure is part of an...
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- please answer do not image formatarrow_forwardFrom the given beam shown below, find the shear value at segment BC (VBC). 20kN 40KN 65kN/m H Ţ A k 2M 4m 4marrow_forward2. For the beam shown below, let w。 = 116 N/m, w₁ = 72 N/m, and P = 30 N. All dimensions are in m. b. c. d. e. 0 Wo W1 ΔΑ АВ I 1 2 3 4 5 6 7 8 Figure 1 Loaded Simply Supported Beam Find the reactions at A and B. Find the loading function q(x) using singularity functions. Find the shear and moment functions V(x) and M(x). P 9 m Determine and plot the shear diagram for the given loading conditions. Determine and plot the moment diagram.arrow_forward
- Please solve the below problem using FBDarrow_forwardFind expressions for shear force V andmoment M at x = x0 of beam AB in terms of peakload intensity q0 and beam length variable L.Let x0 = 2L/3.arrow_forwardThe beam shown below carries point and linearly distributed loads and is supported by a pin on the left and a roller on the right. Note that rollers can be assumed to react to either tensile or compressive loads. a) For each beam, draw all necessary free-body diagrams using the method of sections and find functions for the internal shear force (V(x)) and bending moment (M(x)) due to the external forces where x is a horizontal coordinate along the length of each beam, measured from the left end of each beam, as shown in the figure. Your expression(s) must allow to obtain internal reactions for 0≤x≤L, where L is the length of each beam. Make sure you use the numerical values of the reactions at the supports to get your expressions. Note that “k” stands for “kip” (1000 lbs) in the labels for the point loads and distributed loads. 6 k X -2'- 3'- 8 k/ft -3' 6 k/ftarrow_forward
- For simply supported beam below, find; Free body diagram and reaction forces Shear force value and bending moment value i. ii. ii. Shear force diagram and bending moment diagram iv. Maximum bending moment and its location 10KN 15kN/m В A D 3m 2m 2marrow_forward2. Draw shear force and bending moment diagrams for the beam shown in figure. 50 kN/m 20 kN/m 2 m 2 m - 2 m Ro Hello sir, please the same source as the question solution. 3. Relation between load, shear and moment: The free body diagram wdx :- %3! W (N/m) 严 of segment of this beam of length (dx) is shown M+4M but wdx is the summation of area between (x, and x2) in figure (2). V+av ..V, -V, = AV = (area) nad RI %3! similarly M2 (1) (2) ( dM = Vdx EF, =0= V +wdx-(V+dV)%3D0 w ------- Intensity of load (N/m) . dV =wdx M1 M, - M, = AM = (area ) hm %3! dx M, =0= M+Vdx + (wdx)-(M + dM) =0 shear AP . W =- (dr)? dx (slope of shear diagram) Where: :ero 2 .. dM Vdx dM :.V = dx (slope of moment diagram) for (dV = wdx ) we can integratingarrow_forwardProblem 6: Use element matrices potential energy formulations to solve the beam problem shown in Figure.5. Find nodal displacement values. Make sure to construct the grid information table and one-dimensional elements' line/mesh with appropriate labeling, numbering and displacement, loads nodal points. Steel: E = 14(105) N/cm² A = 20 cm? A = 14 cm? 35500 N ST=14°C 20000 N a = 11(10-6)/C 85 cm 85 -70 Figure.4: Beam under axial loadsarrow_forward
- 1- The below cantilever beam AB of length L= 3m carries a uniformly distributed load of intensity w = 6 kN/m. The beam has a square cross-section of a side length 20 cm., E = 200 GPa, and an elastic curve equation of: Wo (-x* + 4L°X- 3Lª) 24 Elv = Calculate the maximum displacement (Umax), the maximum bending moment Mmax, and the maximum stress õmax. Wo Вarrow_forwardplease write clearly and show all stepsarrow_forward2arrow_forward
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