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 4.3.16P
Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0and beam length variable L. Repeat for beam (b) but at x = L/2.
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Find expressions for shear force V and moment M at x = L/2 of beam AB in structure (a). Express V
and M in terms of peak load intensity go and beam length variable L. Repeat for structure (b) but find
V and M at the mid-span of member BC.
A
A
L/2
V. M at L/2
on AB
L/2
[/2
B
Structure (a)
L/2
B
90
Structure (b)
90
V, Mat
mid-span
of BC
4L/5
4
4L/5
0000
Bridges are usually modeled as simply supported beams. Your role in a building and construction
company is to analyse and design the bridge based on simply supported beam theory. Your manager
asked you to perform a stress analysis for bridge element modelled as simply supported beam shown in
the Figure.1(a), this task is best achieved by performing the following required steps:
2 kN
3 kN/m
3 kN/m
3kN.m
A
0.5 kN
4.5 kN
kN
2 m
1 т+1m-
2 m
R|
-2 m
(а)
(b)
Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section
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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- 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)arrow_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_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 answer do not image formatarrow_forwardusing MATLABarrow_forwardFor 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_forward
- 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.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_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
- For the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. 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. Answers: Ay = Dy= Mi i B Calculate the reaction forces Ay 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 Ax = 0, it has been omitted from the free-body diagram.) PB a PB B a Pc a Pc C kN b KN b D X D₂ Xarrow_forward1- 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_forwardFor the beam illustrated in the figure, find the locations and magnitudes of the maximum tensile bending stress due to M and the maximum shear stress due to V. Parameters are a = 310 mm, b= 135 mm, c = 20 mm, h = 40 mm, and F= 4350 N. a mm FN bmm The moment of inertia is C mm hmm |x105 mm4. The maximum tensile bending stress due to Mis The maximum shear stress due to Vis MPa. MPa.arrow_forward
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