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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 4.3.18P
Find expressions for shear force V and moment M at x = x0of beam AB in terms of peak load intensity q0and beam length variable L. Let x0= L/2.
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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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- 6. Q1: For the beam Shown in Figure 1 (40 Points) 8kN/m 3kN/m 8kN/m 1. Find the reaction at support B RBy, the bending moment at B, and the bending moment at C. B- A 2. Draw the shear force and bending 3m 2m 2m 3m moment diagram for the beam. Figure 1 Q2: (30 Points) For the simply supported beam with loading and cross section shown in Figure 2, determine the following: 1. The location of the centroid measured 10 kN 10 kN 100 from the top fiber in (mm). 2. The moment of inertia about the 50 centroidal x axis (mm“) 3. The maximum compressive stress in 0.6m 0.6 m 0.6 m 30 30 60 30, (MPa) 4. The maximum shear stress at the neutral axis in (MPa) All cross-section 5. The average shear stress on the section dimensions in mm (MPа) If the allowable stress in tension, compression, and shear are 4 MPa, 18 MP, and 12 MPa respectively. is this Figure 2 beam safe?arrow_forwardConsider the beam in the picture below: 7kN/m 5kN/m P N/m Section 1 Section 2 Section 3 - L/3 L/3 L/3 %3D Take P = the last four digits of your student number in N/m. If P<250 N/m then take P = 30OON/m instead. Take L = the third digit of your student number, reading left to reight. If this value is zero then take L = 2 Assume: The reaction at the Pin = V pin 47000L+9PL )N 54 The reaction at the Roller = Vroller = 61000L+9PL 54 and that both reactions act vertically upwards. a) Find an expression for the internal moment for Section 1. Show all working and any relevant free body diagrams. b) What is the maximum magnitude of the internal moment for Section 1? Mark sure you prove that the value you calculate is the maximum. c) Find an expression for the internal moment for Section 2. Show all working and any relevant free body diagrams. d) What is the maximum magnitude of the internal moment for Section 2? Mark sure you prove that the value you calculate is the maximum. e) Find an…arrow_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
- Please answer neatlyarrow_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_forwardFor the beam shown, derive the expressions for shear and moment. Show complete solutions. Simplify all equations. Then draw the shear force and bending moment diagrams below the load diagram. Draw to scale. 1. Shear and Moment Diagram: 18 kN/m 25 kN-m A E |C ImIm - 2 m 3 m· Shear Equation Moment Equation Segment AB Segment BC Segment CD Segment DE Point of Zero Shear: Moment at point of zero shear:arrow_forward
- The beam shown where L1= L2= L3=0.5 m. is subjected to a uniform distributed load of w=50 N/m and a concentrated load of P=100 N. The shear (V) and bending moment (M) diagrams for the beam are shown. Find the following: The reaction force at A is The reaction force at B is The shear force between C and D is The bending moment at C is The bending moment at D is W L1 N. Type your choice in the blank: 54.2 59.6 65.6 72.1 79.4 N. Type your choice in the blank: 58.5 64.4 70.8 77.9 85.7 N. Type your choice in the blank: 26.5 29.2 32.1 35.3 38.9 N-m. Type your choice in the blank: 17.2 18.9 20.8 22.9 25.2 N-m. Type your choice in the blank: 32.2 35.4 38.9 42.8 47.1 P L2 D L3arrow_forwardUse the graphical method to construct the shearforceand bending-moment diagrams for the beams shown in Figurebelow. Label all significant points on each diagram, andidentify the maximum moments (both positive and negative) alongwith their respective locations. Clearly differentiate straight-lineand curved portions of the diagrams.arrow_forwardThe simply supported beam is subjected to the force F = 700 N and the uniform distributed load with intensity w = 150 N/m. Draw the shear force and bending moment diagrams (in your homework documentation) and determine the equations for V(r) and M(x). Take a = 0 at point A. 19 F a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 5.2 m 2.6 m 3.12 m Support Reactions The reaction at A is N. The reaction at D is N. Shear Force and Bending Moment Equations In section AB: V(x)= N and M(x)= N-m. In section BC: v(x)- N and M(x)= N-m. In section CD: V(x)- N and M(x)= N-m. Aarrow_forward
- 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-3.25 m, b=4.75 m, Pg - 35kN, and Pc = 80kN. 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. A Ay- 58.66 - Dy- 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 Ax = 0, it has been omitted from the free-body diagram.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x Dyarrow_forwardConsider the beam in the picture below: 7kN/m 5kN/m P N/m Section 1 Section 2 Section 3 - L/3 L/3 L/3 Take P = the last four digits of your student number in N/m. If P<250 N/m then take P = 30OON/m instead. Take L = the third digit of your student number, reading left to reight. If this value is zero then take L = 2 Assume: The reaction at the Pin = Vnin 47000L+9PL )N %3D 54 The reaction at the Roller = Vroller = 61000L+9PL 54 N and that both reactions act vertically upwards. a) Find an expression for the internal moment for Section 1. Show all working and any relevant free body diagrams. b) What is the maximum magnitude of the internal moment for Section 1? Mark sure you prove that the value you calculate is the maximum. c) Find an expression for the internal moment for Section 2. Show all working and any relevant free body diagrams. d) What is the maximum magnitude of the internal moment for Section 2? Mark sure you prove that the value you calculate is the maximum. e) Find an…arrow_forwardGiven the beam shown below (E=200GPa, I=180x106 mm4, 80mmx300mm), do the following: a. Draw the shear force and bending moment diagrams b. Find the magnitude and location of the maximum tensile bending stress c. Using superposition, find the elastic curve and then the deflection of the beam at B, C, and D 8kN 4kN A B 4m 3m 3marrow_forward
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