Answered: | A Wa a ! B w. b C x

Engineering

Mechanical Engineering

| A Wa a ! B w. b C x

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter4: Shear Forces And Bending Moments

Section: Chapter Questions

Problem 4.3.17P: Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load...

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A counterclockwise moment M0acts at the midpoint of a fixed-end beam ACB of length L (see figure). Beginning with the second-order differential equation of the deflection curve (the bendingmoment equation), determine all reactions of the beam and obtain the equation of the deflection curve for the left-hand half of the beam. Then construct the shear-force and bending-moment diagrams for the entire beam, labeling all critical ordinales. Also, draw the deflection curve for the entire beam.
A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
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A beam ABCD with a vertical arm CE is supported as a simple beam at .1 and D (see figure). A cable passes over a small pulley that is attached to the arm at E. One end of the cable is attached to the beam at point B. The tensile force in the cable is 1800 lb. Draw the shear-Force and bending-moment diagrams for beam A BCD. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations. Repeat part (a) if a roller support is added at C and a shear release is inserted just left of C (see figure part b).
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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=2.75 m, b=5.00 m, PB = 60KN, 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. Answers: Ay = Dy= tel tel a i B a 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 B a PB Pc a C Pc C KN b KN D b D X D₂ X
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 X
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. Answers: Ay= Dy = a M. B a PB 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 Pc a Pc kN b KN D b D X D X
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 Dy
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=8.5 ft, b=24.0 ft, P = 30 kips and w = 5.5 kips/ft. 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.Calculate the reaction forces Ay and Cy 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.) Determine the shear force acting at each of the following locations:(a) x = 8.5- ft (i.e., just to the left of point B)(b) x = 8.5+ ft (i.e., just to the right of point B)(c) x = 30.5 ftNote that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. Determine the bending moment acting at each of…
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=2.75 m, b=5.00 m, PB = 60kN, 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. Answers: Ay = a Dy= a 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.) 36.66 BO 103.33 PB a PB Pc a Pc KN b KN b D D x P X
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=6.5 ft, b=24.0 ft, P = 32 kips and w = 9.5 kips/ft. 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. Calculate the reaction forces Ay and Cy 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.) 2.Determine the shear force acting at each of the following locations: (in kips)(a) x = 6.5- ft (i.e., just to the left of point B)(b) x = 6.5+ ft (i.e., just to the right of point B)(c) x = 28.5 ft 3.Determine the bending moment acting at each of the following locations: (in kips-ft)(a) x = 6.5 ft (i.e., at point B)(b) x = 28.5 ft 4.Use your…