Sketch the graphs of the shear and bending- moment equations for the following situations, where the beam length is L and the point load force is P.
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Q: Find Out Shear and moment equations
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Q: Write shear and bending moment equation and draw it for beam loading as shown in Fig. below:
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- Your answer is partially correct. 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=2.50 m, b=4.25 m, Pg= 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= a 74.189 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.) Dy= i 59.21 B a PB a Pc KN Pc b KN D b D P xExample 5: Draw the shear force and bending moment diagrams for the simply supported beam as shown below. 400 N 500 N 300 N to A E 3m 4m 4m 5m(a) derive equations for the shear force V and the bending momentM for any location in the beam. (Place the origin at point A.)(b) use the derived functions to plot the shear-force and bendingmomentdiagrams for the beam.(c) specify the values for key points on the diagrams.
- 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 X1. The cantilever beam in Figure 1 is fixed at A, and is loaded with a distributed load from A to B and a concentrated moment at C. Use the GRAPHICAL METHOD to plot the shear force and bending moment diagrams for the entire length of the beam. Label values at all key locations on the plots (at changes in loads, maxima, minima, and zeroes). Annotate your diagrams to explain how they were drawn (e.g. "AQAB = (-12 kN/m)(1 m) = -12 kN" and "(dQ/dx)AB = -12 kN/m"). 12 kN/m 5 kNm ZA B D 1 m 0.5 m 0.5 m Figure 1.For the cantilever beam shown in the figure below, invoke the equilibrium of cut free-body sections of the beam to (a) write equations for the shear force and bending moment distributions as functions of x. Include a free-body diagram of each cut section and force and moment balance calculations. Examine the shear force and bending moment formulas and deduce the sign of the deformation within each inter- val. Include a sketch of a deformed material element that illustrates the shear and bending deformation within the interval. (b) Find the shear force of the largest magnitude in the beam and state where it occurs within the beam. (c) Find the bending moment of the largest magnitude in the beam and state where it occurs within the beam. 200 N/m 0.6 m- X 600 N 0.2 m 0.2 m
- Derive the equations for shear force and bending momentFor 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 DyA simply supported beam, 50mm wide by 100mm high and 300 mm long is subjected to a concentrated load of 3000 N at a point 100 mm from one of the supports. Draw the shear force and bending moment diagrams for the beam.
- Draw bending moment diagram for the loading shown in Figure Q15Solve the following questions: Plot the shear and moment diagrams for the beam loaded with both distributed and point loads. What is the value of the shear at x = 0 m?For the beam shown, (1) derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) (2) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Specify the values for key points on the diagrams. Let a = 5.9 ft, b = 7.5 ft, wa = 13 kips/ft, and w, = 5 kips/ft. Derive the equations and construct the shear-force and bending- moment diagrams on paper and use the results to answer the questions. Y || A Wa a (a) at x = 4.9 ft (b) at x = 7.9 ft B V = M = V = M = Wb b (c) Maximum bending moment Mmax = i i с ·X kips kip-ft kips kip-ft kip-ft