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- For the beam AB shown in Cases 1 and 2, derive and plot expressions for the shear force and bending moment acting on section 1 in terms of the distance x (0 < x< L). [Note: Case 1 results in the conventional V- and M-diagrams, in which the loads are fixed and the location of the section varies; the diagrams for Case 2 (called influence diagrams) show the variation of V and M at a fixed section as the location of the load is varied]Two beams (see figure) are loaded the same and have the same support conditions. However, the location of internal axial, shear, and moment releases is different for each beam (see figures). Which beam has the larger maximum moment?A simply supported beam ABC is loaded at the end of a bracket BDE (see figure). Draw axial-force, shear-force, and bending-moment diagrams for ABC.
- Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of the beam as shown in the figure.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.The three beams in the figure have the same loading. However, one has a moment release just to the left of C, the second has a shear release just to the right of C, and the third has an axial release just to the left of C. Which beam has the largest maximum moment? First, find support reactions; then plot axial force (N), shear ( V) and moment (M) diagrams for all three beams. Label all critical N, K, and M values and also the distance to points where N, K and loi M are zero.
- A propped cantilever beam of a length L is loaded by a concentrated moment M0at midpoint C Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam.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=4.00 m, b=5.25 m, c= 2.75 m, P = 36kN and M = 195kN-m. 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 Answers: Ay= Cy= b 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.) i i a M a B M B b kN 2 C KN C Cy C P с X PFor 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=11.0 ft, b-4.5 ft, c= 7.5 ft, w = 4 kips/ft and M = 250 kip-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. 27 W Ay a b 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.) W M a B M C b C C₂ C -X
- 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 xFor 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=12.0 ft, b=6.5 ft, c= 7.0 ft, w = 7 kips/ft and M = 230 kip-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 = 0+ ft (i.e., just to the right of support A)(b) x = 12.0 ft (i,e., at point B)(c) x = 18.5- ft (i.e., just to the left of the support C)(d) x = 18.5+ ft (i.e., just to the right of the support (C)(e) x = 24.5 ftNote that x = 0 at support A. Determine the bending…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=14.0 ft, b=3.0 ft, c= 7.0 ft, w = 9 kips/ft and M = 300 kip-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. " " Answers: Ay= Cy= b 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.) i W i a W M a B M B ес b kips kips с Cy с X с -X