An overhanging beam is loaded as indicated. In order to accommodate communication cables to be installed later the beam is manufactured with two circular channels running through its length. The beam has a weight of q = 300 N/m. Calculate (a) the value and position of the maximum bending moment and sketch the relevant bending moment and shear force diagrams, (b) the position of the neutral axis, and (c) the maximum compressive and tension stress in the beam due to the bending. 2m 3 KN 3m B Bm 1 KN 100 mm 100 mm 20 mm H 30 mm
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- A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?For the beam shown, the magnitude of the distributed load is wo = 11.8 kN/m and the beam length is L = 7.9 m. (a) derive equations for the shear force Vand the bending moment M for any location in the beam. Place the origin at point A. (b) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Use your diagrams to determine the maximum shear force and maximum bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. Wo A В L. Answer: Vmax = kN Mmax kN•mFor the beam shown, the magnitude of the distributed load is Wo = 10.4 kN/m and the beam length is L = 4.8 m. (a) derive equations for the shear force Vand the bending moment M for any location in the beam. Place the origin at point A. (b) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Use your diagrams to determine the maximum shear force and maximum bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. Wo A L Answer: Vmax = kN Mmax = kN•m Save for Later Attempts: 0 of 1 used Submit Answer
- 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=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 -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=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=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…
- wo = 9 kN/m, L = 5.5 m, E = 220 GPa, and I = 100 x 10° mm4. A Part 1 Cut a cross-section through the beam at any point and draw a free body diagram to the right of your cut. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for Mat x= 2.8 m. Wo M(x) L-x Answer: M(x = 2.8 m) = i kN-mFor 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 -XYour 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 x
- Consider an 8-m long simply supported T-beam with overhangs loaded as shown below. 200 mm w kN/m 50 mm 50 kN-m 50 kN-m 200 mm 2 m 4 m 2 m 50 mm 1. Determine the location of the neutral axis measured from the top of the beam and the moment of inertia (in mm4) of the section about its neutral axis. Draw the shear and bending moment diagrams. Annotate all relevant values and distances. Determine the magnitude of the maximum negative 2. moment. Determine the minimum allowable strength of the beam in tension and the minimum allowable strength of the beam in compression. 3. Determine the maximum allowable load, w (in kN/m), that can be applied pn the beam. 4. B.Draw the shear force and bending moment diagrams for the beam with loading shown below, P= 16 kN, w= 30 kN/m, M=40 kN.m. Also, state the maxmium shear force and bending moment in the text box. (Upload the diagrams showing all key values with units as well as neat and clear calculations) P kN P kN w kN/m M KN.m A 0.5 m 1 m 1 m- 1 m- -1 mDraw diagrams of shear force and bending moment for beam and loading shown. Calculate the maximum tensile and compressive stresses in the beam. X=407 N/m Y=2.21 m Z=51,4 mm