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of the ment I shear, sections I5 KN ple ethod. In ontinuities ents are an the beam, es 5 AN 10 AN ree v(AN) No elements selected 10 nly valid M (KN - m) 80 2) and the 40 een (m) To 20 ned Press TAB to navigate between elements on the canvas. Press ALT) to get to the main menu. Press ALTA to modify the attributes. Press ALT- to quit the application. m, and < 1 of 4 Previous Answers ResutstAnseer Submit X Incorrect; Try Again; 2 attempts remaining

of the ment I shear, sections I5 KN ple ethod. In ontinuities ents are an the beam, es 5 AN 10 AN ree v(AN) No elements selected 10 nly valid M (KN - m) 80 2) and the 40 een (m) To 20 ned Press TAB to navigate between elements on the canvas. Press ALT) to get to the main menu. Press ALTA to modify the attributes. Press ALT- to quit the application. m, and < 1 of 4 Previous Answers ResutstAnseer Submit X Incorrect; Try Again; 2 attempts remaining

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Learning Goal: To use the method of sections to derive functions for V and M (in terms of the location on the beam) and use those functions to draw the shear and moment diagrams. The design of a beam requires knowledge of the variations in the internal shear, V, and bending moment, M, along the axis of the beam. The method of sections could be applied to hundreds of points along the beam to find a reasonable approximation for V and M for each point. However, there is a better method. In general, the internal shear and bending moment functions will have discontinuities in their value or slopes only at points where concentrated forces or moments are applied or a distributed load has a discontinuity in value or slope. If we can determine the functions for V and M as a function of z, the location on the beam, 15 kN 5 kN 10 kN then we have the function for that entire section between the discontinuities. 5 For example, the simply-supported beam shown in (Figure 1) requires three coordinates, z1, T2, and z3, as shown in (Figure 2). V (KN ) No elements selected Note that coordinate z, is only valid for points on the beam 0 < I < a, coordinate r2 is only valid for points a <I<b, and coordinate I3 is only valid for points b< rSL. -10 M (kN - m) 80- The following procedure can be used to find the functions V(r) and M(r) and draw the shear and bending-moment diagrams. 60 • Determine the reactions, forces and moments, at the supports Resolve the forces into components parallel and perpendicular to the axis of the beam. • Specify separate coordinates for each segment of the beam between points where point forces, couple moments, and/or changes in distributed loads occur. • Section the beam at each I; chosen in the previous step and use the method of sections to find V(r) and M(r) for that segment. To avoid confusion, always draw V and M in their positive sense according to the sign convention as shown in (Figure 3). • Plot the functions V(r) and M(r), each on its own coordinate system. • Generally, the free-body diagram, shear diagram, and bending- moment diagram are drawn together, arranged vertically, and aligned and drawn to scale so that the ends of the beam and the points of discontinuity are aligned. 40+ 20 I (m) -20 -40 -60 - -80 In the simply-supported beam shown in (Figure 4), di = 14 m, d2 = 7 m, and F = 15 kN. Press TAB to navigate between elements on the canvas. Press ALT+M to get to the main menu. Press ALT+A to modify the attributes. Press ALT+Q to quit the application. Figure < 1 of 4 > Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining
Transcribed Image Text:Learning Goal: To use the method of sections to derive functions for V and M (in terms of the location on the beam) and use those functions to draw the shear and moment diagrams. The design of a beam requires knowledge of the variations in the internal shear, V, and bending moment, M, along the axis of the beam. The method of sections could be applied to hundreds of points along the beam to find a reasonable approximation for V and M for each point. However, there is a better method. In general, the internal shear and bending moment functions will have discontinuities in their value or slopes only at points where concentrated forces or moments are applied or a distributed load has a discontinuity in value or slope. If we can determine the functions for V and M as a function of z, the location on the beam, 15 kN 5 kN 10 kN then we have the function for that entire section between the discontinuities. 5 For example, the simply-supported beam shown in (Figure 1) requires three coordinates, z1, T2, and z3, as shown in (Figure 2). V (KN ) No elements selected Note that coordinate z, is only valid for points on the beam 0 < I < a, coordinate r2 is only valid for points a <I<b, and coordinate I3 is only valid for points b< rSL. -10 M (kN - m) 80- The following procedure can be used to find the functions V(r) and M(r) and draw the shear and bending-moment diagrams. 60 • Determine the reactions, forces and moments, at the supports Resolve the forces into components parallel and perpendicular to the axis of the beam. • Specify separate coordinates for each segment of the beam between points where point forces, couple moments, and/or changes in distributed loads occur. • Section the beam at each I; chosen in the previous step and use the method of sections to find V(r) and M(r) for that segment. To avoid confusion, always draw V and M in their positive sense according to the sign convention as shown in (Figure 3). • Plot the functions V(r) and M(r), each on its own coordinate system. • Generally, the free-body diagram, shear diagram, and bending- moment diagram are drawn together, arranged vertically, and aligned and drawn to scale so that the ends of the beam and the points of discontinuity are aligned. 40+ 20 I (m) -20 -40 -60 - -80 In the simply-supported beam shown in (Figure 4), di = 14 m, d2 = 7 m, and F = 15 kN. Press TAB to navigate between elements on the canvas. Press ALT+M to get to the main menu. Press ALT+A to modify the attributes. Press ALT+Q to quit the application. Figure < 1 of 4 > Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining
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