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Determine quantitatively the influence lines for Ay, ME and VẸ for the statically determine system shown below. Also determine the maximum moment at E if there are two live loads of magnitude P each. These loads are separated by a distance of at least L/4. A В 3L/8 5L/8 L/5 4L/5

Determine quantitatively the influence lines for Ay, ME and VẸ for the statically determine system shown below. Also determine the maximum moment at E if there are two live loads of magnitude P each. These loads are separated by a distance of at least L/4. A В 3L/8 5L/8 L/5 4L/5

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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**Problem Statement:** Determine quantitatively the influence lines for \( A_y \), \( M_E \), and \( V_E \) for the statically determinate system shown below. Also, determine the maximum moment at E if there are two live loads of magnitude P each. These loads are separated by a distance of at least \( L/4 \). **Diagram Explanation:** The diagram shows a beam supported by different types of supports and labeled points along the beam. Here is a detailed description: - **Supports:** - Point A: A pin support (allows rotation but not translation). - Point B: A roller support (allows horizontal translation). - Point C: Another roller support. - Point D: A hinge (an internal hinge or moment release). - **Point E**: Located between points A and B. - **Loads**: - A concentrated vertical load is shown at point D with magnitude P. - **Segment Distances**: - Distance from A to E: \(3L/8\) - Distance from E to B: \(5L/8\) - Distance from B to D: \(L/5\) - Distance from D to C: \(4L/5\) The task involves deriving the influence lines for the vertical reaction at A (\(A_y\)), the bending moment at E (\(M_E\)), and the shear force at E (\(V_E\)). Additionally, the problem asks to calculate the maximum moment at E when two live loads are applied, with these loads being separated by a minimum distance of \(L/4\).
Transcribed Image Text:**Problem Statement:** Determine quantitatively the influence lines for \( A_y \), \( M_E \), and \( V_E \) for the statically determinate system shown below. Also, determine the maximum moment at E if there are two live loads of magnitude P each. These loads are separated by a distance of at least \( L/4 \). **Diagram Explanation:** The diagram shows a beam supported by different types of supports and labeled points along the beam. Here is a detailed description: - **Supports:** - Point A: A pin support (allows rotation but not translation). - Point B: A roller support (allows horizontal translation). - Point C: Another roller support. - Point D: A hinge (an internal hinge or moment release). - **Point E**: Located between points A and B. - **Loads**: - A concentrated vertical load is shown at point D with magnitude P. - **Segment Distances**: - Distance from A to E: \(3L/8\) - Distance from E to B: \(5L/8\) - Distance from B to D: \(L/5\) - Distance from D to C: \(4L/5\) The task involves deriving the influence lines for the vertical reaction at A (\(A_y\)), the bending moment at E (\(M_E\)), and the shear force at E (\(V_E\)). Additionally, the problem asks to calculate the maximum moment at E when two live loads are applied, with these loads being separated by a minimum distance of \(L/4\).
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