7.6 (rotation at A and deflection mid span ). Double integration method The image features a beam labeled AB, supported at two points. The left end of the beam is labeled A, supported by a roller, and the right end is labeled B, supported by a pin. A downward force, labeled P, is applied at a point between the supports.Key Measurements:- The total length of the beam is L.- The distance from end A to the point of force application is 2L/3.- The distance from the point of force application to end B is L/3.- An additional variable x is marked from the leftmost end A.The diagram represents a statically determinate beam with asymmetric loading. It illustrates how forces might be applied and is useful for understanding concepts in mechanics, such as moments and reactions at supports. This configuration allows the analysis of bending moments and shear forces within the beam. The figure is labeled P7.6.

A simply supported beam is loaded with a point load at a distance of 2L/3 from A.Using the double…

Answered: (rotation at A and deflection mid span…

Engineering

Civil Engineering

(rotation at A and deflection mid span ). Double integration method

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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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

7.6 (rotation at A and deflection mid span ). Double integration method

The image features a beam labeled AB, supported at two points. The left end of the beam is labeled A, supported by a roller, and the right end is labeled B, supported by a pin. A downward force, labeled P, is applied at a point between the supports.

Key Measurements:
- The total length of the beam is L.
- The distance from end A to the point of force application is 2L/3.
- The distance from the point of force application to end B is L/3.
- An additional variable x is marked from the leftmost end A.

The diagram represents a statically determinate beam with asymmetric loading. It illustrates how forces might be applied and is useful for understanding concepts in mechanics, such as moments and reactions at supports. This configuration allows the analysis of bending moments and shear forces within the beam.

The figure is labeled P7.6.

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For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at C (positive if counterclockwise and negative if clockwise). (b) the deflection of the beam at C. Assume LAB = 210 mm, LBc = 150 mm, LCD = 120 mm, LpE = 260 mm, Mg = 130 N-m, P = 550 N and a constant value of El = 490 x 106 N- mm2 for the beam. MB C E LAB LBC LcD LpE Answers: rad (a) Oc mm (b) vc =