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Question 3 continued. y w N/m B M L L/2 L/2 Fig. Q3-a Fig. Q3-b y, v w N/m M. Ro 7TTTTTT X,M Fig. Q3-c (**for all parts**) Fig. Q3-d Figure Q1: Beams with various loading and supports Please Note: Parts (b.) to (f.) of the question refer to Fig. Q1-c only!

Question 3 continued. y w N/m B M L L/2 L/2 Fig. Q3-a Fig. Q3-b y, v w N/m M. Ro 7TTTTTT X,M Fig. Q3-c (**for all parts**) Fig. Q3-d Figure Q1: Beams with various loading and supports Please Note: Parts (b.) to (f.) of the question refer to Fig. Q1-c only!

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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Question 3 continued. y w N/m M L/2 L/2 Fig. Q3-a Fig. Q3-b y, v w N/m P D M, Ro 7TTTTTT Fig. Q3-c (**for all parts**) Fig. Q3-d Figure Q1: Beams with various loading and supports Please Note: Parts (b.) to (f.) of the question refer to Fig. Q1-c only!
Transcribed Image Text:Question 3 continued. y w N/m M L/2 L/2 Fig. Q3-a Fig. Q3-b y, v w N/m P D M, Ro 7TTTTTT Fig. Q3-c (**for all parts**) Fig. Q3-d Figure Q1: Beams with various loading and supports Please Note: Parts (b.) to (f.) of the question refer to Fig. Q1-c only!
a) Clearly define the concept of "statically indeterminate structure (beam)" and for each one of the four beams shown in Figures Q3-a, b, c, d state whether it is statically determinate or indeterminate and why? Now, focus on the beam shown in Fig Q3-c. Total length of the beam, AD is 10m. Point loads are: W1=3kN at a=4m and W2=4kN at b=7m from A, and uniformly distributed load (from B to D over the length of 6m) is: w=1 kN/m. b) Sketch the free body diagram, write down independent equilibrium equations, and find The reactions, and plot shear force and bending moment distributions. c) Using Macaulay's method (Singular functions), write down a generic description for the bending moment that covers the entire length of the beam. d) Using the moment-deflection differential equation and the bending moment description found in part c, write down equations for slope and deflection of the beam. e) Find the integration constants and write down “ready to use" equations for slope and deflection as functions of x (from left end, A) along the beam. f) Find the beam deflection at point B (where W1 is applied) and slope at the pin point A (the left end of the beam). Beam Cross Section has l= 2x10-5 m4 and Beam Material is Steel with E=200GPA.
Transcribed Image Text:a) Clearly define the concept of "statically indeterminate structure (beam)" and for each one of the four beams shown in Figures Q3-a, b, c, d state whether it is statically determinate or indeterminate and why? Now, focus on the beam shown in Fig Q3-c. Total length of the beam, AD is 10m. Point loads are: W1=3kN at a=4m and W2=4kN at b=7m from A, and uniformly distributed load (from B to D over the length of 6m) is: w=1 kN/m. b) Sketch the free body diagram, write down independent equilibrium equations, and find The reactions, and plot shear force and bending moment distributions. c) Using Macaulay's method (Singular functions), write down a generic description for the bending moment that covers the entire length of the beam. d) Using the moment-deflection differential equation and the bending moment description found in part c, write down equations for slope and deflection of the beam. e) Find the integration constants and write down “ready to use" equations for slope and deflection as functions of x (from left end, A) along the beam. f) Find the beam deflection at point B (where W1 is applied) and slope at the pin point A (the left end of the beam). Beam Cross Section has l= 2x10-5 m4 and Beam Material is Steel with E=200GPA.
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