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Consider the beam and loading shown. Assume that E=200 GPa and I=38x106 (mm4). P=2.3 kN and L=2.2 m, (a) determine the deflection at B (b) determine the slope at B

Consider the beam and loading shown. Assume that E=200 GPa and I=38x106 (mm4). P=2.3 kN and L=2.2 m, (a) determine the deflection at B (b) determine the slope at B

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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Consider the beam and loading shown. Assume that E=200 GPa and I=38x106 (mm4). P=2.3 kN and L=2.2 m, (a) determine the deflection at B (b) determine the slope at B L. Using the FBD of the entire beam (with units of force in (kN) and length in (m)) EMA=0-MA=5.06 (kN.m) and EFy 0¬AY=2.3 Using the FBD of the cut section, E Mx = 0 M(x) = Deflection curve Using the Euler-Bernoulli equations, d'y %3D = 2.3x - 5.06 M(x) El (을 ~)이(4) = (2.3를-506x + A) →y(+)- (2.3릉 - 506를 +Ar + B) %3D %3D %3D Boundary conditions For the fixed-end support at A YA-0 & 0A-0 Integration constansts YA-0+y(XA=0)=0-B=D0 OA=0+0(xA-0)=0 A-0 Deflection and slope at B (a) The deflection at B is given as 1.074 (mm)(1) 1x10-2 (degrees)() (b) The slope at B is given as
Transcribed Image Text:Consider the beam and loading shown. Assume that E=200 GPa and I=38x106 (mm4). P=2.3 kN and L=2.2 m, (a) determine the deflection at B (b) determine the slope at B L. Using the FBD of the entire beam (with units of force in (kN) and length in (m)) EMA=0-MA=5.06 (kN.m) and EFy 0¬AY=2.3 Using the FBD of the cut section, E Mx = 0 M(x) = Deflection curve Using the Euler-Bernoulli equations, d'y %3D = 2.3x - 5.06 M(x) El (을 ~)이(4) = (2.3를-506x + A) →y(+)- (2.3릉 - 506를 +Ar + B) %3D %3D %3D Boundary conditions For the fixed-end support at A YA-0 & 0A-0 Integration constansts YA-0+y(XA=0)=0-B=D0 OA=0+0(xA-0)=0 A-0 Deflection and slope at B (a) The deflection at B is given as 1.074 (mm)(1) 1x10-2 (degrees)() (b) The slope at B is given as
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