Deflected beam showing slope and deflection results at end B mm 5 4 A B B t y

# Deflected beam showing slope and deflection results

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Deflected beam showing slope and deflection results at end B. mm 5 . 4 / A B B t y
Mechanical and Aerospace Engineering Sample Problem 9.11 9 - 86 SOLUTION: Determine the reactions at supports. Construct shear, bending moment and ( M/EI ) diagrams. Taking the tangent at C as the reference, evaluate the slope and tangential deviations at E . For the prismatic beam and loading shown, determine the slope and deflection at end E .
Mechanical and Aerospace Engineering Sample Problem 9.11 9 - 87 Determine the reactions at supports. Equations of equilibrium Free-body diagram wa wa wa R B 0 ) 2 ( 2 a L wa L R a wa M CCW D B 0 wa R R wa F D B y wa R D
Mechanical and Aerospace Engineering Sample Problem 9.11 9 - 88 Construct shear, bending moment and ( M/EI ) diagrams. Fig. 1 Free-body diagram and construction of the moment-area plot. a x wx x V 0 , ) ( a L x a wa wa x V , 0 ) ( a L x a L wx wa wx wa wa wa x V 2 , ) ( a x wx - x wx x M 0 , 2 1 2 ) ( 2 a L x a wa a x wa a x wa x M , 2 ) ( ) 2 ( ) ( 2 a L x a L a L x w wa a L x a L x w a x wa a x wa x M 2 , 2 ) ( 2 2 ) ( ) ( ) 2 ( ) ( 2 2
Mechanical and Aerospace Engineering Sample Problem 9.11 9 - 89 For rectangle For parabolic spandrel EI L wa L EI wa A 4 2 2 2 2 1 EI wa a EI wa A 6 2 3 1 3 2 2 2 / L b EI wa h 2 2 4 / 2 / L b c a b EI wa h 2 2 4 / 4 / a b c
Mechanical and Aerospace Engineering Sample Problem 9.11 9 - 90 Slope at E: Deflection at E: Fig. 2 Due to symmetry, reference tangent at midpoint C is horizontal. Shown are the slope and deflection at end E related to this reference tangent. EI wa EI L wa A A C E C E C E 6 4 3 2 2 1 a L EI wa E 2 3 12 2 EI L wa EI wa EI L wa EI L wa L A a A L a A t t y C D C E E 16 8 16 4 4 4 3 4 2 2 4 2 2 3 1 2 1 a L EI wa y E 2 8 3
Mechanical and Aerospace Engineering Beams with Unsymmetric Loadings 9 - 91 Define reference tangent at support A . Evaluate q A by determining the tangential deviation at B with respect to A . The slope at other points is found with respect to reference tangent. The deflection at D is found from the tangential deviation at D . Fig. 9.34 (a) Unsymmetric loading. (b) Application of moment-area method to find slope at point A . Fig. 9.36c Deflection of point D and similar triangles used to determine y D . L t A B A A D A D A B A D D A B t L x t EF ED y t L x EF L HB x EF
Mechanical and Aerospace Engineering Concept Application 9.12 9 - 92 SOLUTION: Determine the reactions at supports. Construct shear, bending moment and ( M/EI ) diagrams. Define reference tangent at support A . Evaluate q A by determining the tangential deviation at B with respect to A . The slope at other points is found with respect to reference tangent. The deflection at D is found from the tangential deviation at D . For the prismatic beam and loading shown, determine the slope and deflection at point D .
Mechanical and Aerospace Engineering Sample Problem 9.11