Question

2.5 k 35 k-in. Problem 9.5-7 The cantilever beam ACB shown in the figure has flexural rigidity EI = 2.1 x 106 k-in.2 Calculate the downward deflections and 8, at points Cand B, respectively, due to the simultaneous action of the moment of 35 k-in. applied at point C and the concentrated load of 2.5 k applied at the free end B. B 48 in. 48 in.

***use Method of superposition to solve***

Answer 1

Draw the free hody diagram of the heam. 35 k-in 2.5 k A 48 in. 48 in. find the deflection Use the principle of superposition point B and Write the equation for deflection of free end of cantilever beam due to point load from table of "dellection and slopes beams (be3E Calculate the deflection due to the noint load. 2.5x96 3x2.1x10 - 0.35109 in (Downward) Write the equation for deflection of free end of cantilever beam due to moment from table of "deflection and slopes of beams". (8) ( 21 a) 2EI 2L u 35x48 2x2.1x102x(96)-48) =- 0.0576 in. (upward deflcction) Calculate the total deflection of point B. ()(,) 8-0.35109 0.0576 8-0.293 in(Downward) for deflection of cantilever beam due Write the point load from table "deflction and slopes of beams" Pa (c) 3xa). Here, a is the location dellection is to be delermined which the load is applied and x is the location at which the 2.5x48 (c =x2.]x10 (3(96)-48) - 0.1097 in(Downward) f free end of cantilever bea Write the equation for deflection table "deflection and slopes of beams" due to moment from (6e 2E Herc, Mis the applied moment and a is the location of the point at which the moment is applied 35x48 2x2.1x10 -0.0192 in (upward deflection) Calculate the total deflection of point C -(( 8,-0.1097-0.0192 o-0.0905 in (Downward) o00n(