Question

For the beam below, construct expressions for the shear V (x) and the moment M(x) using free- body diagram of a cut structure. Answer: M(x) = M(x) = M* - (M*/L)x.

For the beam below, construct expressions for the shear V(x) and the moment M(x) using free- body diagram of a cut structure. Answer: M(x) - M* (M*/L)x. 2. 0 ㄧㄨ

Answer 1

LET REACTION AT HINGE SUPPORT = R_A AND REACTION AT ROLLER SUPPORT BE R_B

R_A+R_B=0 (NO EXTERNAL FORCE IN Y DIRECTION)

H_A=0 (NO EXTERNAL FORCE IN X DIRECTION)

TAKING MOMENT ABOUT POINT B

R_A*L+ M^*=0

R_A= -M^*/L

R_B = M^*/L

SHEAR FORCE TO THE RIGHT OF X FROM A SUPPORT IS

V(z) = RA

$V(x)= \frac{-M^{*}}{L}$

MOMENT AT X

M(x) = M*-R, X

  

M*