Problem:
F6-1. Express the shear and moment functions in terms of x, and then draw the shear and moment diagrams for the cantilever beam.
[Chapter – 6, Bending, Mechanics of Materials by R C Hibbeler)
Solution:
Check Other Problems’ Solutions here: (Book Solutions) Mechanics of Materials by R C Hibbeler (Eighth Edition)
Let A be the left end, and B be the right(fixed) end.
As per the static equilibrium,
End support reactions are: RB = 9.0 kN
Moment Reactions are MA = 0 kNm, and MB = -9*3 = -27.0 kNm
Expressions of shear and moment:
Shear at x from left end,
Vx = -9
and Moment at x from the left end,
Mx = -9*x
Maximum positive Bending Moment, Mmax = 0.0 kNm
at x = 0.0 m from the left end.
Minimum Bending Moment, Mmin = -27.0 kNm
at x = 3.0 m from the left end.
Absolute Maximum Bending Moment = 27 kN-m at the fixed end.
Shear and Bending Moment diagrams are drawn as shown in the image below.
