Question:
I tried to plot the shear stress of a cantilever beam, which is loaded
at one free end by a downward force (-y direction). Then I tried to
plot the shear stress of the left half of the beam, and found that the
shear stress (sigma_xy) in the whole left half is negative.
Then I tried to plot the shear stress of the right half of the beam, I
found that all the shear stress in the whole right half is negative
too.
My question: From the free body diagram of the left half, the force
applied by the right half to the left half at the cut-section should
be downward (-y), and the force applied by the left half to the righ
half, at the cut-section, should be positive. HOw comes both shear
stress plotting, for both left and right halves, have all negative
shear stress values?
I may have missed something. But can somebody explain a little, Or if
you know how to interpret ANSYS' shear stress plot?
Answer:
I don't use Ansys, but the usual sign convention for stresses is as follows:
A component of normal stress is positive in tension.
A component of shear stress is positive if it acts in the positive
coordinate direction on a face where the normal stress acts in the positive
coordinate direction.
If it's any help, here's a text representation of the shear, bending,
moment diagroms from Archon's BEAM for a sample cantilever.
(below)
Notice the shear level is constant along the length of the beam, from
the fixed end to the point of application of the force.
Think of slicing the beam vertically at any point. The side towards
the end load always wants to drop. And neglecting self weight, (which
is a distributed load of course) the force to resist the shear is
constant and the same as the force applied at the end.
INPUT DATA
Beam Type =
Beam Classification = W
Total Length = 10.00(ft)
Unbraced Length = 10.00(ft)
Young's Modulus = 2.90E+07(psi)
Moment of Inertia = 10.00(in^4)
Section Modulus = 0(in^3)
Strong Axis Bending!
Left end is fixed, Right end is free.
LOADS
( 1) Point Load = 100.0(lbs)
Located 10.00(ft) from the left side.
OUTPUT
Max. Moment = 1000(ft-lbs)
Max. Shear = 100.0(lbs)
Max Deflection = 0.199(in)
Reaction R1 = 100.0(lbs)
Reaction R2 = 0(lbs)
