Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

ExAmpLE 15.3
A steel hollow structural section (HSS) is supported by a pin connection at A and by an
inclined steel rod (1) at B as shown. A concentrated load of 20 kips is applied to the beam
at C. Determine the principal stresses and maximum shear stress acting at point H.
D
6 in.
56 in.
y
(1)
2.5 in.
H
z
y
10 in.
A H
B
8 in.
C
x
0.25 in.
27 in.
72 in. 36 in.
20 kips
Cross-sectional dimensions.
Plan the Solution
Inclined rod (1), a two-force member, will provide a vertical reaction force to the beam
at B. Since the rod is inclined, it creates an axial force that compresses the beam in the
region between A and B. The rod is also connected 8 in. above the centerline of the HSS,
and this eccentricity produces an additional bending moment in the beam. The analysis
begins by calculating the beam reaction forces at A and B. Once these forces have been
determined, a free-body diagram (FBD) that cuts through the beam at H will be drawn to
establish the equivalent forces acting at the section of interest. The normal and shear
stresses created by the equivalent forces will be calculated and shown on a stress element
for point H. Stress transformations will be used to calculate the principal stresses and the
maximum shear stresses at H.
56 in.
A x
D
(1)
y
F 48 in.
1
33.69°
A H
B
8 in.
C
x
27 in.
A y
20 kips
72 in. 36 in.
SolutioN
Beam Reactions
An FBD of the beam is drawn, showing the horizontal
and vertical reaction forces from the pin
connection at A and the axial force in inclined
rod (1), which is a two-force member. Note that
the angle of rod (1) must take into account the
8 in. offset of the rod connection from the centerline
of the HSS:
56 in. − 8 in.
tanθ =
= 0.66667
72 in.
∴ θ = 33.69°
628