BE 110 - Mechanics of Materials – Spring 2003

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BE 110 - Mechanics of Materials – Spring 2003

Exam 4 – Principal Stresses in Beams; Combined Loads.
1. A 24-ft long double-tee wood beam (cross section details given on next page) supports
the loadings shown. For this beam, there is one location along the entire span of the
beam where both the shear force and the bending moment are simultaneously at their
maximum magnitudes.
a. Using shear force and bending moment diagrams, determine this critical x location
and the corresponding shear force and bending moments that act at this location. (5
points)
b. At the critical x location, determine the principal stresses at point H (refer to cross
section on the next page) and report them on an appropriate sketch that shows the
orientation for the principal stress state. (30 points)


Write legibly – box your answers
Include appropriate units
BE 110 - Mechanics of Materials – Spring 2003

Exam 4 – Principal Stresses in Beams; Combined Loads.
Additional calculation space for problem 1

































Write legibly – box your answers
Include appropriate units
BE 110 - Mechanics of Materials – Spring 2003

Exam 4 – Principal Stresses in Beams; Combined Loads.
2. A vertical force P of
magnitude 240 N is applied to
the crank at point A.
Knowing that the shaft BDE
has a diameter of 18 mm:
(20 points)
a. Determine the normal and
shear stresses acting in
the x and z directions at
point H located at the top
of the shaft, 50 mm to the
right of support D.
b. Draw a stress element
showing these normal and
shear stresses (with
magnitudes) at point H.
c. Determine the maximum
in-plane shear stress state at point H.
d. Report the results on an appropriate sketch that shows the orientation for the
maximum in-plane shear stress state with respect to the x axis.
e. (Note: assume that shaft BDE is connected to a fixed support somewhere to the
left of point E.)
Write legibly – box your answers
Include appropriate units
BE 110 - Mechanics of Materials – Spring 2003

Exam 4 – Principal Stresses in Beams; Combined Loads.
Write legibly – box your answers
Include appropriate units
Additional calculation space for problem 2