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Due: Lecture 39
HOME ASSIGNMENT #8 (Part B)
Warm-Up Exercises
Practice Problems
- A nine-foot long simply-supported beam has an unsymmetric cross-section as shown below. A 220-pound person walks across the beam (assume the weight is applied through the shear center of the beam). The beam is made of steel with a modulus of 30 Msi and a Poisson’s ratio of 0.3.
CROSS-SECTION
z 2 in
0.2 in i 1.5 in 0.1 in i
x
z
9 ft
y
Determine:
(a) the point x along the beam where the person causes the maximum total deflection and the magnitude of that deflection (divide into y- and z- components).
(b) the maximum stress, σxx, in the beam for this condition and its location.
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16.20 Home Assignment #8b Page 2 Fall, 2002
Application Tasks
- A new consumer product is made of several alternating layers of 0.10 inch thick unidirectional (0°) graphite/epoxy and 0.40 inch thick styrofoam. The graphite/epoxy has a longitudinal modulus of 22.0 Msi, a transverse modulus of 3.5 Msi, a (transverse) shear modulus of 0.80 Msi, and a major Poisson’s ratio of 0.28. The (isotropic) styrofoam has a modulus of 0.50 Msi, and a major Poisson’s ratio of 0.35. The application is cantilevered and has a length of 5 feet and width of 10 inches. The loading is a tip load of up to 400 pounds (including a dynamic load factor).
CROSS-SECTION (not to scale)
z
y 10” 400 lb z
x
5 ft
0.40” thick foam
0.40” thick foam
= 0.10” thick unidirectional graphite/epoxy
Find:
(a) the maximum stress, σxx, in the beam and its location.
(b) the through-thickness distribution of the shear stress, σxz, and its maximum value and location (plot it).
(c) the maximum deflection (and divide this into bending and shearing components).
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