HW04
MEMT 212
Last Revised 9/15/24
1. (adapted from Hibbeler 10th ed. probs. 6-125 and 6-126)
The wooden section of the beam is reinforced with two firmly-attached steel plates as
shown. Assume Ewood = 10 GPa and Esteel = 200 GPa.
a. If the beam is subjected to a moment of M = 30 kN*m, find the maximum
bending stresses in the steel and wood.
b. Under the load of part (a.), sketch the stress distribution over the cross
section.
c. Find the maximum moment M that the beam can support if the allowable
stress is 6 MPa for the wood, and 150 MPa for the steel.
Answers: (a.) σmax-steel = 123 MPa, σmax-wood = 5.14 MPa (c.) Mallowable = 35.0 kN*m
2. (adapted from Hibbeler 10th ed. prob. 6-131)
Determine the maximum uniform distributed load w0 that
can be supported by the reinforced concrete beam if the
allowable tensile stress for the steel is 28 ksi and the
allowable compressive stress for the concrete is 3 ksi.
Assume the concrete cannot support a tensile stress. Take Esteel = 29 Mpsi, Econcrete = 3.6 Mpsi.
Answer: w0 = 1.03 kip*ft
3. (adapted from Hibbeler 10th ed. probs. 7-7 and 7-8)
The shaft is supported by spherically articulating bearings at A and
B, where bearing A supports any thrust loads. The shaft is made
from a material having an allowable shear stress of 75 MPa.
a. Find the maximum transverse shearing stress the shaft
carries when P = 20 kN.
b. Find the maximum allowable value of P with regard to
transverse shearing stress.
Answers: (a.) 17.9 MPa; (b.) 83.58 kN
4. (adapted from Hibbeler 10th ed. prob.7-48)
The beam is made from three polystyrene strips that are glued
together as shown, with glue that has a shearing strength of
80 kPa.
a. Find the maximum value of P that can be applied
without causing the glue to lose its bond.
b. Under the load found in part (a.), find the maximum
shearing stress at a horizontal cut through the center point of the cross-section.
Answers: (a.) 237.5 N; (b.) 92 kPa
5. (adapted from Hibbeler 10th ed. probs. 7-43 and 7-44)
The box beam shown is constructed from four boards that are fastened
together using nails that can each resist a shearing force of 50lb.
a. Find the force that each nail will carry under a load of P = 2 kip if the
nail spacing is 2 inches. What is the factor of safety for this
scenario?
b. Find the maximum force P that can be applied if the nail spacing is
held at 2 inches.
c. For the original applied force of 2 kip, find the maximum allowable
nail spacing.
Answers: (a.) FA = 206 lb, FB = 315.6 lb, FS = 0.1582; (b.) P = 316.8 lb; (c.) 0.3168 in
Note: It is only a coincidence that the answer for P in part (b.) is close in value to the
answer for FB in part (a.). Don’t read too much into the similarity of these results.
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