Page 114 - Mechanical Behavior of Materials

Problems and Questions 115

Section 3.6
3.10 For S-glass in Table 3.11, explain why some oxides commonly used in glass are not included
and why the percentage of Al 2 O 3 is high. How would you expect the strength of S-glass fibers
to compare with those of E-glass?
3.11 Consider the data for strength of Al 2 O 3 , SiC, and glass in both bulk and fiber form in
Tables 3.10 and 2.2(b), respectively. Explain the large differences between the strengths in
tension and compression for these materials in bulk form, and also explain why the strengths
of fibers in tension are so much greater than for bulk material.
3.12 The ancient Romans employed a volcanic ash called pozzolana to make a material somewhat
similar to the modern Portland cement concrete. Consult sources beyond this textbook and
write two or three paragraphs about how this material differed from modern concrete, and
how it was similar, and the Roman’s degree of success in using it as a building material.

Section 3.7
3.13 Compute strength-to-density and stiffness-to-density ratios, σ u /ρ and E/ρ,for thefirstfive
metals in Table 3.1 and for the SiC and Al 2 O 3 whiskers and fibers in Table 2.2(a) and (b). Use
the upper limits of strength for the metals. For SiC and Al 2 O 3 , use densities from Table 3.10
as approximate values. Plot σ u /ρ versus E/ρ, using different plotting symbols for metals,
fibers, and whiskers. What trends do you observe? Discuss the significance of these trends
in view of the possibility of making metal matrix composites containing, say, 50% fibers or
whiskers by volume.
3.14 Concisely discuss the differences between precipitation hardening and dispersion hardening.

Section 3.8
3.15 Consider the beam of circular cross section of Fig. 3.29 and Ex. 3.1. As before, the radius r of
the cross section may vary with material, and the beam is required to have length L and carry
load P. However, in this case, the strength requirement is replaced by a requirement that the
deflection not exceed a particular value v max .
(a) Select a material from Table 3.13 such that the mass is minimized.
(b) Repeat the selection with cost being minimized.
(c) Briefly discuss your results, and suggest one or more materials that represent a
reasonable choice, where both light weight and cost are important.
3.16 Consider a tension member that is part of the structure of a personal aircraft. For a preliminary
materials selection, assume that the member has a square cross section of side h that may vary
with material choice. The length L is fixed. There are two functional requirements. First, a
force P must be resisted such that there is a safety factor X against the material exceeding
its failure strength. Second, the deflection due to force P must not exceed a given length
change L. Make a compromise choice among the materials of Table 3.13 that considers these
requirements, light weight, cost, and any other considerations that you believe are important.
Briefly justify your choice.
3.17 A column is a structural member that resists a compressive force. If a column fails, it does so
by buckling—that is, by suddenly deflecting sideways. For relatively long, thin columns, this
occurs at a critical load of