Materials Selection in Mechanical Design
Prof. Vogt
Fall 2020
Homework #4
Problem 1 Determine how much more efficient a circular tube is verses a circular rod of the same diameter.
Problem 2 Finding a substitute for bone. Find an engineering material that most
closely resembles the longitudinal strength of compact bone (cortical bone (L)) in its
strength/weight (σ f / ρ ) characteristics by plotting data for this material, read from
Figure 12.14, onto a copy of the σ f − ρ chart for engineering materials (Figure
4.4). Here σ f is the failure stress and ρ is the density.
Problem 3 Shape factors for tubes (Figure E21).
(a) Evaluate the shape factor eB
φ for stiffness-limited design in bending of a
square box section of outer edge-length h = 100mm and wall thickness t =
3mm. Is this shape more efficient than one made of the same material in the
form of a tube of diameter 2r = 100mm and wall thickness t = 3.82 mm (giving
it the same mass per unit length, m/L)? Treat both as thin-walled shapes.
(b) Make the same comparison for the shape factor fB
φ for strength-limited
design.
Use the expressions given in Table 9.3 of the text for the shape factors eB
φ and
fB
φ.
Problem 4 Microscopic shape: tube arrays (Figure E27). Calculate the gain in
bending efficiency, eB
ψ , when a solid is formed into small, thin-walled tubes
of radius r and wall thickness t that are then assembled and bonded into a
large array, part of which is shown in the figure. Let the solid of which the
tubes are made have modulus Es and density ρs . Express the result in
terms of r and t.