copper

53 - 55 Solved Problems in Maxima and Minima

DiffCalc 016 Largest rectangle inscribed in a circular quadrant

Problem 53
Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

 

Solution to Problem 269 Thermal Stress

269 Copper and aluminum bars supporting a slab

Problem 269

As shown in Fig. P-269, there is a gap between the aluminum bar and the rigid slab that is supported by two copper bars. At 10°C, Δ = 0.18 mm. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased to 95°C. For each copper bar, A = 500 mm2, E = 120 GPa, and α = 16.8 µm/(m·°C). For the aluminum bar, A = 400 mm2, E = 70 GPa, and α = 23.1 µm/(m·°C).

Solution to Problem 237 Statically Indeterminate

Problem 237

In Problem 236, how should the lengths of the two identical copper rods be changed so that each material will be stressed to its allowable limit?

 

Solution to Problem 236 Statically Indeterminate

Problem 236

A rigid block of mass M is supported by three symmetrically spaced rods as shown in Fig. P-236. Each copper rod has an area of 900 mm2; E = 120 GPa; and the allowable stress is 70 MPa. The steel rod has an area of 1200 mm2; E = 200 GPa; and the allowable stress is 140 MPa. Determine the largest mass M which can be supported.

Block supported by three rods

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