Question

) An aluminum rod of 20 mm diameter is completely enclosed in a steel tube
of 30 mm external diameter and both the ends of the assembly are rigidly
connected. If the composite bar is heated through 50 °C, find the stresses
developed in the aluminum rod and steel tube. Modulus of elasticity for
steel and aluminum are 200 GPa and 80 GPa respectively. Asteel= 12 x 10-6
per °C and Gal= 18 x 10-6 per °C​

Answer 1

Answer:

stress in steel = 12 x 10^7

stress al = 72x 10^6

Explanation:

stress thermal = Y x A x Change in temp

and giga means 10^9

Answer 2

Answer:

Stress in both steel and aluminum rod.

Explanation:

Given:

Diameter of aluminum tube, d = $20$mm

Diameter of steel tube, d =$30$mm

Temperature, t = $50^{o}$

Modulus of elasticity, steel = $200$ GPa

Modulus of elasticity, aluminum =$80$ GPa

Calculations:

Area of aluminum = Πr² =$314$mm² = 0.000314m²

Area of aluminum = Πr²=0.0007065m²

Stress of aluminum = Y×A×t

                                =80×0.000314×50

                               = $12$ ×$10^{-6}$ per °C

Similarly for steel we have = $200$×$0.0007065$×50

                                           = $18$×$10^{-6}$ per °C