Question

versidad de Puerto Rico en Mayaguez matic bar AB, made of Titanium alloy a linearly elastic material is held between oyable supports as shown in the figure below. The bar has a modulus of elasticity of 120 GPa and a coefficient of thermal expansion of 9.4310-rc. [45pts] If the temperature of the bar is raised uniformly by 60 °C. determine the thermal stress developed in the bar. In addition, determine the complete state of stress on stress element aligned with inclined section pq, when = 28° Show the results in a diagram Bar's cross section Ra so A7 300mm L=3.0 m 300mm b. Repeat (a) for the bar shown below, assume the spring stiffness k=10kN/m B k WW- L=2.7 m (b)

Answer 1

a)

When temperature increases by the bar will increase length compressive force will develop in the bar

Panke DATE PAGE Stepih 3.om. Remove Suppoats & fond AL) due to tempelature chane (At) (AUG = LOAT = 3.0x 9.4 x 10 (60%) - 0.1692 mm Apply supports o find Reactions.. (Aliamust be balanced by Reaction forcej as change is length will begelo . (ALT=RAL » RA ALXAE) رنگ > RAI 0-1692 x 300x300X1204103 3000 TRA = 60918 IN ERR Lampoosion

The state of stress in the inclination of 28degrees is shown below

-Pankaj DATE: 1 PAGE NO.: SOGUN 209.12 som above figure PEoso=689.12 P=689.87 kN) 589.8710 639.87 km

B)

when a spring of 10kN/m is introduced

ww Ro We know] (AL) == 0.1169am BB Ann Rc 401692 As Spoing Compresses Reaction develops RE KALT Ri= 10 kalm X 0.189am Re = 1.690 KN) =1.976 Ploso = 1.890 kn P= 1.9163 kN

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