Question

The catarrod CD of the assembly is heated from T: -30CDT -165 Cusing dectrical resistance heating. Al the power torrperature The gap beton and the nigd bar is 0.7 mm Rods AB and EF are made of sted, and each cross-sectionarea of 125 mm CD made of aluminum and as a ress-section of 375 mm. Ex-200 GP E- 70 GP anda - 23 (10)/"c Figure 1) Part Determine the force in the red AB caused by the increase in temperature Express your answer to three significant figures and include the appropriate units. Figure 0.7 mm 7,Value Units Sub 240 mm 300 mm Part Determine the force in the red EP caused by the increase in temperature Express your answer to three significant figures and include the appropriate units Valne Units Sub BRA

Answer 1

solo - Given data, Initial temperature, I = 30°c Final temperature, T = 165°c Gap between c and rigid bas, d= 0.7mm S=0.0007m cross-sectional Area of steel bad AB and EF Ą = 125mm2 = 125x156 m² Cross-sectional Area of Aluminium bar co, А = 375x156 m2 Modulus of Elasticity of steel, E = 200 X10 N/m² Modulus of Elasticity of Aluminium, Ear 70x10x/m2 - 375 mm² al Coefficient of thermal expansion of Aluminium, & al = 23x100/oc. Let &s be the displacement in steel rods & = (&a- (sp) - 8 Ss = Es xls Fs x 0.3 ASX Es 125x10 6x 200 x 10 &g = 1.2 x 108 E Deformation of aluminium bas due to raise in tempesature (67) = ha OT - 0.24*23*10*** (165-30)

rod AB caused by the increase 4 (85) 7.45x10 (Sp), be the deformation (displacement) in aluminium bar Copal Adx Eal X 0.24 375x106 x zoxio Spal = 9.143 x 10 9 Fpmi ds = 1-2x10-8F3 = 7.45*10-4 _ 9.143 x1o°F -0.0007 1.2 F5 +0.9143 Fv = 4500 free body Diagram VES VES "Fal Fal = Estes and ③ we get solving Fal - 2Fs = 0 equations Fs = 1485.835 N Fal = 2971.67N Force in the in temperature Fs = 1485.835 N

Force in the rod EF is same as the 6 Force in the rod AB .. Fs Fs = 1485.835 N FAB = FeF = Fs = 1485.835N Force in the in the rod CD, Fal = 2971.670

0.7 mm F BLO C 240 mm 300 mm D ΑΙ EO