Question

The 50-mm-diameter cylinder is made from Magnesium Alloy AZ80 and is placed in the clamp When the temperature is T1 = 20°C. the two bolts of the clamp each have a diameter 10 mm and made of Steel Structural (ASTM-A36), and they hold the cylinder snug with negligible force against the rigid jaws, the temperature of the all the assembly has been increased to T2 = 130°C. determine the force in the cylinder at this temperature. 10 100 mm 150 mm 50

Answer 1

Q. sketch of cylinder and bolt Assembly Somm 1 Isomm -T loomm klomm Material of cylindes is (magnesium Alloy, AZ80 Material Properties of cylinder Ec- 44.80PQ [ Elastic modulus.] ac 26 um m'c [ thermal expansion coefficient] Material of bolts is (ASTM-A36) [Steel structure] Material properties of bolts is Ep = 200Gpa dB = 11 um lmic

FBD of Bolt and cylindes After opening up Mutts. .t At temperature I somm T = 2000 loomm IM T2 = 130°C AT = 110°c klomm somm As the temperature increases both, cyclindes and bolts will eap and. SB - ZEBAT Sc = KELCAT 11x108x150 x 10 x 110 Sc= 26x10x looxio x110 SB = 1.8158104 0, 1815 mm &c= 0.286mm

Sketch of Bolts and cylinder Assembly after free Elongation. dB = 0.1815mm 88- 0. 1815mm 0.286mm 1 loomm 150mm so the value of s will Now, the Assembly ins clamped be same for cylinder and bolts. 80 to achieve that bolts will be in tension and cylinder will be in compression. F de + P 88 1 dc - ASB T SB 1

Equilibrium equation to be used is 2 Fop Equeation of compatibility is (SB) Tension + (8B). (8) - (Sc) compremmin Thermal En Thermal 3 FLB ABEB 0.1815X1D -3 0.286810 - PLC ACEC uring .F=P/2 => 2 AB - R 4 (10)*(109). Ac : (10)(166)m? 200 x 10 9 Nm² EB 2 Ec= 44.88 109 N/m ES 6. 1815 x 20 + Px 150xto 2 x 7.8539 x 10 x 200x109 0.286 x Jones Px looxos 1.9634x10 3 x 44.8x109 3P 0.1815 + = > 0.286 - SP 4398016 6283 12 => 5.9115 xloop 0.1045 P = 17677.186 N force in the cylindes P = 17.677 kN. at this temperature