Question

walls. The length of the duct is 4ft and is heated from room square duct made of ductile material is fixed between two A temperature Determine the following: a) Assuming all dimensions and material properties as variables, determine a formula for the change in temperature (AD) required to cause buckling of the duct, b) If the fixed wall supports are replaced by pin joints in both ends of the duct, what would be the change temperature? Take, E=29x103ksi and a=158 10-6-1 C) If the yield strength of the material is 30 ksi, will the duct yield before youckling? Explain your answer mathematical procedure. What would be the AT in at yielding ATJO 12 in

Answer 1

solution? for or both end fired x="/ le-al = 24 inch ht:24+ Yth Euler's buckling al formula para 281 load . le? Dividing the equation by Area (A) on both sides par TREI le? Thermal stress in the duct due to T2q1 increase in temp le ² YA r=aotę a Di I MEI le? 128 04 2 DEA Ia I (1.2"-Jll) 2 AT To 2 I da le? 1=0.08946 inch" Az 1.2? -;2 D1 = n2x0.08aub 18x10bxo.unx (2412 0.44 inch? DT = 232.25 of ICS Scanned with CamScanner

b> B Pin joint at both ends head.l = lxl Aft=48inch 19 2 Di= T2I a A le? m? +0.08anb is x 10bxo.hux. 48 OTR = 58oF The change in temperature as the end conditions are changed = ato-otz -232.25-58 174.24 of c) Syt - Boksi o for both ends fixed & Dia dot 15x10 bx 232.25*20 x 103 ksi 101.028 ksi before buckling Tix Syt sy Ma material gields before 3) for both enda pinned 02=dotę = 15x100x58x29x10² - 25.23 ksi 3 CS Scanned with CamScanner ' //

6 2 L Syt does not gields before atero buckling gielding temperature of syt dotę. 15x15 b xDTX 29x103 D1 = 68.96of a temperature of which gielding begins 302 CS Scanned with CamScanner