Question

Q2) A designer has to design some roof top for which he is in process of selecting an appropriate beam from the two available standards. Both the beams have same lengths but different cross- section and are made up of Alloy steel having yield strength of 680 MPa and young's Modulus of 2.1 x 10 Pa. (All dimensions are in mm) a) Determine which cross-section would be better for the provided loading condition? (CLO 2, PLO 2, 6marks) b) Identify the point at which point maximum linear deflection will take place and find ymax (for the selected beam only). (CLO 2, PLO_2, 6marks) Cross-section C1 C2 80 100 3.8 12.8 46 5.7 F-5kN 3) For the same selected beam discussed in Question # 2, we know that the most critical region ill be along the fixture that will have maximum bending stress induced. As this is ductile a) Apply DE Fai lure criteria to determine the factor of safety at elements A. Also make failure aterial, envelope showing the load line. (Yield strength of 680 MPa). (CLO 2, PLO 2. Smarks) b) Apply MSS Failure criteria to determine the factor of safety at elements A. Also make fnilure envelope showing the load line. (Vield strength of 680 MPa). (CLO 2. PLO 2 Smarks) тку

Answer 1

らKN 2500mm A3 For cross section Ci" A 46mm B 80mm C-3.8mm D 5.2mm Aa= 239.2 mm2 12 12, 46x52, 3-8 (80-10:4)3 12. = 239.2 (40-2-6) + 十46152, 239.2(40-26) 1 2 776730 313 mm For cross- Secton 2 A 55mm B loom m C=12.8mm D=57mm A= A2 = Ax D 55x5, 7 = 313-5 mm" A3(1oo-4)x 128 1124.08 mm2 INA = 55x57, 31 3-5 (50-2-85)2 t I28(100-114) + 55x575 i212 +313 5 (50-2.85) l 2 = 2137468-963mm4 : Seton Modules oF ,"ZA16750 313 19425 a5 INA 776730 313 19425 252 mm B/a4 sect on Modulus oF a-"ZA-- Tria-2137468963 = 42749.38 mm?

Maximum Moment Carrying Capacity ZnAVTer Forc," Mmax = 1942 5 . 25 2 x 680 = 132-09 2 x ,05 N-mm For C2r Mman 4274 9.38% 680 290-6951 105 N-mm .". Сг" Sect on as better as it has better Moment carrying Capacity by Using Elastic deflection Equation Integrating writ χ. Integrating hort 3 At χ:0, dy:0 putting this in eq. U) AtX-o Y-o putting this i) eq(2) For maximum defRection At χ=L mar, deHec tion ymar occurs 3 2 LP L 2 2.1xI05x 2137468363 3 2500a9-008 mmm ご 5x103 2:I x Iox 2137468 963L a -ve sign shoroing doronnword deftecho

a.3 a> Maximum Bending stress oacurs at extreme fibre at the Fixed end Mrnax.y max TMA = 5000× 250으 x 50 2137468.963 292 402 NImm or MPa Ai extreme Fibre at the Fiked end direct shear stress -o . Stress Element -Ơ 292.402 MPa 292 , 402コ MPa Principal Stresses 0 292 402 MPa . Using Distortfen energy theory Fos 2 a x 292.402 2x Syt fos- Sub- 680- = 2.32 392-402 292.402 b As per Mavimum Shear stress theory Absolut e Maximum shear strevsSySyt Fos 2Fos 292 402 - 680 fos 2:32.