Question

LIU Points A hollow steel tube is bend to quarter circle and welded at base as shown in the figure below. The radius of curvature at the center of cross section area is 400 mm. It is subjected to force F. Use the given data to find 1. The reaction forces and moments at the critical cross section area 2. Find the Von Mises stress at the critical location (Neglect transverse shear) 3. If the yield stress of the materials 320 MPa, check safety using Von Mises criteria F = -661 + 873 +98k (kN) de = 150 (mm): outer diameter of tube di = 100 (mm): inner diameter of tube Sy = 320 (MPa) 400 Center of curvature Given: Force in (kN)and dimensions in (m)

Answer 1

D Given situation is as follows: ണ 400mm let, o be the origin of the co-ordinate system and p be the point of application of force. 2 critical cross-section is the cross- Section containing o. Noco, ining o. Mop = (goo @ +900ê hromom Now, Moment due to force I about o Ñ Box - (400 î+400l2 9x (-46 & +87 9+2312) a KN.mm =1348008 - 35600j-26400] -34800) Nom

Ñ. =-34.8 Â-629+34.8 ) kN.com Them, Reaction force at critical coross section, Freaction - Freaction = (66î ~87 ] = 98E) KN | Reactional moment at critical Cooss-section, MReaction a-mo > Meeaction ? (3468 +629 -34-8@ )i<Nmom Critical cross-section can be drawn as follows - Tom Here, fx = -66kN fra8fIN - 98kN 21 Mar-34.8 kNm Maya-62 kNm M₂ = 34.&kNam (Point A will be the critical point ?

Now, Normal stress at A, I is ā (29-09) Here, 2 ASA (2 de ²) 1 - 19.94xto front A-9817.48x20cm² Now, 5x=(-66d03 6 2x20 x 150xto? 9817.48 X 106 19.94x tot x=(-6.12 – 233.2) mpa » ~-240 MPa Also, shear stress at A, (Neglecting to preverse) Exys My JP 2 (4.8-dt) J = 39.88x to cont Then, Exp = ~34.8%20² x 150x203 - 39.88 x 106 Pa. Txy = -65.45 MPa 17

Principal stresses at A of oxtay + r s t =(-120 + 136.69) MPa I = 16.69 MPa 2 13 = -256.69 MPa Now, Von-Mises stress at A, Svm = 6.62²+(52-53) + 163-872 S = 35. 37 мР 2 ③ Given that, yield stress, Sy = 320 MPa Now, using Nomornises Costeria, factors of Safety, O fat 38.37 0.85 The structure will fail as fsct.