ETSI Industriales: Ampliación de Resistencia de Materiales Máster en Ingeniería Industrial, curso 2017/18. Prof. Ignacio Romero

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1 TSI Industriles: mplición de Resistenci de Mteriles Máster en Ingenierí Industril, curso 2017/18. rof. Igncio Romero 1.1 eterminr el grdo de indeterminción estátic de los sistems de l figur (l celosí NO). 1.2 L estructur de l figur está compuest de dos sólidos prismáticos, uno recto y otro con form de codo, unidos entre sí con un rótul y sujetos en sus extremos por poyos rticuldos fijos. lcul el grdo de hiperestticidd, ls recciones, los leyes de esfuerzos y ls digrms de esfuerzos cundo se plic sobre el conjunto un fuerz puntul como se indic l l l 1

2 Fig nd torque of mgnitude T N? m is pplied t s shown. Knowing tht llowble shering stress is 60 M in ech shft, determine required dimeter of () shft, (b) shft. 1.3 Sbiendo que r rg = 2, encontrr el vlor de T F en función de T Under norml operting conditions motor exerts torque of mgnitude T F lb? in. t F. Knowing tht r 5 8 in., r G 5 3 in., nd llowble shering stress is 10.5 ksi in ech shft, determine required dimeter of () shft, (b) shft FGH. TF F r r G G H T Fig nd Under norml operting conditions motor exerts torque of mgnitude T F t F. The shfts re mde of steel for which llowble shering stress is 12 ksi nd hve dimeters d in. nd d FGH in. Knowing tht r in. nd r G in., determine lrgest llowble vlue of T F. 1.4 ibuj los digrms de esfuerzos en el sólido de l figur. R 1.5 ibuj los digrms de esfuerzos en el sólido de l figur. 1.6 ibuj, sin necesidd de clculr ls leyes de esfuerzo, los digrms de esfuerzos de ls siguientes estructurs: L/2 L/2 2

3 b 3

4 b M 4

5 sher nd bending-moment digrms for g shown, nd determine mximum bsosher, (b) of bending moment. 60 kips 60 kips in. 8 in. 8 in. 1.7 ibuj y cot los digrms 5.9 nd 5.10 rw sher nd bending-moment digrms de esfuerzos F cortntes y momentos bem nd 250 loding mm shown, 250 mm nd determine 250 mm mximum b flectores de l brr. lute vlue () of sher, (b) of bending moment. 12 kn/m 15 kips 40 kn 2 kips/ft ng tht rection of ground is uniformly sher nd bending-moment digrms for ine mximum bsolute vlue () of ding moment. 50 mm 50 mm 75 N Fig ibuj y cot los digrms de esfuerzos cortntes y momentos F flectores 1.5 knde l brr. 1.5 kn 3 in. s/ft /29/10 6:44:18 M user-f499 /Users/user-f499/esktop/Temp Work/on't elete ob/mhq251: ft 0.3 m 0.9 m Fig m 2 m Fig nd 5.14 ssuming tht rection of ground is uniform distributed, drw sher nd bending-moment digrms for t rw sher nd bending-moment digrms bem for roblems nd determine mximum bsolute vlue () 327 of t ding bem shown nd loding nd determine shown, determine mximum mxiue to bending norml sher, (b) of bending moment. nding. 1.9 on L trnsverse brr section t. está unid l brr trvés de 24 kips 2 un kn kips/ft 80 2 kn/m 160 kn kips/ft rótul en. ibuj y cot los 3 kn 24 digrms kn/m de esfuerzos cortntes 2000 lb 1.8 kn/m kn? m y momentos flectores de l brr 80 mm 200 lb/ft 4 in.. 3 ft 3 ft Hinge 3 ft 3 ft 0.3 m 0.9 m W m Fig m Fig in. 300 S250 mm m 1.5 m 2 m 2 m 0.6 m 5.15 nd 5.16 For bem nd loding shown, determine m.5 m 1.5 m mum norml Fig stress ft due 4 to ftbending on 6 ft trnsverse section t. 5 Fig rw sher nd bending-moment digrms for ding shown nd determine mximum norml nding. 1 m 75 N Fig ft 4 ft 4 ft 5.11 nd 5.12 rw sher nd bending-moment digrms bem nd loding shown, nd determine mximum b lute vlue () of sher, (b) of bending moment. Fig kn 60 kips 60 kips 8 in. 8 in. 8 in. 3 kn 1.8 kn/m 80 mm 300 mm

6 1.6 m 3.2 m 5 ft ft 5 ft Fig g tht W 5 12 kn, drw sher nd bending-moment ms for bem nd mximum stress 1.10determine Un vig bipoyd connorml un seccio n bending. de rigidez flexio n constnte est sometid dos fuerzs puntules de vlor 8 kn y tiene ine () mgnitude of uncounterweight for which engnchdo cble como se W indic en l ximum bsolute vlue of bending moment in bem figur. mll s possible, (b) corresponding mximum norml i) lculr ls recciones pr un vlor ue to bending. (Hint: rw bending-moment digrm culquier de W. ute bsolute vlues of lrgest nd negtive bee80288_ch01_ indd ge 46 positive 9/6/10 7:27:48 M user-f499 ii) ibujr el digrm de momentos g moments obtined.) W 8 kn 8 kn W310! 23.8 /Users/user-f499/esktop/Temp Work/on't elete ob/mhq251:eer:20 flectores en l vig pr un vlor de W ine () distnceculquier for which. bsolute vlue of g moment in iii) bem is s smll s possible, (b) corlculr el vlor del peso W que nd 5.27 ding mximum stress due to bending. (See hintenof Figs indd ge 21 9/4/10norml 5:34:29 M user-f499 /Users/user-f499/esktop/Temp Work/on't elete ob/mhq251:eer:201/ch01 minimiz el m ximo momento flector Introduction oncept of Stress 1.62 In mrine crne shown, link is known to hve uniform ) l vig (en vlor bsoluto). cross section of mm. For loding shown, determine norml stress in centrl portion of tht link ncontrr el vlor de los 4 kips/ft esfuerzos normles en todos los elementos de l gru de l figur ch of four verticl links hs n mm uniform rectngulr cross section nd ech of four pins hs 16-mm dimeter. W14!norml 68 eterminehinge mximum vlue of verge stress in inks connecting () points nd, (b) points nd. 15 m 25 m 3m 35 m 18 ft 80 Mg g m 15 m 0.25 m 21 roblems 0.2 m Fig kn 1.12 ncontrr el vlor de todos los esfuerzos en l brr cundo θ = Two wooden plnks, 4 in. ech Fig. 1.7 Knowing tht link is 18 in. thick nd 1 in. wide, determine norml stress in centrl portion of tht link when () u 5 0, (b) u in. thick nd 9 in.4 in. wide, re joined by in. dry mortise joint shown. 12 Knowing tht wood used shers off long its grin when verge shering stress reches 1.20 ksi, determine mgnitude of xil lod tht will cuse 2 in. joint to fil. 6 in. 8 in. 240 lb in. 5 8 in. F 60 lb 1 in. 2 in. 2 in. 1 in.! 9 in. Fig ' 7 in. 5 8 Link hs uniform rectngulr cross section 161 in. thick nd ' Fig in. wide. etermine norml stress in centrl portion of ink. 6 3 in in. b! 1.64 Two wooden members of uniform rectngulr cross section of sides mm nd b 5 60 mm re joined by simple glued joint s shown. Knowing tht ultimte stresses for joint re su M in tension nd tu M in sher nd tht 5 6 kn, determine fctor of sfety for joint when