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scannedproblems1 - PROBLEMS 1.1 Two solid cy lindric al...

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Unformatted text preview: PROBLEMS 1.1 Two solid cy lindric al rods A B a nd B C a re we ld ed toge th er at B and loaded as shown . Determin e the magnitude of th e force P for which th e tens il e stress in rod A B is tw ice the magnitude of th e c o mpressive stress in rod B e. fA 300 111111 25 0111111 3 in . 2 in . 30 ki p L ~ - - - - - 40 i n. - - - -+, I Fig. P1.1 40 kN 1 .2 In P rob. 1.I , kn owing that P = 4 0 kips, determin e the average normal stress at the midsec ti on of ( a) rod A B, (b ) rod B e. 1 .3 Two so lid cylindri ca l rods A B a nd B C a re we ld ed toge ther at B and loa ded as show n. Kn ow in g th at th e ave rage normal stress must not e xcee d 175 M P a in rod A B a nd 150 M P a in rod B C, d etermin e the sma ll es t allowa bl e va lu es of d l a nd d 2 . 1 .4 Two so lid cy lindri ca l rods A B a nd B C a re we ld ed toge th er at B and loa ded as show n. Knowing th at d l = 5 0 m m and el2 = 3 0 mm , find the average norm al stress at th e midsecti on o f (a) rod A B , ( b) rod B e. 1200 N Fig . P1.3 and P1.4 A 1.5 A s tra in g age located at C on th e surface of bone A B indi ca tes th at th e ave rage norm al stress in the bone is 3 .80 M P a w hen the bone is subj ected to two 120 0-N f orces as show n. Ass umin g th e cross section of th e bone at C to be annular and kn ow in g th at it s outer di ameter is 25 mm, determine the in ner di ameter o f the bone 's cross sec ti on at e. 1.6 Two steel pl ates are to be he ld toge th er by mea ns of 16-mm-diameter hi gh-strength stee l bolts fittin g s nu gly in s id e cy lindrical brass space rs. Kn owin g th at th e average norm al stress must not excee d 2 00 M P a in th e bo lt s and 130 M Pa in the space rs, deter mine th e outer di ameter of the spacers th at yields th e most econo mi ca l and safe des ign. c 13 1200 N F ig. P1 .5 F ig. P1 .6 18 PROBLEMS 1 .29 T h e l A-kip load P is supported by two wooden members o f uniform cross section that are j oined by the si mple g lu ed s carf s plice shown. Determin e the normal and shearing stresses in the g lu ed splice. p 3 . 0 ~/~ I 5. 0 in. \ P' Fig. P1.29 a nd P1.30 1.30 Two wooden members o f u niform cross sec ti on are joi ned by the simple sca rf s plice shown . Knowing that the max imum a ll owable shear in g stress in the g lu ed splice is 60 psi, determine (a) the largest load P that can be safely supported , ( b) the corresponding tens il e stress in the s pl ice. 1.31 Two wooden members of unifo rm rectang ul ar cross section are joined by the simple g lu ed sca rf sp li ce show n. Kn ow in g that P = I I kN, determine the normal and shearin g stresses in t he glued spl ice. 1 .32 Tw o wooden members of uniform rectang ul ar cross sec ti on are j o in ed by th e simple g lu ed sca rf s plice shown . Kn ow in g that the max imum a ll owa bl e ten s il e stress in the g lu ed splice is 5 60 kPa, determine ( a) t he largest load P th at can be safely applied, ( b) the corresponding shear in g stress in the splice. 1 .33 A c entric load P is applied to the granite bl ock shown. Know in g th at th e resulting maximum value o f the shearin g stress in the bl ock is 2.5 k si , determi ne (a) the magnitude of P , ( b) the o ri enta ti on o f the surface on w hi ch the max imum shearing stress occurs, (c) th e normal stress exerted on the surface , ( d ) the maximum value o f the normal stress in the bl ock. 1 .34 A 240-kip load P is applied to the granite bl ock shown . Determine the re sulting maximum value o f (a) the normal stress, (b) the shearing stress. Specify th e o ri enta ti on o f th e pl ane on w hi ch each o f these max imum va lu es occurs. ~~ ~ 75 mm ~1) h 5D mm Fig . P1.31 a nd P1.32 r Fig. P1.33 a nd P1.34 33 1.42 L ink A B is to be made of a stee l f or w hi c h the ultimate no rm al stress is 4 50 M Pa. D etermin e th e cross-sec ti o nal a rea f o r A B fo r w hi c h the factor o f s afety will be 3.50 . A ss um e that th e link will be adequ ate ly re in fo rce d around the pins at A a nd B. Problems 35 8 kN/m o B ~ l l l l l l l otE 0 e • 0 .4 m .1 ~o .I. . kN 0 .4 m 0 .4 m l) Fig. P1.42 1.43 T h e two woode n me mb e rs shown , w hi c h suppo rt a 16-kN load, are joined by pl ywood spli ces f ull y g lu ed o n the s urfaces in c o ntac t. T h e ultimate shearing stress in th e glue is 2 .5 M P a a nd th e clearance be t wee n th e me mbe rs is 6 mm . De termin e the re quired length L o f e ac h spli ce i f a f ac to r o f s afety of 2.75 is to be ac hi eved . 16 kN 125 mm 16 kN Fig. P1.43 1.44 Fo r the jo int a nd loa ding o f P rob. 1. 43 , d e termin e the fac to r o f safety, kn owin g that th e length of e ac h spli ce is L = 180 mm. 1.45 T hree 18-mm-di a meter s tee l bo lts are to be used to attach th e stee l pl ate show n to a woode n bea m. Kn ow ing that the pl ate w ill s uppo rt a II O-kN load a nd th at the ultimate shea ring stress fo r the stee l use d is 3 60 M Pa, d e te rmin e th e fac to r of safety fo r thi s des ig n. 1.46 T hree s tee l bolts a re to be used to attac h th e stee l pl ate show n to a woo den bea m. Kn owin g that the pl ate will suppo rt a II O- kN loa d, that the ul tim ate shearing stress fo r the stee l used is 3 60 M Pa, a nd that a fac to r of safety of 3.3 5 is des ired, determine the re quired di a mete r o f th e bo lts. 1.47 A loa d P is sup po rted as shown by a stee l pin that has bee n in se rted in a short wooden me mber hang in g fro m th e c e iling. T h e ultimate stre ngth o f th e wood used is 12 ksi in te nsio n a nd 1.5 ks i in s hea r, while the ultimate streng th of th e steel is 3 0 ksi in s hea r. Kn ow in g th at the di a meter of the pin is d = in . and th at th e magnitude of the load is P = 5 kips, determine ( a) the facto r o f safety for th e pin , ( b) the re quired values o f b a nd c if th e fac to r of safety fo r th e wooden me mbe r is the same as that fo und in part a for the pin . Fig. P1.45 and P 1.46 i 1.48 F or th e suppo rt of Pro b. 1.47, kn ow in g that b = 1.6 in ., c = 2 .2 in ., in ., dete rmin e the loa d P i f a n o ve ra ll fac to r o f s afe ty o f 3 .2 is and d = desired. 1 Fig. P1.47 REVIEW PROBLEMS 1.59 L ink B D c o nsists o f a s ingle bar 1 in . wide and ~ in . t hi c k. Kn owin g th at each pin has a ~ - in . di amete r, determjne the max imum value o f the average norm al stress in link B D if (a) = 0 , (b) = 9 0°. e e Fig. P1 .S9 1.60 Two ho ri zo ntal 5 -kjp f orces are applied to pi n B o f th e a sse mb ly shown . Know in g th at a pin of 0 .8-in . di ame ter is used at e ac h c o nnec ti o n, determine th e max imum va lue of the average nor mal stress (a) in link A B, (b) in lin k B e. 1.61 For th e assembl y and loading o f P rob. 1. 60, d ete rmine (a) the avera ge sheari ng stress in the pin at e, (b) the average bea r ing stress a t e in m e mber Be, (c) th e average bea rin g stress a t B in m e mb er Be. 1.62 Two woode n p lanks, e ac h 2 2 m m t hick and 1 60 m m wide, are joined by th e g lu ed morti se jo int show n. Kn owin g th at th e j oint wi ll f ail w h e n th e ave rage shea ring stress in t he g lu e reac hes 8 20 kPa, dete rmin e the smalles t allowa bl e length d o f the Cllts i f the j o int is to withstand a n ax ial loa d of magni tu de P = 7 .6 kN. 0 .5 i n . Fig. P 1.60 Fig . P 1.62 41 ...
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