cap 1
TRANSCRIPT
C h a p t e r 1
Problem 1.1
3 0 0 m m
2!>G u i m
30 kN
1.1 T T O solid cylindricaj rods AB and BC are wclded together at 5 and loadcd as shown. Kjiowing ihal d. = 51) mm and d, = 30 mm, Cnd average normal stress at (lie midseclion nf (a) rod AB, (b) rod IIC.
6 ^ = 5^.7 Mfti
6 C A 7o£.8£*to'c
6" * WpA -
Problem 1.2
3UkN
1.2 Two solid cyl indrkai rods ^¿f and ¿fC are welded together al 5 wid loadcd as shown. Knowing thal thc avtragc normal stress must not execed HO MPaineither rod, determine ibe sinallest alienable valúes of d, and d¡,
A © .
p r 40 + 30 -jo k\J = 7¿3 y / o 2 ^ -E- - 1 £ 6",
2£, 2 y lo~'L **,
f - 3 o UY] •= 3o*/o 3 N
s ;
- 5 lo
P R O P R T E T A R Y E R I A L 6)2(106 T h e M c G r a w - H i l l C o m p s u i c i , I n c . A l ! righis r e s e i n a i N » p i i r i o P i n i s M a n u i l m a y be d i í p l a j t d , ic¡ii i< J u ^ ^ l <>r d i s i n h u t e d i n any f o r m o r b y any nieans, u-¡itioii( i l ic p i i n r w r i i i e n p p r m t s s i o r i o f rhc p u b h s h e i , o r used b c y o n d ihe IHM^LII d i s t r i b i i t i o n 10 i cachcis am1 cr fucators p e i m i l l e d h y M i ^ C i r a w - H i l l f o r I h c i r i n d i v i d u a l c o u r í e prepaíat ion. I f y t m aru ; i - . l i u l p n l u s i n g l i l i s M a n u a l , y o n are u s i n g n \;jlliL¡uL pEnniísioii
Problem 1.3
(a) í?uüi AB-
!.3 Two solid cylindrical rads AB and ÜC are welded together at B and loaded as shown. Determine the average normal stress at the midsection of (a) rod AB, (h) rod ÜC.
3 ¡n. 2 ¡ n - . T í l . i t ) s B
¿ I
6 ' =r £ . - ^ 1 7 . 7 3 30 in.
(Wi RQJ Be.
A B c r -X^- r . 7 r „ ^ a ^ r ,V
' S í .
4
Problem 1.4 1.4 InProb. I .3, determine the magnitude of the forcé Pforwhich the tensilc stress in rod AB has the same magnilude as the compres si ve stress inrod 8C.
1.3 Two solid cylindrical rods/lB and BC are welded Together at fí and loaded as i v > shown. Determine the average normal stress at the midsection of (a) rod AB,(b) rod
_ P 3 J 1 f 6
r 0 . 3 / 8 3 / P
fe?"' 7 , O é S £
¿ o - P
r = -ta t i p s
7. í> ¿ g £ - 0 J 4 I H 7 P
0.318SI P * S.HS&Z- P P - IS.46 K p 3
P k O P R I E T A R Y M A T E R I A L . O T h t M c G r a w - I I i l l C o m p a n i c s , J n í . A t ! r i g h i s reserved. N o p a n o f i h í s M a n u a l m a y b É di&played, r e p r o d u c e d o r d i s i r i b u i c d i n anv fonn o r b y a n y m c a n s . w i i h o u r ihe p r i o r t r i l l e n p t r m t s ^ i c i n n i " the p i i h l i s h e r , o r used b e y o n d ihe J imi ie i l d i s i r i b i i r k m lo l e - i d i e r s and edi icmors pRnT-iiiral bv M i ; ( i r a ^ - H i l l f o i I h s i i i n d i v i d u a ] ecurse p r e p a r a r o n , I f y o n are a &ludcnt u&íng Ihis M a n u a l , you are u&ing i t wiEhout p e r m i s i ó n .
Problem 1.5 J.S Two sieel piales are lo he held together by nituiis of 16-mm-riiametei high-slrcngth sieel bolls íitlkig siwgly insidc cylindrical brass spaceri. Knowing ihat the average normal stress musí not exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the uulcr diameter of the spacers tlial yields the most economical and safe desigrt
. ñ
f o r c é R oi íhz ¡ooJh A+ 4V.e s ^ e -f.^e -fU 5 p 5 L i . f i / - pusAes
<5¡
^ b T f J¿
4
4
¥ i + g a o (16)
Problem 1.6 J.6 A slrain gage located al C o n Lhc surface of bone AB indi cates thul Uie average norma] stress in the bone is 3.SO MPa when lile bone is subjected to lwo 1200-N forces as shown. Assuming the cross section of the bone al C to he annular and knowing that its onter diaineter is 25 mm, determine the inner diameterof ihc bone's cross section at C.
\2i.\l \
Y
A - 6"
^ 1 T T i r
K (4 V u o o l TT ( 3 . 8 0 * ¡O6
A9 ^ I H . 9 3 " / i ? " ' r* 4 =
Problem 1.7
1 3 5 iT] n i - 2 1 0 m m
120 i n m
<150 nm
1.7 Knowing that the central portion of the linfc HO has a uniibrm cross-sectional área of 801) mm^, determine Ihc magnitudi: of the load P for which the normal stress in that portion o f BD is 50 MPa.
A É D - - Soo<io~
D T - S I V J -fVee. tocíy .-f U J y A B O .
P r 8 5
(C.H5oXf~ ^ ~ 0 . I 3 Í T P - o
P-O.Sé^óV^Mon
C2.7 kVJ - « *
L — 1 U j n . — - i — S i n . — j
1.8 Urdí AC has a uniform rectangular CTOOT section { in. thick and 1 in. wide determine the norma! slrtss in the central porlion of the link.
Use f i n e , p p a + e . - h . ^ t + k e ^
c a n s e s c + Mooflí'i*
y-t > 7 M a = o
A v e a . o f -Pi'^k / A C T A - l m / j ¡ ^ O./35" /n*
Problem 1.9 1.9 Each of the four veilical línks has J ;I 8 \ 36- mm uniform rectangular cross seclioij anJ eacri ol'rhe four pins has a If i - mm diame'ei Determine i he: máximum valué ofihe ¡«vLFiiye normal stress in ÜK lirks conrwcting (<¡) pomls 5 ¡uitl /J í'>)points í" and r
U ^ e W A B C o fres W y .
20 *» je ü - O H o s-|
&
I r 8 D
C 0 . 0 H o ) F ¡ o - (O.OIS +-0.&to)(2.oxtc?) ~ O
- (f 0 . 0 4 o ) - f o . £52.5 ) t > 0 y / O 3 ) = O
C a í A - i 3 * o * / o " *
A r ^ e a . "Pe"*1 e>»->£ -Pín k f i C a » - prtí^iOi -
P R O P R I E T A R Y M A T E R I A L . S 2CÍIG T f i e M c G u v . - H i l K , p a m ^ . ( n . A l l r i g h l s r e w r v c . í v 0 p a n o f rhü M i n u a l inay be d i s p l a y e d . CÍJILHILILOI j r d M n h u t e i l i r nny h n n ar b y ony rnoans, w i t h o m i t ic p r i o r w r i K i n p c t m i i s i o n j f the puLlisl i íL, o< used ijCj-íiniI LÍIL' l i m t t e i i clL^Cnbi Kioti ia teachers i n d e d u c t o r ; p e n m t l c d by McGi í iW-Hi l l ÍÜI iLüir i r u l i v n l u n l c ruir^- p r r p j i r n i i o n l l yí-u at.: a n u c í ; n i j í i n g i h w Manu&J, y o n are u s i n g ;t w i l l i u u l p c m i i v , i v n
Problem 1.10 1.10 Two horizontal 5-kip forces are applied to pin H of the assembly shown. Knowing Ihat a pin of D.B-in diameter is uscd at uach connection, determine the máximum valoe o f the average normal stress (a) in link AB, (b) in tink BC
0 .5 i n .
1.8 in. Ose. J i = m + 3 s.s T^ee- iooJy
10 k-'fí
>f S i l b e s
|0 k«p»
/ o ^ 6 _ =
A«t
- F E
A - 3 . 9 6 5 8
0 . 7 r - 7 . 9 6 kfit'
P R 0 F R I E T A B Y M A T E R I A L . © 2 0 O 6 T h c M c G r a w - H i H C o m p j i i i E s , Inc . A l l n g l i i í l e s e i v e d . N o par í o f this M a n u a l m a y be d i s p l a c e d , r e p t a d u c t d or d i s r r i b u i c d i r any f o n n or b y . m y meant,, i v i l l i o u i t h e p r i o r «Ti l len p e r m i s s i o n o f ihe pobl i sher , o r uscd b e y o n d ihc l i m i t e d d i s t r i b u t i o n to t e n c h e r s a n d ettuüü
Problem 1.11 /.// The rigid bar EFG is supported by the truss systera shown. Knowing that the m e n t e Tí? is a solid circular rod o f 0.75-¡n. diameter, determine the normal stress in CG.
Ü
e V F
F0e
C 6
fFG-
IV-,
6 , ce-
CG.
3 tt
Problem 1.12
"LA 8 C
F
i»)
• 1 ( 1 - - 4 ¡ t - - 4 f t
Tíie rigid bar EFC is supponed by the truss system shown Detennine llie cross-sectional área uf rnembLT.4£ for which ihe normal Í I I Ü S S in the member is 1 ksi.
F A S . G - ¿ —
— ^ * _ F P C £ . O Í - J
15" 0 . 4 0 0
F R O P I Í I K I A R V T*1 A T E H í A L ©rt )06THc M c G r a w - U i l l C o u p i i n t i . I n c . A11 n p h r s r e s r r v c d N o parí o f L>,is M a n u a l m«> b e d i ^ i l u j c d í fpnwinced o r d i s i r i b u t e d m any Tcnn DI L y any m e a u s w i i l i i m L (he p n r j j w r n i c n p e r m i s s i o n o f ihc p u b l i s h e i , oí u-al hervund i h e Eimiicd distribuí i o n Lo teacher í a n d eduLritnra p e r m i i t e d by M r G r a w - H i l l f o r i h e i r i n d i v i d u a l COUESÜ i i i t f i d r a i i c i n . I t y o n -ne a ^HnJcni us ing ( h i l MütiuaJ , y o n a í c vMHJ; i l wiihíiui p^nni ís íor i .
Problem 1.13 1.Í3 Two hydraulic cylindcrs are used to control the posilion of the robotic arm ABC. Knowing Üiat tlie control rods attached at A and D each have a 20-mm diameter and happen to be parallcl in the position shown, determine the average normal stress in (a) mcmber AE, (£) member DG.
W A B C
151» m m 2 0 0 m m
i 6 ,
sw 3 1 ^ / 6 « / O -fe - 12.73 x / o ' f *
5 ; B - 13.73 MPa
Use c a « LineJ ^ ^ ¿ e ^ s ASC « ^ J B F D «5 f^ee iacAy.
Fots. s - IS<x> A 3 . W I ¿ * J O ~ F T
ib) 6 D & -
- 4 . 7 7 y/o
- 4.77
P R O P R I E T A B Y M A T E R I A L . © 2 0 0 6 T h e M c G r a u - H i l l O i n i p a n i t s , [nc . A l 1 r i g h l s reserve d. N o p a n o f rhis M e n n a l m a y lie d i i p l a y e d , r c p r o d i : ; e d t u d i s u i b u l e d in any f o r m or b y a n y m e a n \ v i L l i o u : I h e p r i o r w r i t t e n p e m i i s i i o n o f the publi5>ier, o r used beyond ( l ie l i m i l c d d i s i r i b m i o n 10 i c a i h c r s and t d u c a i o r s p c r m i t t e d b y M c G r a ^ ^ I f y . i u a i e a Bludent u s i n g this M a n u a l , y m i are i i s i n j ; i i w . i l m i i i p e m u s s u m .
Problem 1.14
2 0 0 m m
8 0 m m
1.J4 A couple M of magnitude 1500 N • m is applied to the crank of an engine. For the posilion shown, determine (a) the forcé P required to hold the engine system in equilibrium, (¿) tlie average normal stress in the connccling rod SC, whích has a450-mm1 uniíorm cross section.
U s e p¡&fon } r-odj a,*>Jl cv^kaU.
O Z M A = o
V-l - S.ZSll * | O a w
7
H f > 0
50 a =
p = 17. SÉ * l ü 3 ^
17. S í JtfcJ
" So
8C
S + r « S S
fb) 6a £ - - 4 / _ 4 MPa
a ? S ^ ' 0 ™ * T l « M c G ^ - H i l í C o m p » . * . .nc . A l l [ l g l U s ^ r v P „ . N o p w o f * . , M a n u a l « » > h , d i s p J a y . d . r e p r o d u c á
e d u c a , 0 , s b y M í G r a w J " " f 0 [ » B * « " u » l « s u r * p r c p . r « ¡ o n . I f y c a » . « u d e a , « i n g A i , W l I l u a i , y o u „ „ ¡. w i A o w p e r m i s s i ™
Problem 1.15
15 m m .
Stccl 9 0 m m
1.15 Wben ihe forcé P reached 8 kN, ihe woodcn speciinejj show» failed in ehear along the surface indicated by ihe daslied line. Determine the average shearing stress along thal surface at tlie time of faihire.
Ave^ t>€¡n<í sin e e t y ? o
-O -
-i /TI . v i ^ i '
?3 MPa
Problem 1.16 1.16 Thewoodenmembeis/tandeareto bejoined byplywoodspliceplateswhich w i l l be fiilly glued on the surfaces in conlact. Aapart of the deaign of Ihe j o i n i , and knowing that the clearance between the ends of ihe membersia lo be j in . , determine the smallesl allowable length L i f the average shearing stress in the glue is not tr> exceed 120 psi.
H e 518 *¿.*p - f W * . Tt<JS
•p
Trie ' ejfc^c^íje i k e s t r e s s /s f " IZO ps,'
i '
= / a . 3 3 <«.
Problem 1.17
0.4111.
¡.17 A load P i 1 ; applied (o a sieel rod supported as shown by an aluminum piale inlo which a 0.(5-in.-diamelcr holc has heen rírilled. Kjiowing that the sheuring slress must not exceed 18 ksí in the sieel rod and 10 ksi in Ihe ahirainum píate, determine ihe largest load P that raay be applied to the rud.
" K "
A , - 7T J t = TT ( O . ft^O.
A,rt r ( o . 7 r s o V r a . 1
= 13.57 k.'ps
pe*-" í^-fwi^ ; n u
^ A 2
Problem 1.18
25min,-i ^ 5(S m m
1.18 Twowoodenplanks, each 12mmthrckand 225miiiwide, are joincd by thcdry mortisejoiiitsliown. Knowing thal thewoodused shearsoffalongitsgrainwhen the average shearing stress re ac he s 8 MPa, determine llie magnitude P of Ihe axial load
— ifi i n r i which w i l ! cause Ihe joint to fai l .
j - — 16 i i i u i
u/litvi +íi« joiwf -Píii'J's. t-&.c^ +keSí-
/ fs fttíí tai i
5 0 nuil 2 5 ¡ J i m 2 2 ü ¡ iriui
I T
p - -l'Á = t « >t | o £ X m x 10'* ) - I5S4 N - 1-536 JftJ
S i i-i c c
Problem 1.19 l-*" T ' l e a x i a l f < l r c e í n , h e column supportirig the timber beam shown is P - 75 kN. Determine the smallesl allowabfc lengrh / of the bearins piale i f the bearing stress in ihe timber is no! to exceed 3 0 MPa
Problem 1.20
= 1 0 k \
1 2 0 m 1 0 0 r m n
1.20 A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undistiirhcd soil. Determine (a) Ihe máximum bearing stress on Ihe concrete footing, (b) Üie size of the footing for which the average bearing stress in the soil ¡s 145 kPa.
(o./ Beú>- iVicj- Stress Conc e. '3-
^ A
A \ 2 * í o - *
P = 4 D - / O 3 hJ
3. 23 x )o6 P « L
3 . 3 3 - f i
S"* IMS leP*. = 45 « / O * 'P
O" O- a?58G
Problem 1.21 1.21 An axial load P is supported by a short W8 * 40 column of cross-sectional área A - 11.7 i n . ; and is distributed to a concrete foundation by a sqnare piale as shown. Knowing that the average normal stress in the column musí nol exceed 30 ksi and that the bearing stress on the concrete foundation must not exceed 3.0 ksi, determine the side a of the píate that w i l l provide the raost económica! and safe design.
F<?"~ T"Ue -z-aílí
- 117 .V
<X= 7 ^ - VTiT - JO.82:
K 6- 3. o
P R O P R J E T A R Y M A T E R I A L C 2 0 0 6 T h e M c G r a w - H i l l Comprimes . I n c . A l l rights reserved N i i paiL u f l i l i s M a n u a l may be d i s p l a c e d , j e p i o d u c e d o r d i s l r i b u l e d ITI any Jbrm " r by any meaiis , w i t t i o u l the p r i o r w r i f r e n p e n n i s s i c j i o f Ihe p u b l i s h c r . or u s o i b e y o n d Ihe l i ra i ted dis l r ibulLDn t o leachers and educalors p e m i i l l t d b y M c G r a w - l l i l i f o r Iheir i n d i v i d u a l couisc p r c p a r a i i o n . l f y o u are a s i u d c n l u s m g I h i s M a n u a l , yi.ni are usinR i l u r j i h o u i p e n n i s n i m .
Probiem 1.22 1.22 Three wooiien planks are fasrened lugcther hy a series of bolts to f b n n a
column. I h e diamclcr ofeach boíl is 4 in, and the inner díametet of each washcr
i s f in., which is slighüy iarger ilian the diamelc-r of the holes in ihe planks. Determine ihe smallesi allowableouterdiamelcr J o i the washers, knowing thal the average normal stress in trie bolts is 5 ksi and that (he bearm^ stress helween ihe washers and tlic planks musí not exceed 1 . 2 ksi.
8a vi • A L . J , = £ s |
f; - P
t s , r oí e o l i a ^ e 4 e>r - ó¿ = ^ >
d A ui — 6;
Problem 1.23 1.23 A 0.12-mm-díametcr steel rod AB is titted lo a round hole nearend C o f the wouden member CD. Voi the loading sliown, determine (a) the máximum average normal stress in tlic wood. {b) th¿ distance 6 for which tl\e average stiearing stress is 620 kPaon the surfaces inclicaled by thedashed lines, (cj the average bearing stress on llie wood.
i-e -55 "r~W \AJOUA.
A « e f - (7S- 1 2 ) 0 3 ) r |. 13*, u/o3*.*,*. /. m ^ i d ^ r ^
P = 4.50 (íU =• V.Sb* ¡ o 3 V
P
Lf3fyjcr 4
p
3 . ? 7 M P C Í -
- 3
Col
2 i T & X / S * / o - s ) ( « o x / © a )
- Z o . i n o ' P¿,
P R O r R l K T A R Y M A T K R I A L . © i O O S I T i e M c C r a w - H i l l C o m p a n w s , Inc . A l ] r i g h i s K s e r v e d . h l o p a r t o r i h i s M a m i í h t i a y h c d i s p b y e r f . rüprodiiwd cr dr j i r ibui íd i n a n y f b n n or b y any rm:atií h w i t l K ^ t <bc j a i c í ^ n H e i p r m M s s j M i u t ine p u ^ i a h e r , or u;<rri b c v o n d IITJ l i m u c d di&lritiuiio» lo leachers anJ ed jca l i r r s p c r m i l l c d b y M c G r a w - f l i l i frfr i h e i r i n d i v i d u a l ceñirse p r q j a i a l i c i n . [ f y o u m a ¿ii i ífeul usíng th l^ M a n u a l , y o t i are u ^ i n g i t w i i l i t i u r permiss ion .
Problem 1.24 1.24 I he hydrauMe cyWná&tCF, which partiallycontrols the position of rod /J/V, has
been locked in the positrón shown. Meraber^Z) is ¡ in. thick and is connected to the
vertical rod by a •} -in.-díame ter bolt. Determine (a) the average shearing stress in the bol!, (b) the bearing stress al C in member BD.
Ose m e ^ b é f - 3 C D a*> a í f s e kaJy^ u^A viole fk » i AS '<> a -f-wo -forcé M e « i ) í / ' .
— o
C, - ^ ' - ^ g f - ^ - H o o M I S " r 78.3<f A .
~ 10.84* 10* psí
flj") 8e<Wr s-fress * i C / i M É ^ r ó e A 8CD. ;
P 11 9?. 2
Problem 1.25 1.2S A 6-mn\-diamelcr pin is used al connecnon C of Ihe pedal show». Knowing that P = 500 N . determine («) the average shearing stress in the pin, (b) tlie nomina! hearing stress in the pedal at C, (O the nomina] bearing stress in caen support bracket at C.
9 H U I ]
1 2 5 m m
7 5 m m
i
y
-—• j U ü m m - — • -
P
i rÍ,i-, si w £>T ¿ C D .
Since A C D i-i ir-,
o\ 1 be ii'n-es o"f :V>« cjf -f-Kc ^ / htv -fu/o T~">^ e S . FVoi^ jeoKc-}**y f C E - -[so''*-
1 " 335"muí.
+t ^ = o : % O- - P - o C = ; . C p = (?.£)CfT O C 0
C A d í " U * l L T 3 Y ' 7 ' > < / 0 - 3 )
.i-.'-
- 2.4. / *t° Fe.
- 2 1 . 1 v / o t
24.1 MPa.
Problem 1.26 Knowiiig thal a forcé i 1 of magnitudí 750 N is applied to the pedal shown, determine (o) thediameteroflbepmat (."'for which tlie ave-raye shearing stress in ihe pin ís 40 MPa, (b) the correspondí ng bearing stress in the pedal at C, (c) üie correspondíng bearing stress in (he each iupporl brackel at C.
9 m m
i r ¡2J m m \
- 300 m m •
-«£
he o1
c r—1 D
1 & Í Í H I 1
íJ.iíii^í-t— o í Ac! D -S í « c
J e A C D is ex.
T a W f i i r PI P " i «
oí 4 t s oí" í i f { i o > i of i\ix C-4k?í Iwo "füif-í* S -
* »' X U
c
Frcr-i cj fio i *~e1 »'y j
4c
C - P = o
(a1) Tr,, -
C Ai
c ir f I D » / O ' )
Problem 1.27 ) .27 For the assembiy and loading o f Prob. 1.9, determine (<z) the average shearíng stress in Üie pin at B, (b) the average bearing slress at B in mcmber BD, (c) the average bearing stress al B mmmribei ABC, kiiowingthattiiismemberliasa 10 * 50-mm uniform rectangular cross section.
1.9 Each of the four vertical links has an 8 » 36-mm uniform reclangular cross section and each o f the four pins has a 16-mm diameter. Determine the máximum valué of the average normal stress in the links coiineciing (a) points B and D, (b) points C and £ .
0.01b O.O'io
B c 6D
Peo « * /o3 N
0>) 6 lí 8D A = c J í = (o.oi6)(o.oo&)- !2g W o ' 6 m
6 A 128 * ,0 6
A = dt - (o. oié)(o.cio) - /eo*/o" c w
l
2
P R O P I t l E T A R Y M A T E R I A L . O I 0 0 6 The M c G r a w - l I i l l Companies , [ n c . A l l r i g h l s icseneá. N o p a i l o f l h i s M d n u a l m a y b= ilisplayec), l e p r o d u c e d iirili-.Lnhtile<1 i n any t o r m o í b y ony m e j i n s . w i r j i o i u Ihe p r i o r w n n e n p e r m i s s i o n o f Ihe p u b l i s h c r . o í used b e y o n d Ihe l i m i ( e d distribución 10 Icachers a n d e d u t a l o r s p c m n t t e d b y M c G r a w - H i l l f o r t h e i r i n d i v i d u a l cour&e p r e p a i a l i o i i . I f y c i i i a i e a s l u i f s n i usinj* Elu-. M a n r u i l , y o n are i i s i n g i i wí lhom p c m n s s i o n .
Problem 1.28
0 .5 i n .
1.3 i n .
\2S i-'orlheassembly and lofldingof Prob. t.\0, determine (a) the average shearing stress in the pin at C, ib) Ihe average bearing stress at C in member BC, (c) the average bearing stress at B in member BC.
1.10 Two horizontal 5-kip forces are applied to pin fi of the assembly shown Knowing that a pin of 0.8-in. diameier is uscd at each connection, determine Ihe máximum valué of the average normal stress (a) in link Afí, ib) in link BC.
Usa ^ J O Í M + 8 as -rVee \¡oAy l o kips
Lo,*/ o £ S i n e s
O k!f>s
JO sin HS°
Fe<
Cb) Be^vV.^ Stress co/- C «V ^e-^le^ 8C
A " t o l - ( a r X o . S l - O-f i V
A
61 = 8 . 1 ¿ S 8 \Ll¡ te;
r r i O r R I E T A R Y M A T E R I A L e 2 0 C 6 T h £ M c G r a w - H i l I Q i m p a n i e s , I n c . A l l righls i c s c r v e d . N u p . n o f rhis M a n u a l m a y b c disuJaycit, r e p r c d u c c d i i r r i i ^ t n b u t c d i n any f o n » o r b y a n y ineui is , w i t l i o i i l the p r i o r w r i l l c n p e i i n i s i u i r n i r t h e p u b l i s h e r . o r used b e y o n d ll ie b n i i e d d i s l r i b m i c n l o t cache rs and edúcatela p e t i i u i i e t l b y M c f j r a ^ - H i l l f o r I h e n i n d i v i d u a l t i n i f i p preparación I f y o u are a s l u J e u l i i ^ i n ^ rhis M a n u a l , y o u are usir tg Ll w i i h m i i p e r m i s i ó n
Problem 1.29 1.29 Two wooden members o f uniform rectangular cross section are joined by the simple glued scarf splicc shown. KnowingthatP = 1 1 k N , determine the normal and shearing stresses inthe glued splice.
p r )J kKi = 11 « J O 1 N
C - 4 8 ^ UPA
2K
4 S ? W O 3
Problem 1.30 1.30 Two wooden members of uniform rectangular cross section are joined by the simple glued scarf spliee shown. Knowing that the máximum allowablc shearing stress in the glued splicc is 620 kPa, determine {<i)'the largest load P tlmt cali be saíely applied, (6) the corresponding tensíle stress in the splice.
0 = 10° - 15° = HS°
&9.o kp^ = GZov¿<f Pe r
t
6
p -
2 A F L
(I.ZZ*lO - 5
¿2o /o3
Problem 1.31 1.31 The 1.4 kip load P in supported by two wooden members <\f uniform cross section thal are joined by the simple glued scarf splice shown. Determine ihe normal and shearing stresses ín the glued splice.
3 . 0 i n
¿ _ f i . O i l l
' t í
P - \HQO ib
P c ^ e G = (,'Huo )(cos 3o"')*'
15
C2X IS"")
6"- 7o.op*¿
Problem 1.32
^ S . u i n .
/.52 Two wooden members of uniform cross section are joined by the simple scarf i p l ice shown. Knowing that the inaxihuirnallowable (ensile ¿Ircss in the glued splice is 75 psí, determine (a) the largest load P that can be safely supported, ib) the corresponding stress in the splice.
1 'r
y.
6" *
=10° -Ca r 3e>'
(a) P -b"_A„
O © ¿os 1 3o" P ~ 1 , 5 0 0 ¿<.ps
P l t O r R I E T A R Y M A ' I K K I A l , © ? 0 0 6 T l i e M c G r a P - K i l l C o m p a m t r s , I n r A l l nghts reserved. N a p a r t o f ibis Muim¡.l i i i n y b í d i s p l a y e d , r c p t o d u c e J i» l i i s i r i l i u f p ^ i n a i iy f o m i or by any mcnuis, w i i l i n n i tlic p r i o r wri i r . cn permiss ion o f the [aii iJ i .^icr, o r used b e y a n d the l imitcc l JÍSIUIJUEHTI in teachers nnd cducalors p e r m r t l e i i L y Muí l n i w - E l i l i fcr íheir i n d i v i d u a l cou .se |nu[Hin.i]c.n J f y o u a r í a s tudem u i m j " í l i is MÍIIU.LI, y c t i are uíirlg íi w i i h o u l p s i m i s s i u n
Problem 1.33
5 m m
1.33 A sieel pipeof 300-tttinouíerdiameteris fhbrícated from 6-rnm-thick place by welding along a helix that forms an angle of 25" with a plañe perpendicular to the axis of the pipe. Knowing that a 250-kN axial forcc P is applied to the pipe, determine the normal and shearing stresses iu directions respectively normal and tangeniial lo the weld.
» f& - t = 0. 15o - O. OOQ, = ü . 14 4 m
- ZTox/o* eos* ¿5 ^ 3 "
= - 3 7 - ' * / í > ' 5" = - 37.1 MPa.
ZK 5 L N * E
-•-17.33 Í Í / O '
Problem 1.34 1.34 A steel pipeof 300-rranouterdiameter isfabricated from 6-mm-thick píate by welding along a helix thai forms an arsglc of 25" wi lh a plañe perpendicular to ihe axis of the pipe. Knowing that (he máximum al lo wabie normal and shearing stresses inthe directions resptUivcly normal and tangential to the weld are a= 50 MPa and r = 30 MPu, determine the magnitude P of the largcst axial forcé Ihal can be applied to the pipe.
r ¿ ~ r o - t = o . i s o - o*oot> = 0.144 *
•£ t - ¿o 3 A - t :
e o s "
2A t
S i " -5o"
337 x i c f
434 x/a
Problem 1.35
6in.
1.35 A240-kip load Pis applied lo Ihe granile block shown. Determine theresulting máximum valué of (al the normal stress, (b) the shearing stress. Specify the orieniation of the plañe on which each of these máximum valúes oceurs.
COL*) M»^O T&ist'it s-fr«i4 - O o^t & - fO"
r i f i ó . to-pt-e-is (Ve s4r-es¿ - £ . 6 7 /¿ai" -
Problem 1.36 i .3 6 A centric load P is applied lo the granile block shown. Knowing that.the rcsulting máximum valué of the shearing stress intlie block is 2 . 5 ksi. determine (a) Üie magnitude of P, (b) the orientation of the surface on which the máximum shearing stress oceurs, (c) the normal stress exertedontlte surface, (tf)Úvs máximum valúe o f the normal stress in the block.
Sin %& = / Z8 ~ ¿10° O - 45"° Cb)
6- - £ ^ " A,
^ ^ S ^ ^ = -/fio . , g k • SAo ( ¡ O O O
3 &
P R O P l í t E T A R Y M A T E R I A L , O 2006 T h e M c C r a w - H i l l C o m p a n i e s , Inc . A N n g h h n i surv in l N u p a r l o f l h i s M a n u a l m a y be d i s p l a y c d , r e p r o d u c i d 01 d i a i i i l m l i a l in jin> j i j n n o r b y any means . w i i h o u l ihe p r i o r w r i n e n p e r m i s s i o n o f Ihe p u b i i s h e i , 01 u s e d b c y o i i d t h e h i t i n e d d i s l i i l i u l i n n li> l e , n : h e r s n n d cducalors p e r m i t i e d b y M c G r a w - H i J l f o r Ihei i" i n d i v i d u a l c o u i s c p ie i iara i ims i l y o n ;UP a s índenl u s i n g <his M a n u a l , y o n 3re cising 11 w i t h o u i p c n t i i ^ s i o n .
Problem 1.37
i 1 1 I . t I t KM • a -:
A « B
A Í 7 I.ink ^ f l i s l o he made of a sieel for which the ultímate normal stress is 450 MPa. Determine the cross-sectiona! arca f o r ^ f l for which the factor of safety w i l l be 3.50. Asstime that the link w i l l beadequatelvrehiforcedaroimdthepinsat^ and B.
na
* 6 > *s& y la*
X
P K O P W E T A m M A T E R I A L . © 2 0 0 S T h c M c G r a w - H i H C o m p a n Í e s , ] n c . A l l r i g h t s reserved, N o p a r t o f l h i s M a n u a l m a y be d i í p l a y e u , r e p r w h i c r d or disthbueed i n any f o i m o r by a n y itreans, w i d i o u i ihe p r i m a ñ i l e n p e r m i s s i o n o f i h e p u b l i s h e r . o r used b e y o n d the l i m i i c d d i s L n b u i i o n lo leachers and educarors p e n n i t r e d by M c G r a w - H i l l f o n h e i r i n d i v i d u a l t o u r s c p r e p a r a l i o n . I f y o u a i e a s h i d e i i t u s i n g m i s M a n u a l , y n u a r e u s m g ít v j u h o u i p e r m i s s i o n .
Problem 1.38 1.38 Tlic horizontal linkBC is j in. thick. has a widlh w= 1.25 in. . and is madeof u *teei wilha65-ksi iiitiniale slrength in tensión Whai is ihe facior of sufcly i f ihe struelure shown is dcsígned lo support a load oíP = 10 kips?
D / /
l£>it. •O % M c - o
o
Problem 1.39
- o
1.3t The horizontal Jink BC is j in. thick and is madc of a steel wilh a 65-ksi ultímale slrength in tensión. What shouldbe the width w of the l in t i f the siructurc sho™ is 1 0 be dcsigned lo support a Ioact;>= g kips with a factor ofsafcty equal to 3?
(17 i** 3 o D ) u - 0 * s . * 3 < O G 0
FAS = k ; p s
S i Anp t w
W -
P R O P R I K ' t ' A R Y M A T E R I A L . © 2 0 U í > ITIP M c G r a w - H ü l Compajnes , I n i A I I r i g b i s reservcd. N a ( U i L o f l r n i M a n u a l m a y b e d i s p l a y p t l , r e p r o d u c i d or d isrnf tu ied in aiiy f u n u ' i r h y n n y m c a n s , w t f r w i t tlic \ i f i n r ^ r i a f í i f i c t r n i H i c m Ú\c nahünher . o r u i r ^ b e y o n d Ave I m v i r r t risi<T>b\>iÍNir« 1o I r a t l i c t ^ inri cducaUjr^ p e r m i i i c d b y M c G í a ' v - H i l l A>r r h p i r i n d i v i d u a l course pjt¡ jarcilinn I f v o u are a srudcJiL us ing l lns M a n u a l , y o u are u s i n g n w i i h o n l p e r m i s s i o n
Problem 1.40
-2AQ m m - * l - « - 2 4 ü m m -
1.49 A steel loop^-ffCZJoflength 1.2 m and of !0-mm diameteris placed as shown around a 24-mm-diamulcr aluminum rod AC. Cables RE and /)!•', each of 12-rnm diameter, are used to apply the load Q. Knowing tliat Ihe ultímate strcngth of the sieel used for the loop and the cables ¡s 480 MPa, determine the largest load Q that can he applied i f an ovcrall factor of safety of 11 is desired.
* Q
ü
Qo - 6¿A - ^ f s f * * ( ^ O ^ I 6 £ ) í ( o . ( ? a f r ^ . ^ / o 1 N
AAíL J i e i * J a = ^
P R O P R I E T A R Y M A T E R I A L . O 2006 The M c G r a w - H i t l C o m p a n i c s , Inc . A l l r i g h t s reserved. N o p a n i i l ' l t i i s M n n u n l m a y b e d i s p l a y c d . r e p r o d u c e d u r i l i s t n b t i l e d i n a n y íorm o r b y nny meons , w i r h o u l Ihe p r i o r w n t t e n p e r m i s s i o n o f the p u b l i s f i e r , or usec beyonrJ the l i n i i t e d disüibut ion ni l anché is ano educators p e r m i l t e d b y M c G r a w - H ü l f o r (he i r i n d i v i d u a l couise preparálioii Ff y o n are a sLudcnt u i i n g i h i s M a n u a l , y o u are us ing h wi ihQUt p e r m i s s i o n .
Problem 1.41
-0.75 ni - I
1.4 rn 7 T
0.4 m
T
1.41 Members AB and BC of the truss shown are made o f the same ¿Hoy. f t is known iliat a 20-mm-square bar of the same ailoy was tested to failurcand Ifiat an ultímate load o f 120 k N was recorded. I f a factor of safety of 3.2 isto be achieved fgr bolh bars, determine the required cross- sectional área of (ti) bar AB, (b) bar/id'.
Use e«+>Ve j - f ^ s as o -Pree fee»iy
1 . 4 - ( o . i r ) U s ) = o Ay^iskh)
Ay«>?8 kN
Ust j o ¡ ^ 4 A A S -pret looJy
p . Co.ss-)Qs) . | 7 k W
ras - ú í 7 5 - - ' / * * N
29 kK>
o . »
A t o . & r
F e - T-"iie tnaL.'ft<f\a.$ J j L A
IRQ WQ 4-0O x / O - 1
p-5 - = . G Q A A g (CL ! F Ú - T i-«iv\i)e<s AB
SI
K b ' " F * .
212,-33 ^
AAC~ 2)3
PKOPRIETARY MATERIAL © ¿Üíifi Hie McGrcw-Hi]] Companics, lnc AJI righis reseñad No pail tifiliis Manual may bt dJiplayul fepraJuccd or új'tjibjted ui sny Hirm orby any mrans, ^IIJ-JOILI ihe ptnn wn'irj] permistión cf ilic [luhhvhtr arused l?:ycmi Uie Jjnnie<I riisintinicm lo itechtis amf educaiorí ptrmiiiíd by MtGraw-HtlJ Tur iheir individual comst prepaiaiinn, If y MI are a siudtnl using [fus. Marme], y&u ate uauig if ithour permission-
Problem 1.42
1 . 4 m
1.42 Members AB and BC oí" the truss shown are made of the same alloy. It is known that a 20-mm-squarc bar of the same alloy was tested to fatlure and that an ultímale load of 120 k N was recorded. If bar AB has a cross-sectionai área of 225 m m ' determine (a) the factor of safety for bar AB, (b) Ihe cross-section al área of bar AC.\f it is lo havc the same factor of safety as bar/15.
Ur A B
ha - -¡0.7SZ± O.H** = 0 - 8 5 " ^
Ose e i - h ' r e f w s s a s a kocíy
1 . 4 A x - <¿¿.7S')(2S') = 0 A * - \S k N
A v - 22 =O
U s e j o u t A t x s ív -ee bs*Jy
Ftí>r He •fes'f loAr
(CL) Foy bar- A 8 F.S-
j a A i-loo wo"*
5 a l=>a 17 " / O 3
R S . =r 3 . R 7
( U F o r i w AC F . S . = F¿ _ _§>A
Je
* 60 3 O 0 X / 0 *
P R O P H I E T A R Y M A T E R I A L 9 2006 The M c G r a w - H i l l C o m p a n k s , I n c . A l l righis reserved. N c p a n o f l h i s M a n u a l m a y be d i j p l a y c d , r e p r o d u c i d OJ d i & l i i b u t & d n i any f o m i 01 by any ciieaiis, WÍIIIGUI (he p r i o r w i i t t e n p e u m s ^ m i i o f (he p u b l i c a , cir ii eil bKvimji Ihe h m i l e d cJisIribtitLon l o leaehers a n d educators p e r m i u e d b y M c G r a w - H i l t f o r l h e i r i n d i v i d u a l course p r e p a r a r o n . I f y a ü are a gtudent us ing 1hi5 M a n u a l , y o u are us ing i l w j t h o u l p e r m i ^ i m i .
Problem 1.43 1.43 Three sieel bolts are to be used to ariacli ihe steel píate shown to a wooden beam. Knowing that tlic píate wi l l support a 110 kN load, that the ultímate shearing stress for the steel used is 360 MPa, and tlial a factor of safety of 3.35 i¿ clcsired, determine 'he retjuired diameter of (he bolts.
\ 1 r f 1 1 o V . \
- V» _ F u
T i % ,
Problem 1.44 1.44 Three 18-mm-íliameter steel bofe are tobe used lo attach tlieslce! píate shown to tt wooden beam. Knowing that tiie piale w i l l suppott a 110-kN load and that the ultímate shearing stress fot Ihe sieel ttsedis 360 MPa, determine the factor of safety for this design.
- 25<t.<í7xlOC ^
= m - v s y / o 3 w
F e - ^ t o ^ o í S e j e 4 y
P " l l o » l o 3
F . S .
P R O F H I E T A R Y M A T E R I A ) . . f £ ? f l i J É 7 h e M - G r a ^ v - H i l l l l n m p B m e ^ I n c A [ l i r i j l i t i l e s n v n l N o p a n o f i t i i t M a n u a l m i y be «jispteyed. r e f JUJULLJ t j d i s i i i K m i e i l i n j inv f o m i or b y a n y m t a i i s , ^ l í h o u t i h e p r i o r w r i l t c n u t i i i i i . ^ K i n o f ihe pubJishe 1 . , o r used I i u y c i n i tlxc l i m i t e d distuliuíiun to icachcrs and íducators p c r m U t t t J by Mc! Í j ' i i " ' -Hi ] f fot Ihetr i n d i vi-ituul coi irse preparación líycn ait: n s í i idrnl u s i n g l i t i s M a n u a l , y n u nre u s i n g i i v/iUnnjt j ieriTiission
Problem 1.45 ÍAS Two plates, each j in. thick, are used to splicc a plástic strip as shown. Knowing that the ultímate shearing stress of Ihe bonding between the surfaces is 130 nsi, determine the factor of safety wifh respect to shear w h c n i * = 325 Ib.
F-S. - £ . f f f - U Í O O
Problem 1.46
5 . 5 ¡ n .
1.46 Two wooden members o f 3.5 * 5.5-in. uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that the máximum aIlowable shearing stressinthc glued splice is 75 psi, determine the lurgesl axial load P that can be safcly applied.
3.5 i si. f\0 = (3,S)(5.S) r 13 .25-
Y - - f - S i \ & e . * * © = j^L 5 l V ' ^
4. 4? t ^ .
P K U l ' H I t ' . T A R Y ÍMA'I K . H P A I . O Z(KJ6 T l i u ML(Í Í ! I IV-HIII ( . , nmp¡!iiies l Inc . A i l righi= reserved. N o par ; o f ih i s M a n u a l m a y be d i s p l a y e d , K p t o d u c e d o r d i s t r i b u l c d i n any f o m i or b y any means, w i t h o u l [he p r i o r w r i l r e n p e r m i s s i o n o f ;he p u b l i s h e i , 111 used h i ; y n r i i l l l i e Junileri ihs inbuí ion l a leachers n n d educatorc p c r m i i t c d by M c G r a w - H i l l f o r ü i c i r i n d i v i d u a l conree p re paran on. J f y o u are a s t u d e n i u s i p g i h i s M a n u a l , y o u are u s i n g i i vv i lhoul p e i m i s s i o n
1.47 A luad P is supported as shown by a steel pin that has been inserled in a short wooden member hanging from llie ceiling. 'ITie ultímale sirenyth of Ihe wood used is 60 MPA in tensión and 7.5 MPa inshear, whiie the ultímale strengthol the sieel is 145 MPainsliear. Knowing that h = 40 mm, c = 55 mm. a n d J = 12 mm. dctermin. the luad P i f an overall factor ofsufetyof 3.2 is desired.
B a s e d qv\ s J o - j í a í e i* p i n
P, - A <S0 = w ( b - ¿ K _
= 3 3 . o x/o 3 N
Use sr^Jhd PQ - 32.8 */<>J ^
? B O P R J E l A K > M A T K R I A L , £>20()ú The M c O r a ^ T E i l l C o m p a m c s . Inc A N n r , M s r e ^ r v c l N o p a n o í Lhn M a n u a l m a y b r d j . p l a y a l . r^produced i n d i s t r i b u i d in any f o n n o r by any lucans. w i t h o m ihe p r k i r u n i i e n j .üuii issiai i o f xkc p u b l i - h c r , used b e y o n d i h e Limticdl d i s t r i b u y e n l e r i c h i j ^ and <Jucai0i3pemilni-A b y M c í j r a v ^ H i l I lur l l i c i r i n d i v i d u a l coUr&E preparal ícn . [ f y n u a r e o st«cttím UÜIFI_«> tf i is M a n u a l , y o u a i s u s i i i g i( w i l l i o m p c n t u i s í o n .
Problem 1.48
Co) T e n s i ó n i* vJood
1.48 For the support of Prob. 1.47, knowing that the diameter of Ihe pin is d = 16 nirn and that the magnitude o f the load is ¡ ' = 20 k N , determine (a) the factor of safety for the pin, (6) the requíred valúes of b and c i f the factor of safety for the wooden members is the same as that found inpart a for the pin.
1.47 A load P is supported as shown by a steel pin that has been ínserted in a short wooden member hanging from the ceiling. The ultímate slrengrh of the wood used is 60 MPa intensión and 7.5 MPa in shcar, wbile the ultímate slrcngth ofthe stcel is 145 MPainshear. Knowing thal b^ 40 mm, c "= 55 nun, ¡má<i= 12 mm, determine dic load P i f an ove-rail factor o f safety of 3.2 is desired.
-<3
b = i +
p = 7.0 k i N í ^ I D * N
r r _ R L . ¿ T i ? , 3 3 6 * / O * _ - - —
P U = £ S . 3 3 & x t o 3 W 4 V F.S.
H 6 . , 5 * . 3 3 6 y /Q"
2A
c -
eac-L) ^ e a ís. A =
_r3__ 3 w c
2 w t o ' t¿XO*Qlo)(?*S*¡0*)
P R O P R 1 E T A R Y M A T E R I A L . © 2 0 0 6 T h e M c C r a u - I I i l l Compair ies , Inc . A l l r ighrs reserven. N o parí o f ib i s M a n u a l m a y be d i s p l a y e d . r e p r o d u c e d
or d i s l r i b u l c d i n any f o r m or b y a n y mesns , w i l h o n l I h e p r i o r w n l l e n permissic in oT I h e p u N i ^ L e i . ai u s t d J:eyoiLd [he IITTHIHI [ f c l i i h u l i n i i In l is icl iers and
educaiois pe i i iuLled b y M c G r a w - H i l l f o r flieir i n d i v i d u a l oouisc p r e p a r a l i c n . I f y o u are a s iudert i u s i n g d i i s M a n u a l , y o n are u s i n g i ; w i t h o u t p i r m i s s i o n .
Problem 1.49 1.4? A steci piale j¿ in. thick is embedded in u horizontal concrete slab and is used lu anchor a high-slrcnjíili vertical cable ai shown. Ihe diameter of the hole in the piale i s f in. , Ihe ultímate slrcngth of the steel used is 36 ksi, and the ultímate honding stress belween piale and concretéis 300 psi. Knowing that a factor ni safety i jf 3.60 is desired when P =2.5 kips. determine (a) the required width a of the píate, (f>) ihe mínimum deplh h lo which a piale of lliat w idih should he embedded in the concrete slab. (Ncglert Ihe normal stresses between the concrete and (he lower end of Ihe piale.)
7.5 k.'pt
A = ( a - á ) t
Fu •= 6» A
• • p P
(cO CX. ~ I. SS'O . —
le sJU
Pa-'TuA = ZTuCa+-t)b' F . s . -- P¿ P
P K O P H I K T A R Y M A T E R I A L , T h e M c C n a w H i l l C o m p a n i c s . Inc . A l l n g h t s i e s e i . e d N o parí o f l h i s M a n u a l m a y be d j i rila yeri, r e p r o d u c i d o r d i s t r i b u l c d i n any f i i n r i t u hy any meai i5 , w u h o u l Ibe p r i o r w r m e i i n c n r . i s s i o n o f dio p u b l i s h e r , or used b s j o n d l i i i : üinited d i s i r i b i u i o n lo tcacl ie is añil cduci i io ts p c r m i i t c d b y M c G i a w - l l i l l fo t l l i e n m i l i v i d u a l conrsc p r c p a r a l i o i i . I f y c u a i c J sLudcnt u s i n g I h i i M a n u a l , y o u are us ing i i w i i b o n t f í m i i s s i o n .
Problem 1.50 1,50 Determine tlie factor of safety for Ihe cable anchor in Prob. 1.49 when P = 3 kips, knowing that a = 2 in. and h = 7.5 in.
1.49 A steel ylate ^ in . thick is embedded in a Iwíiionta! concrete slab and is used to anchor a high-strength vertical cable as shown. The diameter of the hole in the piale is 4- in. , the ultímate strengtli of Ihe steel used is 36 ksi, and the ultímate b und i ng stress between píate and conercic is 300 psi Knowing ihal a factor of safety of 3.60 is desired when f' = 2 5 kips, determine (u) the reqinred width a of Ihe píate, ib) the mínimum depth b lo which a píate of that widlh should be embedded in the concrete slab. (Neglect the normal slrcsscs between the concrele and the lowerend oí'llie píate.)
3 kl'pS
S o - s e d s i s e a r b e i w ^ e r - i p - P a f e c o o c ^ e - f e í ^ a t
- f w A = C O . 3 0 0 > Í 3 ^ 6?) - J O . 4 ! Jo'pr
F R O P H I K l A K V M A T E R I A L © 2 ( j n 6 T l i e M c G r a w - H i f l C o m p a t i i c i . I n c . A l l r i g h i s r e s í n i d . N o p a n o f I tus M a n u a l ™ y b e d i s p l f i y e d , r e p r o d u e c í or di í i r ibuted w a n y forra o r by any mcans , w i d i o u l fhe p i i o r w r i i r i : n p e r m i s s i o n o f i h f p u b h s h c r . o r u W beyond t h e l i m i i c d c i s t r i b u r i c i i l o l e a c h n s and eduenrors p e r m i l t e d b y M f C r a w - H i l l f e r i h e i r i n d i v i d u a l conree p r e p a r a d o r I f y o u a r e a s tudent m i n * i lus M a n u a l , y o n «re u s i n g i l w n h o u t permis t ión
Problem 1.51 1.51 Link AC is made of a steel vtitli a65-ksi ultímale nurmnl stress and has 1 7 «
2 - in. uniform rectangular cross section. It is conneeted to a support at A and lu
member BCD at C by f -in.-diameler pins, whilc member III. 'D is conneeted to its
support at by a -in -díameterpin, all of the pinsare made of a steel wíth a 2.5-ksi ultímate shearing stress and are in single shcar. Knowing thal a factor of safety o f 3.25 is desired, determine me laigest load P Ihat can be applied at {>. Note that link A C is not reinforced around the pin holes
6,
Use JV« B C D .
e n
+3 M c = O : - 6 E , - 4 P = O
-3 P ;
Cz)
6T
S i. £ rS
F ^ - ( O P - ( o ^ o s - s s X o . s s w ^ o „ 4 / £
hSUout+JJ* i / c J U * e."f P ;» f i e s^UL^ ^ c J u e . P e o . 3 a o k ; p s
T R O r H l E T A R V M A T E R I A L . C KKKiTte M c G i a w - H d l C o m p a r a ; 1 , hte A l l r i j l i c i i c e i v e d NLI parí i»r~Lhis M a n u a l r r i y he í h s p l a y ; d , reproduced o r . l i s l n b i i t e d i n nny f o r n i or b y any m e a r i . u . i t f iou( Iho p r i o r w r i i ' . g i i p e r m u i i c n o f t h ; p u b l i s h i r , o r used b e y o n d (he l i . n i ' e d i i i l r i b u t i o n lo tcaclieis and e d u c a r o n penmlTed by IVkCjraw-Hiíl íoi rhcn i n d i v i d u a l u u v r ' c l u ^ r w n i i u m r i y i . n . i r t . i - . n i i l r n i u ' . i r ^ ib i s M a n u a l , y o n are u s i n g ir w i i n o u t p e r m i s i ó n .
Problem 1.52
E in.
8;
le
1.52 SolveProb. I .5 l ,assujninglhal Ihes i j^ctmehasbeenredes¡gnedtou5e 17-in.-diamclcr pins al A and C as well as al B and that no other change has been made.
1.51 Link AC is made of a steel with a 65-ksi ultímale normal stress and has a j *
7 in. uniform rectangular cross section. It is conneeted to a support at A and to
member BCD at C'byf-in.-diameter pins, while member BCD is conneeted to its
support at B hy a -in.-diamcler pin; all of the pins are made of a steel with a 25-ksi ultímate shearing stress and are in single shear. Knowing that a factor of safety of 3.25 is desired, determine the LtrgcsLluad P that may be applied al D. Ñute that link AC is nul reinforced around the pin lióles.
O ^ H B = O- C^&Kc) - 10 P = O
P » O.fft F ^ 0 1
8 ^ § P i
F n ^ ( t " l P ^ (O.Yítfo.S'gM* i* = fc.pj
P H Í J F R I K T A R V M A T E R I A L © 2 0 0 6 T h e M c G r a w - H i l l C o m p a n i c s , Inc A l l n g h i s reserved N o p a n o f this M a n u a l m a y be d i s p l a y e d , i c p r o d u c e d or di£lr ibul :d i n any f o r m o r b y any means, w j l l i o u l the p i i o i t i t i l e n f i c i r n i s s i o i i o f Uie p u b l i ' i h t r , o r t i s & l Éieyond ihe I r n i j i e d t i s t r ibu d o n to leachers a n d edueatars pcrrníiic-d by M c G r a v v - H i l I f o r t h c i r i n d i v i d u a l t o u r s e p r e p a r a i i o n . I f y o u are a student u s i n g I h i s M a n u a l y o n are us ing if w i U m u i p n r m i s s i o n .
P r D b l e m 1 . 5 3 1.53 In the slrueturc shown, an 8-mm-diameter pin is used at A, and 12-nim-diameter pins are used at B and D. Knowing ihatthe ultímate shearing stress is 100 MPa at all connections and that the ultímate normal stress is 250 MPa in each o f the iwo links ji.'íiiing fi and I). determine the allowabk load P i f an overall factor of safety of 3 0 is desired.
-200 m n — ( — IbO i n m - * j i ; i ^
1 )
A B C
A B C
'°1
Sfah'cs. • U s e A B C < .s T-Ve-e bocly.
A 6
al 8 mm
12 mm-Fi rint view
-8 mm
i D
Mide view
f " * Feo
= o 0.2o F f l - 0J8 P = O
A F.S. " 3.o
P ~ =- 3.73 * Í O j N
A = - f (0.0(3? r /13.1o
F. S. 3- o
r s D F .S. 3. o
Va.) J e
2 6 . 7 ^ / 0 S
3 . 7 2 W o * A I
3.72 k/0
Problem 1.54
Top vicw
-200 m m - 4 — 1!>0 mm
1.54 in an altcmali ve designfor the structure of Prob. 1.53, a pin of 10-mm-diameter is to be used al A. Assuming that all other spccificalions remain unchanged, determine the allowable load P i f an overull factor of safety of 3.0 is desited.
1.53 In the structure shown, an 8-mm-diameter pin is used at A, and 12-mm-diaméter pins are used a t5and D. Knowing that the ultímale shearing stress is 100 MPa at all connections and that the ultímate normal stress ¡s 250 MPa in each of the two linlrs joinmg B and D, determine the allowable load I ' i f an overall factor of safety of 3.0 is desired.
- a l ... i
T 1 )
—rH i A S Stafi'cs
A
Use A B C e s íVe« b o J
ñ
y
D
-20mm f r ñ r u i n ->
Front view 12 mm -
8 mm
Sidc
l~A Feo
? M B - o o.zo F « - o . f& P - a
Z M A = o O.lo R » - o . S S P = o
P " y ^ r F B » B c L s e d o n d o ü L l e s K « c t ^ p í * A
A F . S . 3 . ü
p = ^ FA =r *ÍO* N
F - 3 £ ¿ _ flO6oo*/oc)0i3.fo»fo"*> _ T C Í I V I ^ M • e D — F S " ~ 3~o ~
P = 7 ^ FfeD = I 4 . 0 ' i > j o 3 A/
3 - 7 7 K M
Problem 1.55
Fri nt vie-A'
18 mm
1.55 III tlie slce! sinicture shown, a 6-mtn-dÍamcter pin is used at C and 10-mm-diameter pins ate used al B and D. The ultímale shearing slress ¡s 150 MPa at all conneclions, and liie ultímate normal stress is 400 MPa in Jink RD. Kjiowing that a tactor of safety o f J is desired, determine the largestload P that can be applied at 4. Note íhai link BD is not reinforced around the pin hules
O s e - f r e e \>oJ*f A B C .
0 " S M t = O :
p - c a o F,», = O
-•—160 mm
- 6 rr.m
I B
Sí He viev.-
O . I t O P - Ü J 2 0 C = O
P - i c
F ,
= 5" A , J O - A .
9 C^0*<O%Y(O*Xl<B-\0)Qo'^
. S i l e i " p * *fl <vf
P- U 8 S
Probfem 1.56 1.56 Solve Prob. 1.55, assumtng that the structure has been redesigned lo use 12-mm-diameler pins at B and D and no other change has been mude.
1.55 In the steel structure shown, a 6-nini-diameter pin is used at C and 10-mm-diameter pins are used at H and 1). The ultímate shearing stress is 150 MPa at all connections, and the ultímate normal stress is 400 MPa in link BD. Knowng that a Factor of safety o f 3 is desired, determine the largest load P that many be applied at A. Note that link BD is not reinforced around the pin holes.
Frunt vicv
-IS mu
U_se. free WUy A S C .
-6 mm
-160 mm - -120 mm- S i J e vitw
Trjp vt e\v
0 . 2 8 O P - o.\xo F B D = o
O I M E - o:
pe e-4 5 e c - 4 i ' " v , «V i ^ l c e o .
F.s.
^ ^ ^ ) ( £ , i o 3 X i 2 - , ^ o 3 )
*1.S7 Tlic Load and Kesistance Factor Design methorí is tobe used tosclcct the two cable; that wjl l raise and lower a píatforra suppürtinf/. Uve, window wasliers. The platform weigbts ióO Ib and each of the window washers is assumed to weight 195 Ib with euuipment. Since these workers are free to move on the plalform, 75% of their total weight aud the weight o f their equipniciit w i l l he used as tiie desiim live load of each cable, (a) Assuiiiing a rcsislance factor <P= 0.85 and load factors y, 1.2 and y, = 1.5, determine the requíred mínimum ultímate load of one cable. |ó) What is the convenlional tactor of safety fortín; selectcd cables?
p B r r t p t = <p R ,
9 - X P P + Y ? , , r u -
o . a s
= GZ1 A .
C o n \je^> 4 i ov\ a$ •pA.oio^ o f sa.l : i y
p ^ P D + p L r g o + 0.7S * Z* W
P R O K K I K T A R Y M A T E R I A L . G 200S T h e M c G i a w - H i l l U c m p n m r s , I I K . A l l rigíics reserved. N o p a i t n l l i t i s M o m i a ] m a y be d i s p l a c e d , r e p i u d u L u J o r d i s t r i b u i d ; i n ¡lay for.ni o r by j n y rnuarvi w i t h o m ihc p r i o r w r i i i c i i ¡ x i m i s s i í m ttY'hn pubhsher , o r used b e y o n d rhc l i n u t e d di - . 'r ibn Ison t o (cachera sad ^•lnL"i(on permílced b y M c C n w - l J i l l for, t l i d t ¡ndivuLnal i-euirw p r e p a r a r o n . I f yQU i r é J i t u d c r f USLII¿ i r i i s M m n a l , y o n are ' j s m g Jt u i t h o u t p c r r u i j - i i n r
Problem 1.58
l . S m
*1.58 A 40-kg platform is artached to the end B of a 50-kg wooden beam AB, which is supported as shown hy a pin at A and by a slender steel tod BC with a 12-kN ultimare load, (a) Using the Load and Rcsistance Factor Design method with a resistance factor (p - **.9Ü and load factors y¡¡ = 1,25 and y, = 1.6, determine the largesl load Üial can be safcly placed on the platform. (b) What is the corresponding convenlional factor of safety for rod BC?
r D p D + r L p , = f R
L Y L / .C
P • P D + P L r / . Ü ó ^ g v / O * 4 £„9ZDx)o* 6 . ^ 3 ^ / 0 N
F.s. •= L 7 l á
P H U P K I K i A K V M A J L K l A L . £ TJic M c G r a w - H i l l C o m p a n i e s , Ins . A l l r igh ls rese ived. N o paiE o f t lus M a n u a l m a y be d isptayed , t e j u o d u c e d o r d i s t r i b u i d in any f o r m o r b y a n y means h iviüiout ihe p r i o r wrircen p c r m i g í i o i i o f ihe publíshcr . o r used b e y o n d the l i m i i e d d i s i r i b u i i o n lo tcachers a n d educafors p e r m i l l e d b y MrGr¡ iw-Hi1l l o i t t ie ir intlivitiiiül tnnt : ¡e prEparci iuin . ] Tycm ¡im a sl i ir ieni usm^, ih i i j M a n u a l h y o n are usinp il wiiITÍTnf p e n n i s s i i i r i -
Problem 1.59 1.59 For the Pratt bridge truss and loading shown. determine the average stress in member BE, knowing that the cross-seelional área of that member is 3750 mm\
B n
\ 4 ni
r c c [*-3 m- »\ - - 3 r n — — 3 m — —.1 ni——J
U s e e n f t > e . -jwa as. §r*< ícJy
+ 5 2 H H = o :
C 3 1 Í 3 S O ) - * C 4 Y 3 t o U tfY3co) - 1 2 = o
Use p o r f i é c r í • f k v s s + 0 - H e a s e e * , '
c * / f h i * ^ m f ^ U r t B D j B H j A „ d CS.
- + t Z F y = O
Problem 1.60
4 in. 4 in.
l e
Coífc
/.<W Knowing that linkZ)£ is I in. wideand } in. thick, determine the normal stress in the central portion of that link when (a) 0~ 0, (b) 6= 90°.
Use me^lei' CE F a. -f-Ve¿ b yr
F o t = - ¿ f o s ; « © ~ S b ^ ^ s e A
Cal 8 =• o: Fe* = - So K.
er "So...
6, ce
Problem 1.61 1.61 Two wooden planks, each 22 mm thick and 160 mm wide. are joined by the glued mortisc jo int shown. Knowing that the joint w i l l fail whcn the average shearing stress i n the glue reaches 820 kPa, determine the smalfest allowable lenglh d of ihe cuts i f the joint is to withstand an axial load o f mitgnitudc P = 7,6 kN.
-- Che
160 mm
3
T 7A A -7 ^ Í7"lts^o>-ío s')
•* 1.32.4 0 4 ^¿o 3
t 1*1 u ,
Problem 1.62 1.62 Link ^5 , o f width b = 2 in. and thicknessr = |- in. , is used to support the end of a horizontal beam. Knowing that the average normal stress in the link is -20 ksi, and that the average shearing stress in each of the two pins is 12 ksi, determine («) the diameter d of the pins, (b) the average bearing stress in the link.
Roo! A 8 '"s i'n co^p/,esE''s/7. A = b £ wXe^t b - 3. íw el £ = ^ ¡vi
A -
P R O P R I E T A R Y M A T E R I A L . 6 2006 The M¿rGra«-H¡ l l C o m p a r e s , I n c . A l l r ights reserved. N o parí ¡>f Ihis M a n u a l m a y Le d i s r i l a y e i l , r u j i n x l u c r a i o r d i s u i b u i c d i n a n y forra o r b y a n y m t a n s , v . i1houi ihe p r i o r w r i t i c n p e r m i s s i o n o f ihe p u b l i s h c r . o : used b c > o n d i h e l i m i l c d d i s m b u i i o n to i t a c h í r s and educnlorR p e i m i f l e d h y M c O r a w . H i l ] f o r llitíiriniliviiliial i;í]iirí.e rtreT | aia[i(in I f yi>u are a sIuiieiiE u s i n g Ehis M a n u a l , y o n IITR n s i n g i l w i l h a u r p e r m i s i ó n
Problem 1.63 1.63 Two ¡denticul linkage-and-hydraulic-cylrnder syslcms control the positrón o f (he forks oí a fork-líft truck. The load supported by the one sysiem shown is 1500
Ib. Knowing that tlie rhtckncss of member UO ¡s -¿ in., determine (a) the average
slicaring stress in the y -in.-diameter pin at B. (h) the bearing stress at B inincmber
fíl).
1 B j - isoo - o
t l f . = O
(o. ' l S V . e a ' r ' hoj 5 4 v~ttíi-; i n p',v- ¿ j f 6 .
(VA B e o i ' i m
A f - 0. t«t£SS
6 - B
5 - í r r s s aj^ " B .
KKOPRlETAftY M A T E R I A L « 2 0 0 f t T h c McGraw-Hill Coiiip^TiiEü, Inc. A l l rights itseruccl No pan of ihis Manual may lie riisplaycd. reprodur.nl or drsnibuted in any tenn or by any means, wrrluiuE Ih.s prior wniier» permission <>flhí publishcr , or used bey mu! rht l imiEcd disiribulio» tu Lirarhers and mil] c EIIO rs pcnniHcd by Mcfiia-..-i-íill ror ihcir individua! ctfui se prtpnrarion. I f yon are a sludeni 115KIJ di is Manual, ycuarc UKIIEI 11 wiihout pcmiiísiun
Problem 1.64 1.64 Determine the Iaigest load P that ean be applied sí. A when 8= 60°, knowing that the average shearing stress in the 10-mm-diameter pin al B must not exceed 120 MPa and that the average bearing stress in member AB and in die bracket a t ^ m u s l not exceed 90 MPa.
Use Joín*f A as 'ír-ee hoJty
P
• T v x ' < * w 5 j . P * ABC ¡s
a n e j e s Srioww hev-e
A C
3* sin 3o' Sí*» | 2 0 '
Ap = f o t * * f fo.0Jo>1 = 78.54 x/í>-£ kv,1
I F te«^¡r**j &"i"v es.s m w te*- A8 «.+ b^cke-i- ¿>+ A is ev.'-fi'c*-/
A b - t a l * (0.0l€,)(o>0¡°) l é o W o " 4
F A S - = ( /écoy/ü _ < : X=ío^jü 6 ) - I f . 40 x /o* W
A J , - 2 í ¿¿ = ( 2 ) ( o . o i - z Y o - O i b ) ~ Í 4 0 f / ü " f i fvi7*
S W í c s P«/*w " ¿0.£"7735" y/'^.+o* /o 3") 8 . 3 / v/¿T A/
Problem 1.65 1.65 The 2000-lb load may be moved along the beam BD lo any position between stops at F and F. Knowing that o,,, = 6 ksi for the steel used in ruds AB and CD, determine whers the stops should be placed i f the permitted motion of the load is to be as large as possiblc.
H i . i m e t t '
F
U— -X,
4 7.000 X
r p = Í F c ^ U - ^ A c p , íOff )«:#)*•
P = Xooo - 2.000 k„ s
Go F c o - x P - o
p 2 . . 0 0 0
«S1^ M V M
f
A T E R I , A L - * 2 C M T t B L M C , ' , a W - H Í " C O , " p a n l C ! > I n C - A i l ™ d N o f a " « f * - « . " - a l • » > b e d h p k » * reproduce* .
cducators j : , , , , , , . ! ™ ! b y M c G r w - l l d ] f 0 [ , H E L R „ , J , ™ l l l a l ™ u r s c p t , p 3 ^ , 0 n . I f y c u a r e a .«. .dent us ing rhis M a n u a l , y o u J r e , , s ¡ r .g ,t w i . h o u , p e r m i s s i o n .
Problem 1.66
125 mm
1.66 Two wooden members of 75 » 125-mm uniform rectangular cross section are joined by the simple glued joint shown. Knowing that P = 3.6 k N and that the ultímate strength o f the glueis 1.1 M f a in tensión and 1.4 MPa inshear, determine the factor of safelv.
_ P
^ S / J ' . f l . í a i o * Po .
6"^ , . / y , o '
2 A „ " &.)(%Z7S-*(Qr3)
F.s. s i 9.52-
P H O P R I E T A R V M A T E R I A L ©2U<]fi 'Hii ; M c G r a w - H i l l C u m p a mes, I n c . A l ] r i g h l s rese ived. N o part o f l h i s M a n u a l m a y b e d i í p l a y c d , r e p r o d u c e d or dis ir iüutedin any f o r a i o r by a n j mcans, w i i b o u i (he p r i o r w f i n e n p e r m i s s i o n o f üic publ i shcr . o r used b c y o t i d i h c l i r a i t e d d i s t r i b u l i o n lo rcachrrs and educators p e n n i t i c d by M o G r a w - H i l l for Their i n d i v i d u a l c o u r s e p re paral i o n l i y o n ure n sEi i JenluMiiE l lus M m n i d l , y o n are i i s ing iE w i E i i o u t i i e i i i i i s s i o n .
P r o b l e m 1 . 6 7 1.67 Each of ihe Uvo vertical lirias íl7/"coniiecting [he two horizontal members AD and F.G has a 10 * 40-mni uniform rectangular cross section and is made of a steel with an ultímate strength in tensión of 400 MPa, while each of tile pins at ('.-ind /•" hasa20-unndiamuti;randisinadeofasteel with aniillimate strength in shearof 150 MPa. Determine the o vera! 1 factor of safety for the links CF and the pins connecting them lo the horizontal membeis.
Use meimker FFG «-a -Vee fc¡¡*Jy,
F
OAo 0,25"
0.4o F t F -(O.&S^vlO1) * O
24 kN
A - C t - d ) t = ( o . o v o - o.ozYo.oio) - 7.0o *\o'c v ^ v (oM&tk}
F = íZ. 2^ A = ÍZ)(lSo*fO(-)(3ftt.l¿. - ^ . ¿ 4 8 * / ü ;
A r l . J W ,': r'« sntMe* yJ^e^ U F u r *to3 N
Ff-c+a/ oí ¿ « v t e r y K 5. = —— •= _ _ ~ ¿.^2 Fe C F 3^ *IO*
P H O P R I R T A R V M A T E R I A L O 2 0 0 ü T l i c M ^ l i r a v - HiJ] C o m p a n i e s , Inc . A l l u g l u s j e r a ved» NO part o f ihts M a m i a l n u y be uVplHyer ' , reproduced or d f c l r i b u t c d ¡n any f u n n nr by nny m c a n i , w i t l i o u i Lhc p n o i " w i u l c n f iermissicm o f ihe p u b l i s h í r . a r used l i e y i m d Ihe HmiTed d i s c r i b u l i o n ( t a c h é i s ainJ ed i t rntors p e n n i r r e d b y M í ü r a w - H i l l fot ihuir i n d i v i d u é coursc p r e p i r a t i c n . I f y a u JÍU a s l u c k r i i us ing ihis M a n u a l , yon a ie u s m ^ i l w i i h n u r p e r m i s s i o n .
Problem 1.68 1.68 A forcé P is applied as shown lo a sieel reinforcing bar ihal has buen embedded in a block of concrete. Determine the smallesHength ¿ for which the ful l allowable normal stress in the bar can be developed. Express the result in terms nf the diameter d of the bar. the allowable normal stress aM in the steel, and the averuge allowable bond stress r^, between the concrete and the cylindrical surface of the bar. (Neglect the normal stresses between the concrete and tiie end of the bar.)
P - T l í/ A - ~K d L
Problem 1.69
L 2 . 4 k i p s
1.69 The two portions o f member AB are glued together along aplane forming an angle í with the horizontal. Knowing Ihat the ultímate stress for the glued joint is 2.5 ksi in tensión and 1.3 ksi in shcar, determine (a) the valué of 6 for which the factor of safety of the member is máximum, (i>) the correspondí ng valué of the factor of safety. (rYiHí: Equate the expressions obtained for the faclors of safety with respect to normal stress and shear.)
A"f tVe oph'vno*» a*\3Je ( F S - V TCF$.).
1.25 i n . (F.$.\ -
6a \ vi* s-rv-es: Ao" p *
1.3 7 . 5 (al 27.5'
P * -
P 2.4 3 . 3 /
Problem 1.70 L 70 The two portions of member AB are glued together along a plañe forniing an angle ¿Jwith the horizontal. Knowing that the ultímale stress for (he glued jo int is 2.5 ksi in tensión and 1 . J ksi in shear, determine the rango of valúes of f?for whieh the factor of safetv of the members is al least 3.0.
-1.25 in.
CO&Q
eos.e - o.^zic^
2o = 2JS^LL _ C Í X ^ - ^ O V J . S " )
7.2 <9 ? 2 1 . 3 °
2 e = G4.£-x" " 7 . 2
O - 9 0 3 7 2
0 * 3 3 . 3 '
X 1 3 ' ¿ a ¿ " 3 2 - 3
F K O r K l K T A R Y M A T E R I A L © 2 r » 6 T h e M c G r í w - H i l l C o r a p 9 n i c i , l n c . A l l rights r e s : r v e d . N o p a n o f i h i s M a n u a l m a y b e d i s p l a y e d , r e p i o d u s e d a r d i s i r i b u c e d in any f o r m n r b y a n y mcai is , widioLit Ihe p r i o i i iEai IKIIIII^MOII >»f i l i u puFilisher, <w used bsi '^nci [ l i s l i i n i t e r i d i s t n b u i i o n ra teachers and « h i c a m r s perrnitíed by M c G r o w - H i l l for ihc i r i n d i v i d u a l c o u r s c p r e p a r a r o n , [ f y o u are i sLudent u s i n g Ihis M a m i g l , yoa are i i s i n g i l witliüul p c i m i s s i u r i .
P R O B L E M I . C I
Element n
Element 1
l .CJ A solid sieel rod consisting of n cilindrica] elemenls welded together is subjected to Ihe loading shown. The diameler of element / is denoted by d, and the load applied to its lower end by P, with the magnitude of Ihis load being assumed positive i f P, is directed downward as shown and negativo otherwise. (a) Write a computer program that can be used with either SI or U.S. customary units to determine the average stress in each element of the rod. (b) Use this program to solve Probs. I 1 aitd 1.3.
SOLC'TÍON
ít ¡5 fhesum ai the f o r r e s applied
1o fhat ele me i A a n d a II [ovJer 0*'-'\S
> n
A\J£K_(\<SE STRESS' IN g L E / ^ E W T l '
Arca = A¿=j- K<£ Ave stress = A . H Ai
P r o b l e m 1 . 1 Element . S t r e s s (MPa)
P r o b l e m 1 . 3 E l e r a e n t S t r e s s ( k s i ;
4 2 . 4 4 1 3 5 . 6 5 1
1 2 . 7 3 2 - 2 . B 2 9
P R O P R i E T A H V M A T E R I A L 0 2IH)f> I h e M o ü m w - H i l l C o m p u n i e s , I n c . A l l r ights rescr^cd. N o p i n o f l h i s M a n u a l m a y b e d i s p l a y e d , l e p i o d u c c d or d i s t r i b w c d i n any f o r m a r b y any means, w i t h c u l t h e p r i o r w r i l t e n p e n n i s s i o n o f i\ic [ m h l i . h e r , t i n i s p d h e y o n i ihe l i m i t e d d i s i r i b u t i o n lo icacl iers ar.d educalors Eiermilltid by M n G r a ^ - H i l t f o r I h e i r i n d i v i d u a l coursc prepararían. I f y a u are a s tudent u s i n g this Manml, y o u are u s i n g i l w i l h n u L p e n n i s s i o n .
P R O B L E M 1.C2
:2l.l L N
\.i'2 A 20-kN load is applied as shown to the horizontal member ABC. Member .45(7 has a 10 * 5(j-mm uniform rectangular cross section and is supported by tour vertical liuks, cuch of fi * 36-mm uniform rectangular eioss seclion. F.ach o f the four pins at A, B, C, and D has the same diameter d and is in double iheai. ia) Write a compnter program to calcúlate for valúes of i/from 10 to 30 mm, using I -mni incrementa, (1) Ihe máximum valué of the average nounal stress in the links connecting pins B and D, (2) the average normal stress in the links connecting pins C und E. (3) ihe average sheanng stress in pin 6, t'4) the average shearing stress in pin C, (5) tlie average bearing stress at B in member ABC, (6) the average bearing stress at C in member ABC, í_b) Chcck your program by comparing the valúes oblaincdford= lómmwiththeanswersgiveiiforProbs. 1.9and 1.27, (V)Usediis program to find the permissible valúes of the diameter ¿ o f the pins, knowing that the allowable valúes of the normal, shearing. and bearing stresses for the steel used are, respeclively 150 MPa. 90 MPa, and 230 MPa. (d) Solvepan c, assuming thal the thiekness of member ABC has been reduced Irom i 0 to 8 mm.
SOLTJTIOIN
FORÍE5 ¡ri / _ /NK5
P = 2 0 k N
A
2 ^ .
F B D r P (f\ c)/z (B 6 ("fTNSIOÑ)
+ 3 > ' M E = 0 ; 2 F,L (BC) - ?(*S.) = O
C
•-1
ElLLA
~ 4 ^BD/^BCJ
C¿) LiNk CE
\^F~~
(6 ) 3 ztifVy G _ S R K ^...
- T c£./ • -( C O N T I N l i r . D )
P R O B L E M 1.C2 CONTTNUED P R O G R A M OUTPUTS
I K P U T D A T A FOR PARTS (a), (b), ( c ) : P - 20 k N , A B = 0.25 m, B C - 0 40 m, AC = 0 65 m. T L - S mm, \VL = 36 mm, T A C = 10 mm, W A C " 50 mm
S i g m a BD S i g ^ a CE T a u B T a u C. S i g B e a r E S i g B e a i C
"i 0 . C o ! I - 00
oc 0 0
00 00 00
1 7 l í 14 15 ie>
78 13 8 1 . 2 5 8 4 . 6 4 88 . 32 92 . 3 3 36 . 73
1 0 1 . 5 6
- 2 1 •21
7 r i . 7C
2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 8 0 7 8 2
18 . 0 0 1 9 . 0 0 2 3 . 00 2 y OC 22 - 00 2 1 . 00 24 - 00 25 . 0 0 26-. 00 2 7 . C 0 28 . 0C 2? ;oo 3 0 . 00
1 1 2 . 85 1 1 9 . 4 9 1 2.6 . 35 1 3 5 . 4 2 1 4 5 . 0 9
- zr."7 u - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0
63 . a s 57 . 3 1 5 1 . 73 46 . 9 2 42 . 7 5 3 9 . 1 1 35 . 92 33 . 1 0 30 . 6 1 28 . 35 26 5 9 2 4 . SO 2 2 . 99
79 5 6 1 2 b 00 ?5 77 113 G4 55 26 2-í-rx. -4 104 1 7 47 09 96 15 4C 60 '¿32 89 23 35 37 216 6 7 83 33 3 1 Ofi 203 12 7S 13 •¿T 54 1 9 1 i a )¿ b J 24 5 6 180 56 69 4 4 2 2 04 1 7 1 05 6b 79 : 9 a s 1 6 2 50 62 5 0 15 04 1S4 76 5 9 52 16 44 1 4 7 73 56 82 15 04 1 4 1 30 54 35 13 62 135 42 52 08 12 73 1 3 0 00 50 00 1 1 77 125 00 48 08 10 92 1 2 0 3 7 46 30 10 15 116 07 44 é4
9 46 1 1 2 0 7 43 10 6 ti 4 10 íi 3 3 4 1 67
(c) A N S W E R . 16 mm < d ú 22 m m C H E C K : For d - 22 mm, Tau A C = 65 MPa < 90 M P a O K.
I N P U T D A T A FOR P A R T (d). P = 20 k N , A B = 0.25 m, BC = 0.40 m , A C ^ 0.65 m, T L = S mm, "WL = 36 mm, T A C - 8 mm, W A C - 50 m m
^ ( t )
5 i g m a BD S i g m a CE T a u B T a u C S i g B e a r B S i g B e a r C
10 . 0 0 1 1 . 00 12 . 00 13 . DÚ 14 . 00 15 . 0 0 1 6 . 0 0 17 . 0 0 18 . Ú0 19 . 00 20 . 00 2 1 . 0 0 22 . 0 0 23 . 00 24 . 00 25 . 00 26 . 00 2 7 . 0 0 28 . 00 29 . 00 30 . DO
- 2 1 . 7 0 - 2 1 . 70 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 • 2 1 . 7 0 - 2 1 . 7 0 •21 . 7C - 2 1 •21
70 70
- 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0 - 2 1 . 7 0
7 9 . 58 6 5 . 7 7 5 5 . 2 6 47 . 09 4 0 . 6 0 35 . 37 3 1 . OS 27 . 5 4 24 . 56 22 . 04 19 . 6 9 15 . 04 16 . 4 4 15 . 04 13 . 82 12 , 73 1 1 . 7 7 1 0 . 52 10 . 1 5
9 . 4 6 8 . 84
2 2 5 .G9 213 82 203 12 í 93 4S 184 66 176 63 1 6 9 27 1 6 2 50 156 25 1 5 0 46 1 4 5 0 9 1 4 0 09 1 3 5 42
1 5 6 . 3 5 1 4 2 . 0 5 1 3 0 . 2 1 1 2 0 . 1 9 1 1 1 . 6 1 1 0 4 . 1 7
9 7 . ¿ 6 9 1 . 9 1 66 , 8 1 82 . 24 7 8 . 1 3 74 . 4 0 71 . 0 2 67 . $2 65 . 1 0 62 . 50 60 . 10 5 7 . 8 7 5 5 . 8 0 53 . 8 8 52 . 08
r w ™ * ™ ( d ) A N S W E R 18 m m c d * 22 mm ^ fy) C H E C K : hor d = 22 mm, Tau A C = SI 25 M P a < 90 MPa O.K V
n t O J H . E M 1.C3 1.C3 Two horizontal 5-kiu fortes are applied to pin ti of the assembly
shown. Each nf the three pins ai A. 0.and Chas the saine diarncterriand isdouble sheai. (a) Write a «unputer program to calcúlate for vahies of rffrorn 0.50 lo 1.50 in., usmgO.UÍ-in. increments, (1) the máximum valúe of ihe average normal stress in member AB, (2) the average normal stress in member BC, Q) the average shearing stress ¡n pin A, (4) the average shearing stress in pin C, (5) the average hearíng stress at A in member AB, (6) the average bearing stress at d'in member BC, (7) the average heanng stress at B in nicinber BC. (y) Chcck your program by comparingthe valúes obtained for d=0 Sin. with the answtrs given for Probs. 1.10 and 1 28. (c.) Use this program to find ihe permissihle valúes of the diametet rfof the pins, knowing that the allowable valúes of the normal, shearing, and bearing stresses for the sieel used, are respectively, 22 ksi, 13 ksi, and 36 ksi. (J) Salve part c, assuniing that a new dcsign is being investigated, in which tlte tliickncss and width of the two members are changed. respectively, form 0.5 to (1.3 in. and from 1.8 lo 2.4 in.
S O L U T I O N
FORCEA IN MSMBFKS fts ftMz> a c
f F ñ B Width - • t v
( 3 ) PIN A
^~(rAeAY(ndz/*)
f n s , Feo - g P
5'f¡ ~ SlnéC? Si*v7S*
F zr 2,P('SinUSY<sh 75*) A B y
( ? ) A ^ E , S T R E S S ¡ N S C
5 % 8 e a r f t •=• F w / d t
Be
Z
% c = F B c / * e c
•c (FTJZ\/{Tdytf)
3
IN ME_MR?R P,r._
S i s Bear F £ C / d t
( C O N T I N U K D )
PROBLEM 1.C3 CONTINUE» P R O G R A M OUTPÜTS
INPUT DATA PORPARTS (a), >"b), (c)" P = 5 kips, w = 1.8 in , t • 0 5 in
D • n .
S I G A S k s i
IGBRGA SIGBRGC S I GE?GE
7 2 9 2 8 918 18 3 0 1 r, 4 5 0 7 9 00 17 2 2 5 5 7 5 4 7 0 4 7 16 2 6 8 5 J 64 6 324 15 4 1 2 4 6 6 0 5 70B 14 6 4 1 4 2 2 7 5 1 7 7 13 944 3 952 4 7 1 7 13 3 1 0 3 524 4 316 12 7 3 1 3 236 3 9 6 4 12 2 0 1 2 983 3 6 53 1 1 713 2 758 3 3 7 7 1 1 2 6 2 2 557 3 1 3 2 10 8 4 5 2 378 2 912 10 453 2 ¿ 1 7 2 715 10 0S7
D71 5 3 7 9 7 6 1
k s i
3 b . a s 3 22 . 603 2 9 . a B6 2 7 . 5 87 2 5 . 6 1 6 23.. 9 0 9 2 2 . 4 1 4 2 1 . 096 19 . 924 16 . 8 7 5 17 , 17 . 16 . 15 . 14 14 13 1 3 '12 1 2
1 1
9 3 2 076 3 0 1 593 34 3 3 4 5 793 283 808 3 6 7 954
k s i
17 . 93 2 1 6 . 3 0 1 14 . 94 3 1 3 . 7 9 3 1 2 . 8 0 8 1 1 . 9 5 4 1 1 . 2 0 7 1 0 . 5 4 3
9 . 9 6 2 9 . 4 3 8 8 . 966 8 . 5 3 9 8 . 1 5 1 7 . 796 1 . 4 7 1 7 . 1 7 3 6 . 8 9 7 6 . 6 4 1 6 . 4 0 4 6 . 1 83 5 . 577
I N P U T D A T A FOR P A R I ' (d): P
S I G A B D i n .
0 . 5 0 0 ¿ 7 . 5 5 0 C: 6 0 0 0 . 65D 0 . 7 0 0 0 . 7 5 0 0 . 80 0 0 . 8 5 0 0 . 9 0 0 0 . 950 1 . 0 0 0 1 . 0 5 0 1 . 1 0 0 1 . 1 5 0 1 . 2 0 0 1 . 2 5 0 1 . 3 0 0 1 . 3 5 0 1 . 4 0 0 1 . 4 5 0 1 . 5 0 0
k s i
12 843 13 190 13 b b 6 13 944 14 3 5 4 14 7 8 9 15 2 5 1 15 743 16 268 16 8 2 9 17 4 3 0 18 075 18 7 7 1 19 5 2 1 20 3 3 5 2 1 •219
S1GBC k s i
- 1 2 - 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 12 . 4 5 2 - 1 2 . 4 5 2 - j 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 • 12 . 4 5 2 - 12 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 52 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2 - 1 2 . 4 5 2
(c) A N S W E R . 0.70 in. ¿ d < 1 10 in
•• 5 kips, w = 2.4 in , t = 0 3 in.
TAUA TAÜC S I G B R G ñ SIGBRGC SIGERGB k s i k s i k s i k s i k s i
12 . 94 5 1 1 . 0 3 0
9 . 5 1 1 8 . 285 7 . 282 6 . 4 5 0 5 . 7 5 4
. 1 6 4
. 6 5 0
. 2 2 7
. 8 5 2
. 5 2 4
. 2 3 6
. 983
. 758
. 5 5 7
. 378
5 . 4 . 4 3 3 3 2 2 2 2 2 . 2 1 7 2 . 0 7 1
T I - 645 34 8 6 0 l O 1 4 7 32 536-
8 9 1 6 30 502^ 7 90 0 28 708 7 0 4 7 27 113 6 3 24 25 686 5 7 0 0 24 4 0 2 5 1 7 7 23 2 4 0 4 7 1 7 22 183 4 3 1 6 2 1 2 1 9
S64 20 335 3 653 19 5 2 1 3 3 7 7 18 7 7 1
1 3 2 18 075 2 9 1 2 17 4 3 0 2 7 1 5 16 825 2 5 3 7 16 268
(d) A N S W E R : 0.85 in. <dú 1.25 in.
P R O B L E M 1.C4
a y p 1.C4 A 4-kip forcé P formiiíg an angle c wílh the vertical is applied as
shown to member ABC. which is supponed byapin and brackel at Cand bya cable BD fonning an angle /Jwith the horizontal, (a) Knowing that the ultímate load of the cable ¡s 25 kips, wrilc a computer program to cunstruct a table of the values of ihe factor of salety o f tiie cable for valúes ot ir and ¡5 from 0 to 45'', usiug incremenls in a and J) corresponditig lo 0.1 incremente in tan ííund tan p (b) Check that for any givcn valué of rrihe máximum valué of the tactor of safcly is obtained for ¡3= 38.66° and explain wtiy. ir) Determine Lhe; ibievahe of tlie factor of safety for /}= 38.66", as well as Ihe corresponding valué of a, and explain the resuk obtained
S O L U T I O N
O ) DRbwl F. b, DtHGfjftn OF A B C J
12 in.
-(Fco¿p)-(l5in.)--(Fsh)p)(}zinJ
p - p fss'mct + 3o a¿,^
IS Cctfi -f- fl 5/0/3
F 5, = F U ¡ T / F
>ÜI0J
- 0
O t - ' T P U
V A L U A S O ? F S B E T A
— 1 • TL
0 : . 7 i_ 1 1 . 3 1 1 6 . 7 0 2 . . 3 0 2 J " " 3 T ^ 6 3 ' _ . ? 9 • í ¡ . 6 6 4 - . 9 9 4 5 . 0 0
J 1 í 1
0 0 0 3 . 1 2 r -¡ -.; 5 5 5 i 7 1 2 3 8 3 0 S 1 3 3 . í 6 6 3 9 f i 4 4 C 0 2 3 0'JS T 9 7 7
5 7 1 1 —i y y : 3 2 1 4 3 4 0 2 3 5 5 2 3 6 6 6 3 7 4 b 3 7 9 6 3 6 2 3 3 a . 3 0 3 8 2 4 "-A b'j i i i 3 1 0 2 3 1 1 3 3 ¿ y b 3 4 4 1 3 5 5 1 3 6 2 8 3 6 7 7 3 7 0 3 3 7 1 0 3 7 0 4 3 6 3 7
6 9 9 2 a y 3 0 4 9 T 2 2 7 :t 3 7 0 3 4 7 7 3 b b 3 3 6 0 0 ~i S 2 G 3 6 3 3 3 6 2 7 3 6 1 1
6 0 1 2 3 0 5 O l í 3 i y o 3 3 3 1 3 4 3 Q 3 5 1 2 • í s n 3 5 8 5 3 5 9 2 3 s e s 3 5 7 0
f á p c . 6 i 2 7 3 b. 0 0 4 3 1 7 9 3 3 2 0 3 4 2 6 b O Ü 3 . 5 4 7 3 5 7 2 i 3 5 7 3 3 5 5 3 )
3 0 3 6 4 2 8 0 3 0 1 3 3 1 8 9 3 " " 3 3 0 3" 4 3 6 5 1 0 3 5 5 ñ 3 5 8 3 i b y u 3 3 t ¡ 4 3 5 6 Í 3
3 4 9 9 2 2 8 2 6 3 C 3 6 3 2 1 4 3 3 5 6 3 4 6 3 5 3 B 3 b d f c 3 6 1 1 i 6 1 9 3 6 1 2 3 5 9 6
3 9 6 6 0 2 8 5 9 3 0 7 2 - 3 2 5 2 3 i y s 3 5 0 3 J 5 7 9 3 6 2 3 3 6 5 3 i 6 6 1 3 6 5 5 3 6 3 8
4 1 9 8 7 ?. 8 9 9 3 1 1 6 3 2 9 8 i 4 4 4 3 5 5 4 3 6 3 1 3 6 3 0 3 7 0 6 ! 7 1 3 3 7 0 7 3 6 9 0
4 5 0 0 0 2 9 4 6 3 1 6 6 3 3 5 1 3 4 3 9 i 6 1 1 6 3 9 3 7 3 9 3 7 f i 5 ! 7 7 3 ¡ 3 7 6 7 3 7 5 2
C/)j Whenfi - 3 P , ¿ ¿ ; foW/i - ü , d no.d caík k D ¡ c .P>£r pen á i c i>l« ¡'
U ida ¡f \'C r r), Í,Í B e . '
NOTE!
CP olftr fo i-he.
7 7 . t - v o A - c / " " r > .
n a
/3>- 38.66 ' r ^ j J y / í f ¡ n r c , ; / r / i ^ i c
r •'(•/><• 1ir¡/ K S/U>\'F). fin* I \ Í ' /h'n -i n>As" r i fi¡
P R O B L E M 1.C5 l . C S A load P is supported as shown by two wooden members of uniform
rectangular crosssection that are joined by a simple glued scarf spiice. (a) Denoting by tr(,and rL„ respectively, the ullimate strength of the joint in tensión and in shear, wríte a computer program which, for given valúes of a, b, P, <7 (,and r„, expressed ineither Sí orU.S. customary units, and for valúes of afrom 5 to 85° at 5" intervals, can be used to calcúlate (1) the normal stress ¡n ¡he joint, (2) the shearing stress in the joint, (3) the factor of safety relativc to faiiure in tensión, (4) the factor of safety rclalivc to faiiure in shear. (5) the overall factor of safety for the glued joint. (b) Apply tliis program, using tlie dimensions and loading of the members ofProbs. 1.29 and 1.31, knowing that i7,,= 1.26 MP and r u = 1.50 MPa for iheglue used in Prob. 1.29, and that c ( , 150 psi and ru 214 psi for lhe glue used in Prob. 1.31. (c) Veriry in each of these two cases that the shearing stress is máximum for Í T = 45°.
S O U J T I O N
Arca.. - ab/sin <V
Norma i stress :
Area.
F - FÓ in 'x ~ o F ' PjinOC
¿3) fcZ.for tensión (n^J ^ f r ^ s s ^ s )
F S N =r Cru/¿?
r.$. for shear;
do) S/h^K co^Oc
F55 - u. y
F S - The smoiler of fsU F55>
(CONTINUE»)
P R I W L E M l .CS C O N T I N U A D
r>Ff ÍM Q U T P U T .
Froblerr, 1 .29 a - 150 mm b = 7 5 inri
RTGU = 1 . 2 6 MPa TP.ni; = i . 50 M=a
PHA S I G (MPa) TAI! (MPa) FoS FS
5 . 007 .095 169 .644 1 7 . 6 6 9 17 .669 10 . 029 . 167 4 2 . 7 3 6 a . 971 8. 971 1.5 .065 .21-1 19 .237 6 . 1 3 6 6 .136 20 .114 . 3 1 4 11 .016 4 .773 4 .773 25 .175 . 375 7 . 2 1 5 •1.005 4. 005 30 .214 . 423 5 . 155 3 . 543 3 . 5 4 3 35 . 322 .459 3 . 917 3 . 265 3 . 2 6 5 40 .404 .481 3 . 119 3 . 1 1 6 3 . 116
45 . 489 .489 2 . 5 7 7 3 . 0 6 3 2 . 5 7 7 50 . 574 .481 2 . 196 3 . 116 2 ; 1 9 6 55 . 656 .4 59 1. 920 3 . 2 6 5 i . 9 ; o
60 . 7 3 3 . 423 1 . 718 3 . 543 1 .718 65 . 803 . 375 1 . 5 6 9 4. 005 1 .569 70 .363 .314 1 . 459 4. 773 1 .459 75 .912 .241 1. 361 6 . 1 3 6 1 . 381 SO .948 . 167 1 . 329 8 . 971 1 .329 •Tj .970 . 085 1 . 2 S 8 17 .669 1. 298
« ( b ) j ( c )
Problem 1 . 31 a =* 5 i n . L = 3 i n . . = 1-3 :>o i c
S I L U ••= : ¿ o p s i Tñ'JU = 214 p s i
PHA S I G T A U ( p 3 Í f F ;N F S S F S
5 709 8 104 211 574 26 40B 2 6 . 4 0 8 10 2. 614 15 961 53 2 38 13 408 13 .408 15 6 2 52 23 333 2 3 992 y 171 9 .171 20 10 918 29 997 13 739 7 134 7 .134 25 16 670 35 749 8 998 5 986 5 . 9fS6 30 23 333 40 415 6 429 5 295 5 .2 95 35 ¿0 706 43 3 52 4 885 4 880 4 .880 40 38 563 45 958 3 P90 4 656 3 .890 45 46 667 46 667 3 214 4 586 3 .214 50 54 770 45 958 2 739 4 656 2 . 7 3 9 55 62 623 43 852 ? 3 95 4 a s o 2 . 3 9 5 60 70 000 40 415 2 113 5 295 2 . 1 4 3 65 76 663 35 749 1 557 986 1 . 957 70 82 415 29 997 \ 820 i 134 1 . 820 7 5 87 031 23 333 1 723 a 171 1 .723 80 90 519 15 961 1 657 l 3 408 1. 657 85 92 624 6 104 1 619 26 408 1 .619
•< ( c )
PROPRIETARY MATERIAL. ©2006 Ule McGiaw-Hill r.'uriiiuniB^, ¡nc. All ligh's reservcd. No par! oflhis Manual mayfce disjilaytd, icpriidiiced or distribuid) ifumy formo! by nny mcam, wirticui the prior wrilten permission oflhe publisliei, oí uSeil hcynml ihr limiced dislribution lo tcach;rí arid educatorí pcnnitl-dby MsGi.w-Hill Id? llior nnliviilu.il m u r a prep.iraiion Ifyoij ore i ¡ luden t mi iigIhisManual, yeuareu-mg ii wittimitp-rnii5sion.
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