12-61 Determine the maximum slope and the maximum deflection of the beam E/ is constant
1 £1I mM &L Mo L MoL Ôc/A n3) 2EI Oc = Ocia + đạ 0= Mok + 0, 2EI —=MọoL MẹL Ans 6, ax = 6A = ——_ ~ ¬rự m 2EI 2EI TT ns
Amax = ltacl = EI 2 4 SEI
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Trang 212-62 The rod is constructed from two shafts for which
the moment of inertia of AB is J and of BC is 2/ Determine the maximum slope and deflection of the rod due to the loading The modulus of elasticity is E
: 1 -PL_oL -PL_L =PL LL -5PL? _ SPL?
đục = (FED * Ge? * (Sepa) * Teer — 16EI
OO, = Bac + Oc
SPL’ o= SPL?
Omax = max 4 TOE! = + 16Eƒ Ans
Âmx = ÂA# lwcl -PL LL -PL LoL “PL LLL = —— — _ —=}+(——)(-)(—- _ 20006) + GPP * 5) Sep PG +P _ 3PL3 16EI
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Trang 312-63 Determine the deflection and slope at C E/ is con- stant c[= A c CM, F= = == aT] 3m ) |, 1,—M, Mạt? ta = 1G ML) =~ "ser Ac= HA —2| taal _7MoL* Mo To
tora = NLL + 5 D+ yng )= SEI 2 1MạLˆ Mọi? _ 5MạL A = -(2X4——)=— ns Ae = ee OC = EFT 6, = \taval = MoL aL 6EI _3MoL _ 3MoL
6c = nang + Ay = SEI SEI
Oc = Ocr + Og
ge = Mol _ Mol 4MoL Ans
2EI 6EI 3EI
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Trang 4*12-64 The shalt supports the pulley at its end C Determine the deflection at C and the slopes at the bearings
A and B Elis constant
Yz “2 1,-PL ul -PL’ Ly -PL ~ i spt MS) = Ser L M Ac = ltcial — (z) Ital # 2 = PL? ~2 PL = PLP Ans
SEI - 48EI 12EI
: 2 = Pk
8, = {taal _ eel -Ö PL Ans Si
aE Lo 24EI
1 -PL L._ -PL? _ PL
{REI 2° 8El 8EI
8 =—— -~ — = Ans
b” SÉT - 24E1 12EI
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Trang 512-65 The shaft supports the pulley at its end C Determine its maximum deflection within region AB ET is constant The bearings exert only vertical reactions on the shaft
tana ta Ob1a >= ——- (ÿ) Icky Py lyk Ty = 220) x = 0.288675 L 2 El (@) 1,P(0 Amax = 1 P(0.288675 L) 288675 ») 0.288675 1)(2) (0.288675 L) 2 El 3 3 Am, = 0.00882PL Ans EI
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Trang 612-66 Determine the deflection at C and the slope of the beam at A, B, and C EJ is constant
1 (=8)¢6)(2) = 8 tua = 5G OO = Fr 18 = = 18 tora = 5 Gp Oe +2)+ G 3)01.5) Er 9, ,_156 948 84 ng b Ac =Itc/Al~ CHeAl = ý EN El 2 tanc 5 M — teal _ 8 Ans EL 6 ET ; T 1-8 24 _ 24 | = +( = = O54 np 6) El EI -8 Ez On = Opa t 94 24 8 _ l6 Ans 98-7) EI El 1-8 -8 48 48 =) (3y6+ (3) === ==
%c¿A sư” d+ EPO) EI El Oc = Oca + 94
48 8 _ 40
awe Zee Ans
c= Fr" Er EI
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Trang 712-67 The flat spring is made of A-36 steel and has a rec- tangular cross section as shown Determine the maximum elastic load P that can be applied What is the deflection at 8 when P reaches its maximum value? Assume that the spring is fixed supported at A
/4P | tr ` | ——+ on a i # S él I= (1500) = 0.125(107?) in* 6, = Mc 36(10°) = 146009) P=643lb Ans I 0.1250) 1 ~-90 Ap = tara B= tava = ~(——)(14)(9.333+3 5! Ei (14) ) = = = 2.14 in Ans El 29(10*)(0.125)(1073)
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Trang 8*12-68 The acrobat has a weight of 150 Ih, and suspends himself uniformly from the center of the high bar Determine the maximum bending stress in the pipe (bar) and its maxi- mum deflection The pipe is made of L2 steel and has an outer diameter of 1 in and a wall thickness of 0.125 in
131 _†+ +— 3d TT ¢ E—:a S 4 4 Zf {is 3t Toth = 75th 7sIb 7/6 428 eft (FF Mmax = 75(3) = 225 Ib- ft I= Zo" ~ 0.375%) = 0.033556 in*
Omax = = —————— = 40.2 ksi Ans
I 0.033556 40.2 ksi < oy =102ksi OK
225 1,225 1244.53 lb - fr Amax = tac = (—~)(0.75)(3.375) + —(—~)(3)(2) = —— AIC (7 )( ) 5 ep! )(2) ET
3
¬— ` Ans
29(10°)(0.033556)
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Trang 912-69 Determine the siope at C and the deflection at B E7 is constant Gey tana ™— ey, M "Er tang Ỉ Ị ==za 4 apa Ft ET FI 2Pa 1/ Pa ĐcA =[—“—” z ( EI }2+{ m9 -|—— _ _5Pa! _ 5Pa? ) 2EI 2EI Ốc = cra Œa = Pa? = “` 2E 1 Pa 2a lf Pa 2a 2Pa a ẢAn= =—Ì|—— —_— —-|—— — —— - 3 = {inal ( mJ'2(Ÿ)*3( a) (at s+ EI }2(3) 3 - 23Pa + Ans 6EI From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X
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Trang 1012-70 The bar is supported by a rolier constraint at 8, which allows vertical displacement but resists axial load and moment If the bar is subjected to the loading shown, determine the slope at A and the deflection at C El is
constant LPL LPL EL _3PL?
Oye = (= KEO)“ "sEï Ủ
I Oa = On 2£ 2 + , = PL Ans | 8EI
1 PL LOL PL LOL LỘ 1iPL3 = ~(——\(-\(-) + — Ee +=
tare = 3 (DG) * er 99 * = ABET
fore = Fer DD? = Tent
Ac et _1iPL? PL? _ PL?
c = tae lca Teer 16EI GEI Ans
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Trang 1112-71 Determine the maximum deflection of the shaft ET is constant The bearings exert only vertical reactions
on the shaft [-i-t —* ——+—i—]| E te P t * ơ Fz “2% Ì 3¿ $ ⁄ P P P P (a) -tan A | “22c fh Er (b) La 282 (cy Ana = tac = Pa : Co + 2) + 1gG)) a a 1 Pa a a = 11Pa° 48E7 Ans
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Trang 12*12 72 The beam is subjected to the load P as shown Determine the magnitude of force F that must be applied at the end of the overhang C so that the deflection at C is zero El is constant 1, Pa Pa? 2Fa? =^(— *(-—^X2a\(Ša)=——— ‘ava 2E 422)4)+ 1 mí Š a= 2EI 3EI
tem = AES y(20)(20) + 2 1 yaaya + 22) +
2a Pa” 2Fa` 2C Xa a )= EH EF 3
Ac = tera — tA =0
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Trang 1312-73 Determine the slope at B and deflection at C EJ is constant fame 82S J fname 94 mamxei
Onc = 2C 2@)+ LP Fe y0) + Paya) = EE
2 CE EI 4EI 7Pa?* = = Al Os = Onc = ms 1,P
Ac =limcl =: a ys oars a+22)+
9Pa?
=)= A
= aa a+ 2)” GET ns
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Trang 1412-74 The A-36 steel shaft is subjected to the loadings developed in the belts passing over the two pulleys If the bearings at A and & exert only vertical reactions on the shaft, determine the slope at A The shaft has a diameter of
0.75 in, | 300 th 300 Ih 342-861 J0tb — 67/16 beolb 1,6171.48 1,6171.48 ¡ =2 0) + = 3(11.08)(20.31) bia = 3! zl )(18)(30) 5! aT 1 -7200 2160231.8 *(Cˆ“—)(1292)(431= ———— + 2C a lai _ 5143441 _ 51434.1 Os = TT ET — 29059(70(0.375) = 0.114rad = 6.54° Ans
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Trang 1512-7§ The A-36 steel shaft is subjected to the loadings developed in the belts passing over the two pulleys If the bearings at A and B exert only vertical reactions on the shaft, determine the deflection at C The shaft has a diameter of
0.75 in
3#2861Á 4;erb HEFL lá booth
1 6171.48 1 6171.48 tya BA = TT )(18)0) 3! EI )(11.08) (20.31) = —( 18)(30) + - 1 _~7200 + z(C——)(1292)(441) = 71602318 aH EI , 54 2 tạ = (tgA)(—) = 2777441 42 EI 1 6171.48 1 6171.48 tia 1A = - 56 EI )(18)(42) + 5! EI )(11.08) (32.31) 18)(42 - 1 -7200 1 -7200 2333287.6 + -( 7L g7 )(12.92)(16.31)+ -(——— )( ) 5! EI )(12)(8) =o E Ac =ien — g —— -4153 29(10)(7)(0375)1 Ac = 0.987in Ans
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Trang 16*12-76 The 25-mm-diameter A-36 steel shaft is supported at A and B by bearings If the tension in the belt on the pul- ley at C is 0.75 kN, determine the largest belt tension 7 on the pulley at D so that the slope of the shaft at A or B does not exceed 0.02 rad The bearings exert only vertical reac-
tions on the shaft
10.247 10.247 = -(— 5° El )(0.2)(0.1333) + 3! El )(0.3)¢ ~(——)(0.3)(02 + 01 ) 7 ao 1 -150 00147 12.5 ~(——)(0.5)(0.3333) = ~——— * 2 EI 0-5) ) EI EI 6, = teal _„ 00287 _ 25 qd) 0.5 EI EI 10.24 T 1 0.247 = —(———)(0.2) + —(——)(0.43 65/4 5! El )(0.2) 53! El )(0.3) 1-150 0.06T 37.5 mm 5) =— ——— 15 kN 2T * 3! EI (0.5) EI EI Og = Opa + 94 6 = Er er er TH 12.5 _ 00327 _ 125 @ EI EI
For O4 = 0.02 rad mon
EI From Eq (1) : | 0.02(ED = 0.028 T - 25 2247 0.02(200)(10°)(19.175)(10°) = 0.028 T — 25 T = 3632N For 63 = 0.02 rad From Eq (2) : 0.02(E D = 0.032 T - 12.5 0.02(200)(107)(19.175)(10”) = 0.032 T — 12.5; T = 2787 N = 2.79 kN controls Ans
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Trang 1712-77 The 25-mm-diameter A-36 steel shaft is supported al A and B by bearings If the tension in the belt on the pul- ley at C is 0.75 kN, determine the largest belt tension T on the pulley at D so that the slope of the shaft at A is zero The bearings exert only vertical reactions on the shaft
100 mm 300 mm ——T†— 200 mm | Ụ “1 ao 200mm | 2BT+Lôo | 19 KA T LAT~0-5 MỸ EL tana
oi, nĂ Tana
Require tg, = 0 1 —1500 2 1 0.247 ft BIA = —(——)(0.5)(-)(0.5) + -(———)(0.3)(0.3 5! Ei )( Gre ) 5! Bĩ )(0.3)(0.3) 1,0247 2 + ~(——)(02)(-)(0.2)= 0 5! Er )( IGM ) T = 8928.6N = 8.93 kN Ans
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Trang 1812-78 The beam is subjected to the loading shown Determine the slope al B and deflection at C E/ is constant
The slope : 1 —Moa
wa = leash < DI a)(2a)
+ te yaya + 2 -) 2 tas b)
_ Mo(b? + 3abt - 2a")
~ 6EKa + b)
0g =
a+b 6EKa+ by? E7
_ : —® —)(b\( 2 Mob tcp = Aen b) 6El(a + b) b Ac = >? tạp —ÍC(B , Mạb (bÈ + 3ab - 24) — — Mạb - 6El{a + b} 6El(a + b)
- Moa b(b-a) Ans 3EKa + b)
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Trang 1912-79 If the bearings at A and B exert only vertical reac- lions on the ’shaft, determine the slope at A and the maxi- mum deflection +r 17Pa° 3EI 1,Pa a Pa = -(— 3 ~})+(—)¿ +a)= toa 5p a+) ( 7 a)(a+a
Ans Assume Amax is at point D located at 0 <x < 2a
1 Pa Pa Pa’ Pax
= ~(—— +(— =——+——
Sova 2 ET a) 7 1) 2EI EI
Op = 0 = Ops + G4
Pa? Pax ~17Pa’
0 = — + —— +(—_—— 2EI EI 12EI lt x= a@ 12 Pa lL (2a-t4a) 481Pa? = =(— 2 ~—— —— ooo Ans
Amax Itapl ps a 1221 2 a] 288EI
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Trang 20*12-80 The two bars are pin connected at D Determine the stope at A and the deflection at D E/ is constant
M tr £r fa SEL + L 1 | T T ¥ Ỷ
Am Pa “4` 2'2EI 4EI
Os = On, + 9 2 0= =Èa + 8ạ 4EI 2 = Pa" Ans 4EI Pa?
"Oy = 04 = Bees SEI
Pa An = Đ›a=—— Ans
p= 7885 xpy
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Trang 211281 A beam having a constant £/ is supported as shown Attached to the beam at A is a pointer, free of load Both the beam and pointer are originally horizontal when no load is applied to the beam Determine the distance between the end of the beam and the pointer after each has been dis- placed by the loading shown
{5S kN 20kN | CT : — | = — ali? ame bid iS BN 20kN 1 >»k im I am {SEN T ce 4» ting Determine t CLA „ 1/30 2/2 toa= 3 gp HD2 40 †C/A = — Ans EI
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Trang 2212-82 The two A-36 steel bars have a thickness of 1 in and a width of 4 in They are designed to act as a spring for the machine which exerts a force of 4 kip on them at 4 and B If the supports exert only vertical forces on the bars, determine the maximum deflection of the bottom bar
for Setram plate
4rr 4F? A | (F | 4 ship 4*ï orn Smax c1 M | #@ % _ 48 1,48
Anas = tye B/C (EPUB + 12)+ 2œ?2/) = (— sy
_ 20448 20448
El” 200 %ENaK) Ảng
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Trang 2312-83 Beams made of fiber-reinforced plastic may one day replace many of those made of A-36 steel since they are onc- fourth the weight of steel and are corrosion resistant Using the table in Appendix B, with cajow = 22 ksi and tajiow = 12 ksi,
select the lightcst-weight steel wide-flange beam that will 5 kip safely support the S-kip load, then compute its maximum
deflection What would be the maximum deflection of 4 € 2 this beam if it were made of a fiber-reinforced plastic with
Ep = 18(102) ksi and had the same moment of inertia as the
# ⁄2z/( steel beam? Zs 22 - 7/4 ) a, 5 kíp tana taf) AS he 2 0 - tane (b) be-—— 100 4 lon- -— vá) z.e Mmax = 25 kip: ft M(-Ft) Z§
Steq'd = Mes = 2 = 13.63 in? a N
Santow 22 ¬
Cy
Select W 12x 14
(S,=149in? 7, =886in' d=119lin 4, = 0.200in.)
Check shear :
Tmax = Mass = —— = 1.05 ksi < Tayow = 12 ksi OK
A, 11.91(0.200)
Use W 12x 14 Ans
1 25 2 833.33 kip - ft
Amax = Ít, [tact = -(—)(10)(—-)(10) = —————— 3 ep! Gt ) EI
For the A-~36 steel beam :
833.33(122)
= —————- = 0.560 in Ans 29( 103)( 88.6)
max
For fiber - reinforced plastic beam :
833.33(12?) _ = 3 in Ans
18(103)(88.6)
Amax =
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Trang 24*12-84 Determine the slope at C and deflection at B EI is constant
Support Reactions and Elastic Curve : As shown
Wa,
M/E! Diagram : As shown
A ef 4 Moment-Area Theorems : The slope at support A is zero The ae le
slope at C is a
a
Z'¢
1( wat wa?
6.=18, c~I®eal =2|-E }a+(-se}a =~-l—— —
wa?
eT Ans
The displacement at B is
_ _ tf wa 2 wat
As = [fal = air )o+34}+($8 ales 5) at _ wa? 3 3L zz/2 (52) 4lwa*$ = “Ee L Ans
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Trang 2512-85 The A-36 steel shaft is used to support a rotor that exerts a uniform load of 5 KN/m within the region CD of the shaft Determine the slope of the shaft at the bearings A and B.The bearings exert only vertical reactions on the shaft 22m“m sm 8 ITTIIIIItLLL aH form Ph £t Kc wet |? | | Soe mm | ama 759 750" 156 4.805 Ben = 2G)04)+ cee — (0.15) + + NÓ 19-52 4805 4.805 aS = —— 2 = 0.00306 rad = 0.175° El ¥)£(0.01)* 64 = 8g = Ans From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X
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Trang 261286 The beam is subjected to the loading shown Determine the slope at 8 and deflection at C £/is constant
| +—+— — 2 2 3 wa’ a 2.wa Twa
Sw (-) + -(-— la) = me = TD * 3 DEP * 12p
7wa”
6p = Đg¿c a = Onc = 12ET A ns 2 2 Ke = tyre = 4 (5Xa+ 3+ 24 € = đực 2011 3 3'agr)G2) Yayv>
25wa*
= Ans 48EI
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Trang 2712-87 The, two bars are pin connected at D, Determine the slope at A and the deflection at D E† is constant
| AVR EME oe le ail am D a | ;———i———t— A t ề £ 2% £ z (4) whe 2EL te, -PL?
t BIA = = —(—— sư XG by = DET
2
A, = oval „ Pr Ans L 12EI
- :
ae -PL LoL tia DIA = A SL 5 =(—— —+— 3)† 24 sea)? -——
_ Pv ~ 4EI ‡L r3 Ap = Ital - " )fmal = ——- - -(——) = —— Ans 4EI 2 12EI SEI
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Trang 28"12-88 Determine the maximum deflection of the beam E/ is constant ~- wor - wae 2£? E1 2
~wa ava ~wa
tye = (—Y\(-\(-) = —~ ve = Oe OG * Ten 4 wa Ag =| fee] = —— 16EI 2 2 4
“Wwa“ a a, 1.-wa 3a Twa
toe = (S=— oat -) += 78 EP 009 6:00 —)=——— r NT:
Áp +1 tovel —ltwel = Twa" _ wa" = wae 16EI l16EI 8EI 3wa†
§EI
Amax = Ap =
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 2912-89 The W8 x 48 cantilevered beam is made of A-36
steel and is subjected to the loading shown Determine the
deflection at its end A
10 kip tui ===: | 6A —| - Sf: + lo FÌ? †„/@#7a'° A Cr L 8 £ , io Ki? a “ee | 1S xip-ft ~<—— ú, SPL’ _ 5(0)(12') _ 1800 ;
(Aah = 48EI — 48EI “REI BÍ EI
ML? = 15(127) _ 1080 1080 | (Ase = 957281 ET 100 1080 2880 +4 Ag =(Aah + Aah = TT =F El 2880(1728) _ 9.933 in Ans ='39(10°)(184)
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3012-9 The W12 x 45 simply supported beam is made of A-36 steel and is subjected to the loading shown Determine the deflection at its center C
PL? 12024) 3456 A, = FELL 1204) _ 3456 (Gch = tear al” ET Ỷ Mx f 1 A 2) = (2 -3Lx ri +2L) 2 Lh Kip-ft x = > Km At point C, rok oe „ 2 MC) L 2 A, — + (Ach = moe -tLễ )+2L’) ML? “soe _ 1800 | "I6 1681 EI _ 3256(1728)
=——————- 2200650 =0.895 in 895in.l — Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 311291 The W14 x 43 simply supported beam is made of A-36 steel and is subjected to the loading shown Determine the deflection at its center C
2 kip/It 40 kip-ft = = oa C B L 101 J 10 ft { LRP Lt 46 kự-k — ‹ & “2t 70 fe it 222/7 Se + (A), — 4erpkt 5w1ˆ 5(2)(20° 2083.33
(Ac), = ee = IC) 768EI — 768EI EI 1
Mx ; 2 2 40(10)„.„¿ ?
Ac)2 = x —3Lx4+2L’) = ————[10* ~ 3(20)(10) + 2(20
(Ac)2 cai | ) 520) ET! (20)(10) + 2(20)”]
_ 1000 EI 2083.33 + —- 1000 Ac = (Ac)i + (Ac)2 = EI EI - 3083.33 kip: £¢ EI
Numerical substitution for W 14 x 43, , = 428 in‘
083.33( 12?
c= BOP = 0.429 in, 29(102)(428) Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X
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Trang 32*1291 The WI14 x 43 simply supported beam is made of A -36 steel and is subjected ta the loading shawn Determine the slope at A and B
Ar 1 ĩ 2 kinH | | | 40 kip-t 10 ñ † 10 -| 6u Ox It 6a, + Oa, 71wLŸ „ ML 384EI 6EI 7) (240°) „ 4012)(240) _ — 61,200 384 EI 6EI — 29(10)(428) 0.00493 rad = 0.283° Ans Ổp, + Op, 3w17 „ ML 128EI 3E 32240) „ 4012240) _ _ 92,400 128 ET 3EI ———«-29( 10) (428) 0.007444 rad = 0.427° Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3312-93 The W& x 24 simply supported beam is made of A-36 steel and is subjected to the loading shown Determine the deflection at its center C
5 kipft
1=82.8 mÝ )
+ TS (Acỳ ha
(ac); = SWE’ 5(6)(16*) _ 2560 768El 768EI EI
M Áa¿@=-——@?~31x+ 2L2) 6LEI At point C, - 2 MG) ob (Ac) =— 2 6LEI° 4 .(*⁄_ ~ 3G)+2L) + 2 - ML? _ 56) _ 80 l6 16EI ET Ac = (Ac); +(Ac)2 ~ 2560 | 80 _ 2640 El El EI = 76401728) _ 90; 29(10°(82.8) 77 Ảng
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3412-94 The beam supports the loading shown Code restric- tions, due to a plaster ceiling, require the maximum deflec- tion not to exceed 1/360 of the span length Select the light- est-weight A-36 steel wide-flange beam from Appendix B
that will satisfy this requirement and safely support the load
The allowable bending stress is @ajjow = 24 ksi and the allow- able shear stress is Tayjoy = 14 ksi Assume A is a roller and
Bisapin
đua =36 kip ? Sokip
Musas = 162 kip - ft Strength criterion : M lé Satiow = " Sreq'd a 4+ 162(12) % sp qd ầ sị” ° £ x 24= Sreqra = 81 in”
Choose W 16x50, S=810in, 4, =0.380in, d= 16.26in., I, = 659 in‘
Check shear : ŸạHow = —— web 36 142 ——— _ = 5.83 ksi (16.26)(0.380) ksi OK Deflection Criterion; wL* (41242) 1
Vinax = 0.006563 3 EI =0.006563(—————-“~.) =0.7875in « —— 2q0X69)) 7875 in < 34022) 0800 = OK Use W16 x50 Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3512-95 The simply supported beam carries a uniform load of 2 kip/f Code restrictions, due to a plaster ceiling, require the maximum deflection not to exceed 1/360 of the span length Select the lightest-weight A-36 steel wide-flange beam from Appendix B that will satisfy this requirement and safely support the load The allowable bending stress iS Catow = 24 ksi and the allowable shear stress is Tallow = 14 ksi Assume A is a pin and B a roller support
the
Mraz = 96 kip - ft Shy
PUTT PGT A e/fs
Strength criterion : tH sy leet
24 by, ự 24 fp, ` Ổaliow = ———— M req'd 24 = 26412) Sreq'd Sega = 48 in’
Choose W 14x34, S=48.6in’, 1, = 0.285 in, dđ=1398in, 7=340in
Tàjiow # ———
'web
>———= 6.02 ksi (13.980.285) *S! OK
Deflection criterion; Maximum is at center
nn = ae 384E7 ` SETA) 4 (9 PCB) SEI lle) ~ (4)? ~ (8) 9112)? ~r3@6)1 „11 330 384E7 4.571108) * 39(10%)(340) ~ 000464 in < 35(16)(12) = 0.533 in OK JseW 14x34 Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 36*12-% The W10 x 30 steel cantilevered beam is made of A-36 stecf and is subjected to unsymmetrical bending causcd by the applied moment Determine the deflection of the centroid at its end A due to the loading, Hint: Resolve the moment into components and use superposition
kL=170in, 1 =167inf - (Msin 8 )Lˆ _ 4.5(sin 30°)(15°)(12)° 2E1, 229409167) 09032 in max _ (M cos 8)12 ~ 4:5(cos 30°)(152)(12) 2EI, 2(29)(101(170) A4=y0.9032?-0.1537?=0.9l6óin Ans max = 0.1537 in,
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3712-97 Determine the vertical deflection at the end A of the bracket Assume that the bracket is fixed supported at its base B and neglect axial deflection E/ is constant
Pa?b b El (Aa) = 64) = As = PL’ _ Pa?
(ah = Sey SEI
Path | Pa? _ Pa’(3b+a)
Aaa (Aah + (Bade = Er * agp” SET Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X
© 2005 R C Hibbeler Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ All rights reserved
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Trang 3812-98 The rod is pinned at its end A and attached to a tor-
sional spring having a stiffness k, which measures the torque
per radian of rotation of the spring If a force P is always applied perpendicular to the end of the rod, determine the
displacement of the force EJ is constant
ia
k
In order to maintain equilibrium, the rod has to fotate through an angle @ GEM =0 k-PL=0, 9 = PL k Hence, A’ = Le = Pe) _ PL k k Elastic deformation - 3 A” = PL 3EI Therfore, 2
A=A'+A”= TE PLY pal L k 3EI k
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 3912-99 The pipe assembly consists of three equal-sized pipes with flexibility stiffness EJ and torsional stiffness GJ
Determine the vertical deflection at point A
_ PG? PL Ap = 3EI 24EI le Pty? 3 (Ay), = GX PLY P 3EI 24ET e e ( = gn Th _ PLIDG) _ PL Ce) JG JG AIG LJ ~~ ~ Ae, Pus ¬ 4, = SEI 2n, (84); = 6(È) = PL 23 8G Ø
Ag = Ag+ (Ag) +(Ag)2 † Ps
PD PL` PIẺ =
= MEI 24EI BIG + ~~ PT (a 4 (As),
1 1 B
= PL (—— + -—_ oe nh Ans = đa A
FE],
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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Trang 40*12-100 Determine the vertical deflection and slope at the
end A of the bracket Assume that the bracket is fixed sup- ported at its base, and neglect the axial deformation of seg- ment AB ET is constant
44=——=——=—= Ans
= ea Ans
From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X © 2005 R C Hibbeler Published by Pearson Prentice Hall,
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