Benamor.belgacemقضية الشعر الجاهلي في كتابات ابن سلام محمود شاكر
Mech0110
1. I
I
I
""a'18UqJ (Contents)
1
VlanafiUlA1aUlsrl"::>ltJ (General Principles)
2
1.1 fHlfl'lffl'l{ (Mechanics) 3
1.2 uUJmlJJfil9l~'W:[l'W (Fundamental Concepts) 4
1.3 'I1U1Uf11'lll9l (Unit of Measurement) 5
1.4 'l~UU'I1U1UfflfHl (The International System of Units) 7
1.5 f11'lr11UJblll'llW'IJ (Numerical Calculations) 8
1.6 lTIfm'V1%j~1i1lml~'I1 (General Procedure for Analysis) 9
l'il'Vlu'VlU'Vll'W (Problems) 11
3
l::>nlAElSUSJ (Force Vectors) 13
2.1 ,fflfHnfll,,::nfHl'ltlW'{Scalars and Vectors) 13
2.2 lTI'Vll'lI'Vlf1i1f1'1JtI'Il1fHl'ltif (Vector Operations) 14
2.3 f11'lUlfHlflll'ltlf'IJtI'I'I1i:llfJU'l'l (Vector Addition of Forces) 15
2.4 'l~UUf11JJllJn'W'lJtI.Ju'l.J~t1~lm~'W1Ulfi1nn'W (Addition of a System of Coplanar Forces) 21
2.5 I1fHl'ltlfl'W'l::1J1J'Vlnl9l111f) (Cartesian Vectors) 28
2.6 f);'lUlf)U"::f11'l"Ul1fl1l'ltlfl'W'l~u1J'Vln9l111f) (Addition and Subtraction of CartesianVe.ctors) 33
2.7 I1fl1l'l[)f'j~1J~h!l'l1U'l (Position Vectors) 39
2.8 nfHl'ltl{II'l.J~iiViI1'Vll.Jl'llJJUUJlff'W (Force Veg:or Directed Along a Line) 42
2.9__~~.~rul;.Jfflf1~1{~~ct) 47
l'il'VlU'VlU'Vll'W (Problems) 53 ... '.
2. {u~atJaJaun1A (Equilibrium of a Particle). .
1-
3.1 trfll'WtrlJl'ltl'Utl'Hl'4fllfl (Condition for the Equilibrium of a Particle) 77 '
3.2 vr,r)9itlvtr':i:: (The Free - Body Diagram) 77
3.3 'j:;UUtl'j-:Jh!':i:;'U1Ul~tl1n'W (Coplanar Force Systems) 81
3.4 .':i::uUU'j-:Jtrl'IJljiij (Three-Dimensional Force Systems) 86
l'il'VlV'Vl1J'Vll'W (Problems) 93
lJaaW8S:UUllSJ (Force System Resultants)
~..J~ v ~ ~ ~I ~
'1 4.1 J:-la~ru'Utl-:JnfH9itl'j'Vll~J:-laa'W1Jlu'WnfH9itl'j (Cross Product) 109
4.2 llJllJ'WIPi''Utl~U':i~-~t1trlJf)l':itrlf)mf (Moment of a Force-Scal.ar Formulation) 112
4.3 lmlJ'WIPi''Utl~U'j~ -~tltrlJfl1'jl1fH9itlf (Moment of a Force-Vector Formulation) 114
4.4 rnllJtrllJl'jt)1'Wfl1'jl~tl'WlillUl1ll-:J'Jtl-:JU'j-:J1W:;'Utl-:JllJllJ'WlPi' (Principle of Moments) 124
77
109
4.5 ' 1lJ1lJ'WIPi''Jtl~1l'j~'jtlUllf)'W1~ <) ~nll1'W~~'W (Moment of a Force About a Specified Axis) 127
.>'4.6 lmlJ'WIPi''Jtl~u'j~~rn1J (Moment of Couple) 133
4. 7 fl1'Jlfl~tlWrltJ'Utl.Jll':i~U'Wl91tlU;U'Hf)1.J (Movement of a Force on a Rigid Body) 140
4.8 Na«'Wli'Utl~u'J~ua:;'J:;uu'Utl~u'J~~rn1J (Resultants of a Force and Couple System) 142
4.9 fl1'Ja~Hl'J.Jlla:;':i:;1J1J'Utl.JU':i.J~rn1J (Further Reduction of a Force and Couple System) 147
4~ 10 " fl1':ia9i':itl~cl'I1Ill1Uf)~f)'j:;YllUUUf)'j::'illtJtlthffi1J)~ .--
(Reduction of a Simple Distributed Loading) 157
l'il'VlrJ'VlU'Vl1'W (Problems) 165
fU~atJaJ5~QlliJJLnSJ (I;:quilibrium of a Rigid Body) '.
5.1 iitl'Wl'U-a1l1'r1JtrlJl'ltll9itlll;U~!f)~~ (Conditions for Rigid-Body E~uilibrium) 193
_ trJJl'la1'Wtrtl.Jljiij (Equilibljum in Two Dimensions) 195
5.2 vr-:Jl9itlvtr':i:; (Free-Body Diagrams) 195
5.3 1:1"JJfl1'j1:1"lJ~1;1 (Equations of Equilibrium) 204
193
3. ./
v
5.4 'BlHhlHHl-:JI1Cl:;l.YllJl1':i':] (Two-and Three"':Force Members) 213
~~~CllUl.YllJiJ~ (Equilibrium in Three Dimensions) 215
5.5 N-:JllllfjVl.Y':i:; (Free-Body Diagrams) 215
5.6 l.YlJf11':i'UCl-:Jl.YlJ~Cl (Equations of Equilibrium) 219
5.7 ~Clihnmhl1ful~HlU~-:Jlf)~'1 (Constraints for a Rigid Body) 220
l1l'Vl£hmvnu (Problems) 231
I'
iI
n1s5lAS1::vifAsuaS1U (Structural Analysis) • 253
7
fl.1 lm-:Jt1fH!UU~ltJ (Simple Trusses) 253
6.2 l~ fml'11~9I9iCl (The Method of Joints) 256
6.3~lJ'rilUI1':i'l~l1mntJlu'ti~Cl~uriTu~1lifu!!':i'l !t1UIJ'Ut! (Zero-Force Members) 262
6.4 l~f11'Jl'11f11fl~9I (The Method of Sections) 265
0.5 lfl'J'It1nl.YllJmi (:Space Trusses) 271 .
6.6 lm'lmClu!!t'l:;!fl~Cl'l,]mflt'l (Frames and Machines) 273
l1l'Vltl'VlU'l'llU (Problems) 291
llsufl1s1u (Internal Forces) ~7
7.1 !!'J-:JfI1tJlu~!fi9l~ulu~urilulm-:Jl.Yfl-:J (Internal Force Developed in Structural Members) 317
7.2 N-:J um:l.YlJfll'J'Utl-:J U'J-:J !i1u'U!!t'l:!:l.YlJf11'J'UCl-:JllJ !lJUI'l~9I
(Shear and Moment Equations ana Diagrams) 326
7.'3 fnllJfflJl1Ulf'J:;i1i"1'llhtnl'fl m:;'I'h UUU m:;'illtJ f11':iL{fCl'U UClUlJ ;~TJIlt~
"
(Relations Between Distributed Load, Shear, and Moment) 331
7.4 LflLDt'l (Cables) 338
l'il'Vltl'V1U'VlJ'U (Problems) 350
4. nUla8~n1U (Friction)
8.1 af)1Jru::;'Jil'lmllJl~V9l'vn'Ul!UUUr1'l (Characteristics of Dry Fric'tion) 371
8.2 iftJ'l1lI~WH)UmlJJl~V91'V1l'Ul!UUlIr1'l (Problems Involving Dry Friction) 376
8.3 i;1lJ (Wedges) 387
8.4 lI'J'HffVI9l'Vll'UU'Ufff)~ (Frictional Forces on Screws) 389
8.5 1I'J'llffVI9l'Vll'UU'UfflV'V'I1'UlIUUlI1Jl,ll1VU (Frictional Forces on Flat Belts) 393
8.6 11'J~Iff(J91'Vll'UU'UlIU~~IIUUU ftil f), lIU~'lllUU.uill'i il~lJf) ftlJ IW::;llH'Uf) ftlJ
(Frictional Forces on Collar Bearings, Pivot Bearings and Disks) 396
8.7 IL'Wfftll9l'Vll'UU'U!!u1'l!!UU Journal (Frictional Forces on Journal Bearings) 400
S.S mllJI'i'1'U'V1l'U1'Uf)lm~'l (Rolling Resistance) 402
1'U'VlcJ'VlU'Vll'U (Problems) 405
~lJuarbJlla::munsa8~ (Center of GraviW and Centroid) •
~I ~ Q v
9.1 ~l9ltrlWmlII(j:;~l9ltrlWn(jlll.rm1:fl/1'Jm:;UU'lJillil'4mfl
(Center of Gravity and Center of Mass for a System of Particles) 431
9.2 'U19lf1''Ucfril~, 1l19lf1''Ucfnftll'lJlft l!ft::;I9f'Umiltl~'IJillil'lfiq <tI q qJ. q
(Center of Gravity, Center of Mass, and Centroid for a Body) 433
~J 119lt:jU1::;f)ilU (Composite Bodies) 443
9.4 'Vltl1J~'JillllUuifffllft::;Qft~hrff (Theorems of Pappus and Guldinus) 447
371
431
9.5 Nfta'V'lli'Jil~1::;'lJ'lJ1I'J~l!U~m::;~mJJ*T "Resultant of a General Distributed Force System) 451
9.6 m~~u;Ut1~l11-(j (Fluid Pressure) 452
11l'VlcJ'VlU'Vll'U (Problems) 460
5. "l
·10 :1.
•
rUlUU~lJa)A~)I1fQa8 (Moments of Inertia) • 487
10.1 iltlllJ'Ue'lllJtlJ'WI'1'Uti-~mllJt~etl'Ue'l~'Wyj (Definition of Moments of Inertia for Areas) 487
11
" ,
10.2 'V1f)lJ~tm'W~'U'Wl'W'Uil,:rw'W'Vi (Parallel-Axis Theorem for an Area) 488
10.3 ff1iil'iJt'Ji''W'Ue'l~'Wyj (Radius of Gyration of an Area) 489
lOA IlJ tlJ'Wl'l'Ue'lmllJ t~e tI1:hl1fll'i~/'Wyjl~tlfl1'JtJ'WVi tf1'JI'I
(Moments of In~rtia for an Area by Integration) 489
10.51lJtlJ'WI'1'Ue'lmllJt~etl'Ue'l~'Wyjlh::;f11llJ (Moments of Inertia for Composite Areas) 495
10.6 ~'Hli!lru'Ue'lmlm~mJ'Uil'l~'Wyj (Product of Inertia for an Area) 498
10,7 IlJ tlJ'WI'l'Ue~mllJ t~etl'Ue.:J~'Wyj'JelJ Ufl'Wt~tI'l
(Moments of Inertia for an Area About Inclined Axes) 502
10.8 J'I~ft'jJl'jJ"j'Ue.:Jl'jJt'jJ'WI'l'Ue.:JmllJt~etl (Mohr's Circle for Moments of Inertia) 506
10.9 IlJtlJ'WI'1'Ue-lmll.H~iltl'Uil.:Jm" (Mass Moment of Inertia) 509
1'1'YltJ'YlU'VlJ'W (Problems) 516
J1ULauau (Virtual Work)
11.1 iltlllJ'Ue'l.:Jl'WU"::;-ll'Wl'ffiie'W (Definition of Work and Virtual Work) 539
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11.2 l1ftflf)1'J'Ue'l.:Jl'Wnl'jJ1l'W'Ue.:Je~mflUft::;JI'I tlu'U-ltf1'J'l
(Principle of Virtual Work for a Particle and a Rigid Body) 541
<V "'" 'U ~ c;$.c:::t~ ,IV
11.3 l11lflf)1'J'Ue.:J-ll'W'fflJe'W'Ue'l'J::;uu'UenI'lQu'U.:J tf1'J.:J'Yl!'liillJl'lil fl'W
(Principle of Virtual Work for a System of Connected Rigid Bodies) 542
11.4 U'j'.:J1l~ffnr (Conservative Forces) 550_
11.5 vnl.:J':l1w1fltJ (Potential Energy) 551...
11.6 mtucvl'Ue.:JVli:i'.:J.:Jl'Wrrf1V'Ue.:J'ff~ft (Potential - Energy Criterion for Equilibrium) 553
11.7 n"fitl'j'mVl'Ue.:J'ff~9,!ft (Stability of Equilibrium) 554
l'iJ'YltJ'YlU'VlJ'W (Problems) 563
1/
539
17. 2
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(Force Vectors)
1J'I'l~ 2 iff) cirJ n'l'11 t1f) f)11"'UU'l U1"'l UCI::l1i f)11"1"1lJ 111"'lIf)11"unifqJ'111 U1"'l i'l f) ci111UU<tTU9IeJU
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2.1 ama1sua:l::>nlflEJS (Scalars and Vectors)
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mlJ1runmOlBfllj;'f~-:J~1(J{lflf'l1" ~'l'il:;;1Jtlf1.vf-:J'UU1~IIC1dlf'l'l'll'l 'UUWI (Magnitude) 'Utl-:J nf1
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20' 1~m'Ul~~U1Wf)1'il1mlf1wS'1'lV'lIW:;;iiVif'l'l'l1'l;j'U1u~1'l'IJ11 ~~ 0 lUU'ff1U'111'1 (Tail) 'IJ~'1
nmOltJ{ UCl::~~ P lU'U'fflu(JtJ9I'11~mr, (Tip or Head) 'UtJ'InmOlu{
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.2 58n1JlnAilAlJall::>m~aS(Vector Operations)
fl1'jflrull":::flTnlTinflll1lel~~'l£Jalmn~ (Multiplication and Division of a Vector
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by a Scalar) u"ilJ1UHlflllPltl"i A tll:l::'f1'If)i;'11"i a 'il::IPlll aA 'li'1lu'Wu"imUHlflllPltl"i!!l:l::lJ'IJ'WlPl
ril'IJtl'1 a iirillU'Wlnfllrltl a IU'Wrillnfllll:l::ril'IJtl'1 aA iiril!U'WmJ Irltl a !U'Wrill:lU ~'1J'W
mlJlrunflllPlvf~!U'W1;!1Jhi''illflm"it!ru mmrunfllIPlVf9l1tJ'f1'!fll:llf (-1) ~'1~1J~ 2 - 2 -ffll1i"'U
flT.il1l"i1J'1mrun fl !lPltlf~, tJ 'f1'lfl l:llf'il ::utJllJ1Pl tJ1'lifl~ fll"it!ru~ltJil 1l:l'IJ~!UUlft'IHh'W ilil til'1
li'W Ala =(l/a)A, a -oF 0 ~'1~1J~ 2-3
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1lfl!lPlilfrl''Y'ffl R = A + B. 1PltJ1'1ffl~#Il1~tJlJ.®J.1J.1l1Q'W (Parallelogram Law) A Ul:l:: B 'il::
~m~mJfl'U~ff1'U1J'l1m,f'1~ ~1J~ 2-~ ('lJ) U'f1'~'1!5'U1J"J::'IJ'Wl'W'il1flri"Jlnr1'IJtJ'1ul'itl::nf1llPltJfm11
miPlf)'W ru 'ilPl~nll1'WPl U"i'1rl'~,r R fitJ !5'W'Vl!W'1lJlJ'lJil'1"i1J#!11~tJlJ~1'W'lJ'Wl'W~l:llfl'illflffTu1JmtJ• q •
'lJil'1 A Utl:: B 11Jv'1'ilPl~Pl ~nll1'WPl'lJtl-.l15'W1J"i::q
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fll'J1J1fl!1n1I'l!l f
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fll"ilnf1l1f11lPltlf B Ul:l:: A 'f1'llJl'lfl1'lifll'l'f1'fl'1~1J'f1'llJ!l1~tJlJ (Triangle Construction)
1PltJthnf1l~ltJf B mUlflflUllf1llPltlf A 1'1fl1rl'flffl'W'l11I'itlflUril'W111'1 (Head-to-Tail Fashion)
~'1~1J~ 2-4 (ft) Ilf1l'l'afrl'~,r R fiil 15'W~mfl'illflril'Wl1l'1'IJil'1 A 11JV'1ri1'W'l11'lJV'1 B 1'W'vll'Wil'1
1~,tJlfl'U'f1'lmmV1l1~i'W~1J~ 2- 4 ('1) ~'1J'W 'f1'llJl"JfI'f1'till~il R = A + B = B + A
1'WmruVllft'1l t1mf1l~ltlf Am!:: B iirl'flllru::1U'WU'Wl1«'WI'l'l'11~tJlfl'W (Collinear) UMI'1
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ffl'IJ1~m~tJ'..!tl~lU~U'IJtl.:J
R' = A - B=A+(-B) /I
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IU'WI.Yl'l.nJ'J:;f1tlufftl'ltflu CJ1'11'i£Jf1':h uUlf11~m:;vh (Lines of Action)'hwlci'f1~~tl~I'I1~£JlJ
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nUl'd'wl'Ul a UCI:; b lm:;ril'UU'J:;fltlU A UC!:; B 'II:;CI1f1'ii1flffl'U'M1.:J'lJtl'l R ltliJ'I'II9lI'l9l~li191~'Uq •
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2.3 01SU3nl3nlVltlSUtlUVla1t1USU (Vector Addition of Forces)
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+ F2 uci'11JlfHvi'IJnUI1~'1~ffl'IJ'II:;I~p.jC!«~,r'IJU'I11~'1vf'l1-1'IJ9I,rufiu FR = (F, + F2) +
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ifty'M1trffll../1~flunUty'Ml19ltJl'li1~~:;uuVifl9lmfl (Rectangular-Component Method)
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liillT'Hbl'lr1.l?!fl~J~li _(p'rocedure for Analysis) ifqpnvhnfJ'J'11tJlnlJfiW.f'JiJ
!!J.:J~eJ.:J !!J.:Jl!Cl::iitleJ.:J;1ulbhjymlJfhtlllJl'HlunifqJ'I1l19ilf!I:JI'1i1~llml::MI9i'I~tJ1U-Q
flJJ~tl~l'I1gtlll~TU'llU1U (Parallelogram Law) tl~llfllWrfjl'J '1 Utl19Flnl1'lJdfinml'ltJ{
If! fJHfit]~U~I'I1~I:JlJ 19l1'U'UUl'U fllliJ'Ulull9lrn1'l11~lJfl1l:Jl'U~u~m~I:JlJ 19l1:tJ-'Il'Ul'U'il1 fi ~ul'lll
l1''lJlflrul'l'IJtJlI'il'l'HJifuJ'111 ..rl-Q vHn'JlJ'lJtJllJlJ..rl'l1lJ~'il:::#ltJlM 360
0
rillJlJ>'il1'l #lUlutlf!ll'11'
'If~l'il'U..rl ril~fllt1:::1~f 'UtJ fi'il~~'d~u-l;~~~iJ~-~~~~'~19l1~~~~;£;~~~~~~Inl1'lJd fi ri'J'U
111>'itJ ri1'U'I111 UlJlJ~UtlllJ l'I1~I:JlJ'UtJ.:JeJI rlU1'::: fiUlJlr'U '1
ll~lfiruilCl (Trigonometry) 1i'l1clfinl1'I'l~lfiruD~'I11;'Jmh~hhmlJrilh1'illfi'11mJil~il
l'U~utlllJ l'I1~tllJ fll~'lJl'Utll'lJI'll ~I:JlJhjil~'lJl~il ril 90
0
fitll'lJl1'ftUl fit]'UtJl9I1I:JUllil:::lfl9l1 tlU
lJlU1':::~fiI'l1'lf1I9lI9i'I~U~ 2-9
".itl~2-9
"
('II)
. .~ .
fiJJ'lH)l9Iltlii (Sine Law):
A B C
sin a sin b sin c
C = ~A2+B2 _2AB cos c-
~U F Uil::: F 'ill'l1l'U'Ul~llil:::
~tl~ 2-10
l'
1 2
360°- 2(650
)
----=115°
. 2
. ~~L-~,-~___
(f'i)
, ,
21. ..
~d 0'
~]jm
fl~4U~I'I1~tJ:IJ~TU'IJU1U (Parallelogram Law) n~~U#m5t1lJ~lU'llU1UU'il~.:!1u~tl~
2-10 ('II) 1'l1uU)'11-i'l'1':l1Ufh.J-:J'iltl-:J fitl'UU1~'Utl-:J FR lU't~l.JlJ e'illn~tl~ 2-10 ('II) ~U'illlJm~tI'lJ
mllPltl1'ill'lJl),()'iltl.:!1u~u~ 2-10 (fl)
n~l'IjlfltuiJ~ (Trigonometry) FR ml~I~(JH'f)t1'11tl-:J1f1'lil(Ju
FR = ~(100 N)2+(150 N)2-:- 2(100 N)(150 N) cosIlY
= ~~0000+22500-30000(-0.4226) ~ 212.6 N
= 213 N
1.J'lJ e ml~~tltl)'~~f)Pl1'lif)t1'Utl-:J'liltiu uCl~1'lifh FR ~ri'1'Ulru'lJ1M'Ii'1-:J~U
150 N 212.6 N
sine", sin11's°
sine 150 N (0.9063)
212.6 N,
e == 39.8°
v
l'l,nT'U Y1i'1'Vll.:.! <j> 'Utl.:.! FR l~'illf)U'Ul),l1J 'il~1~",i1
<I> = 39.8° +15.0° = 54.8° d <l>
pbm.hun 2-2
,-, .
'il-:Jm,h'Utl)'~f)()1J~()(J'U().:.!11'j'':'! 200 Ib ~m~'I'h~tlMl.J~~.:.!U'il~.:.!1'U~tl 2-11 (n) t-u (n)
Y1i'1'Vll-:J x l1Cl~ y UCl~ 1('11) V1i'1'Vll-:J x' UCl~ 'y'''
y
:t<;
; . -1 _ __ _ ---= 200 1b
I£-_ _-l----'~I-- x '
~r
('IJ)
(n)
'jU~ 2-11
" ('iJ)
17
~"'.
/ .
22. ,'J "
18
"
" ."
.' '
,/
/
"'...1Ji111
, 1'Uullia~mru'll~1'1fnOlU~!l1~tJlJI9.l1'U'U'Ul'ULYiVl11 F 1'UlU'UVILL~IavtJ'ffVI L;L~Iu"'1lh'lu'fff1.l
~U'ffllJ!l1~tJlJL1 fHl'lVfLYifll11 ~a~1La'Ul~tJ1'1fl'ljlmulJ~
(n) mnnnL1fHl'lflf F = F + F LL~l1'U:iU~ 2-11 ('U) l~tJmVmflal'l~'l 'WU':i1fl11lJ
x Y, CU I 1
tJ11'UVILL:i'laVtJ ln1~1'l11JLLn'U X ua~ y li'ff~ll Lff'UU:i~~'U'Ul'Uf1uun'Ul'lllJnOluiY!l1atJlJ ~1'U'U'Ul'U
'IIlnlU'ffllJ!l1~tJlJL1m~vfillU~ 2-11 (f1)
F = 200 cos 40· = 153 Ib IlHlUx
F = 200 sin 40· = 129 Ib I'II'I'Uy
('U) m:iU1fHlfHl'lflf F = F + F !L'ff9l'l1mu~ 2-11 ('l) U:i~tJ,f)~f)fl'Utl.:J9fll'Jlr!La:x' y cu "6J
1'1f'lJVl.Jtl~flQ1'U~U'ffllJLl1~tJlJL1fHI'lV{~I~U~ 2-11 ('II) 'II~'Ml1
Fx' 200 Ib
sin 50° sin 60°
F, = 200 1b(sin ,500) = 177, Ib ~HlUx sin 60°, , _
Fy 200 Ib
sin 70° sin 60°
F = 200 Ib(sin 70°)=217 Ib 1'1flU
Y sin 60°
U:i~ F m~l'11IlivlmlmvU~llU~ .2 - 12 (n) liii'U'UWI 500 N LL(I~'ffllJl:imLUlVvmlJ'U
'fftl'l!L:i.:JatltJl'lllJ'lJVI'iV AB !La: AC 1l'll11lJ,lJ e ~1~h1!L'U1'jlU LYiflYi'll:MLm~fltJ F
" AC
Vift''I11'1'illf)' A 'lucY'l C !Lt'l:ii'U'Ul~ 400 N rt ~<
~B~_ __ ~,
/ ('I)
'F=500'N _ .J;. 1
(0)
-.,/_-
23. .. ,
~500N
. () l:W 600 .
~c=400N
(.:.t)
'jtJ~ 2-12
"
"'.. '
ltiTll
lflIJHfl~ltl~tl1~IJlJ ~lU'IJU1U fll'l"Ul fl n ~I~ ()f'1e~IIj.:J ti{) 1J~.:J~{).:.t'il::;I~~1;1 l:l'Vnfi.:Jltl~
2-12 ('1) «.:Jlfl~111~h~{)llj;]i:l'Vnfflflllr1ltll1Julmti{)V~{);]lIj.:.t F 111;1::; F ~-lflm::;1J~'"WIIUlI qJ AB AC 'U q
nrll'U{);]f11jm:::l'll ltl~llJtl1~VlJnfll~{){~{)flflael'HI~fl;]1ultl~ 2-12 (f1) ~lJ e ~llJTl"f1
l11i~1~V1'J5f1~'IJ{);]'b'1VU
400 N500 N
. sin' .<!> sin· 60°
"' . (400 N) ,sin 'l' = - - sm
500 N
<!> = 43.9°
60° = 0,6928
e = 180' - 60' - 43,9' = 76.1')' ~9
1-hf1~ 8 .QMlJltl'l::;~fl~1'J5n1Jfl~'1{)'lIf1'b'lVU'il~M F AB ii'IJU1~IVllfllJ ~~_~ .N 'Il;]U
ftllJl'lflflTl.nullmil F 1I1;1:::tlTU1u!'VI1'V1f1'V11;]~'lfi{) l,jlJ 8 ~1~'illf11l'Ul'nlJi'lII~~;]1ultl~ 2-12
(-l) l~vtY'lfl-lihmti{)1J F {)fj 1um&n 8= 16.1' 111;1:: FAB = 161 NAC ~
,I.
.
/
" 19
:-:
, I<
24. 20
"
.1-
--
I (
1.:J1t'l11'Ultff~.:Jl'U~1l~ 2-13 (n) lnm::;'I'll~ltJll'j.:Jfft).:]It'j.:J F 1tC1::; • F t11~tNm'jIt'j.:]1 ~ 2
~'V'nj~ii'n"h~ i kN lw::;iiVifl''V1l.:]yj':]C1'll'll'IJU'Ul~':] 'il'l'l1l (n) 'U'Ul~,Hl.:J F 1tC1::; F lntJ
.... q 1 2
e= 30· 1tC1::; ('U) 'U'U1~'UtJ'l F lW::; F t11 F iifilUtH.lVi'l'~
1 2 2
-:i1l~ 2-13
"
"'...ltifll
(n) 11Wlfll'l'lfl111 '1 l~tJlnUfll'j~lflllflll'ltJfl'll'IJfltl~tl~l'I1~tJ'IJ~l'U'U'Ul'U~'l~ll~ 2-13 ('U)
'ill n~llffl'IJl'I1~tJ'IJn flll'lt)f~ffrl'lI'U~ll~ 2-13 (fl) 'U'Ul~'UtJ'Hil F1 lW::; F2 ~.:]rNlli'Vl'Jlu,r'U
1"1'IJl'jfI'1111~VItJ1'Iifl tl'U tJ.:J9l'1tJU
Fl 1000 N
sin 30° sin lJO°
F[ =653 N
Fz lDOO N
sin 20° sin 130°
F2 =446N IlHlU
' , :4: .
25. f ,
..
('IJ) tll'hiM1:::'l.lfh e 'il'UlU~llJt'I15rJlJ'lJfl-:J!!1-:JlulUl1fHl'ltl{rl-:JlU~ 2-1 3' (-:J) 'f>I1y,h F2
, 'i):::(1'llJl'Jtl1J'JflnlJ F h1"'HnrJl1il'vlfllY11~!!'ml'f>1'fi 1000 N l~tJlll'f>ll:::mh.:,jt.:,j mllJrJl"l,rVrJ~~1'l1 -.-- .--.•-------- .q
l1~fl'IJ'Ul~'lJfl-:J F J'U11:::ln~9J'UlriVU'I,r.JI~'U1!1.:,jm:::y'li.:,jlnf)nu F ri"l'U1'U'ViffVm~'U <') 1'Ji'U OA. _ • • 0- - 2 ._- -_. - . -- ' ~' - " ... - .. . - -" - .. - ---- _. .-. . 1
-~~V OB l1:::vhhr F iifhlJlf)f)",h ~.:,jJ'U I~tl e= 90· ~ 20· = 70· 111:11 F 'il:::iifh,rvrJ~1:I'1'l2 2 •
1l1f)l1l1:l'1lJt'I15rJlJ1'Ulllii 2-1 3 (11) 'f>IU'l1
1000 sin 70° N = 940 N ..
1000 sin 20· N = 342 N
"
VlflU
VlflU '
024308
21
2.4 s::uun1sS3unUlJt))lLsJIla~1us::u1ul~f.J3nu (Addition of a System of Coplanar Forces)
1'Uri1'Ud'il:::Ufll'IJuWl1lI11.:,jUI'll:'l:::U1.:,j1I'Wf)1111I'lfllu'UlmvvrJ F 111:1::: F ~.:,jtlv1'Uuu"luf)'U xv x y <u
IW::: y 1'l1lJi:i'1I'1U l'1.:,jlll~ 2-14 (n) 111:1::: ('IJ) 1I'lrJf)OlllaI11~rJlJ~1'U'lJU1'U 11:::Ml1
F = F +Fx y
111:1::: F = F" + F"x y
y ~y
lZJ_
F
- < /
(f)
lU~ 2-14'IJ
F'
('II)
'illmtl~ 2-14 Yif('V1l'l'Uv;m~l:'l:::li1'lljmJll~I'l'lil1rJ111Mff'J 1'Uf)1'Jllml::...hl:::l91fl'liiff'wtrfllJru'U • 'lI U
• Yif('V11~'lJV.:,jriTUU1:::f)VUvvti~i'lln f) nu'Uv'I UI'l l:'l::11 fl Il'ltlfl'U'J:::U1U I~rJ1 nU~lrJ 1191 rJ m:::vhM
'~
1:I'tyl:lfllJo1mmni (Scalar Notation) 111'1VVrJ F 1'Ulll~ 2- 14 (f) IU'UI'il1:l'lfl(;1l{
1J'Jflvr'l F IW::: F 1'l1lJYiff'Vll'l~IU'U1J'Jfl'IJfl-:Jllfl'U x Ul:'l::: y I'lllJr.11~U -a111i'UI11.:,jVVrJ F' 1'U'J1l~x v y • IV 'U
2-14 ('IJ) uti'f>lUl1 F' iiYiff'Vll~1UIlf)'U y vitU'UI:1U l'1'1u'U 11:::11911!1'lVVrJ F' iirillUUI:1U
y y
atyil'ollWldml'le,iltf:i:::1J1JYlOVllllfl (Cartesian Vector Notation) f)1~U1:I'I91'1111'1civrJ1'U
11l'IJV'I11 flIl'l v111i1'lm.brJ1'U1:::1JuVlnl'll1f) (Cartesian Urrlt Yestors') ..,~:;if1l1:::1t)'IIYlJlfl1'Uf)1':icu . . ,- _ .• ____•
unU11J11l1'il'Vlt11:1'1lJii~ ri"l'U1'Umruh'VlcJ1:I'v,dJ~ I1fl1I'lV{11~'l11)l!~1'U,':i:::1JuVl,rll91lnn i l!l:'l::: j 11:::
1i'u1:I'1'l'l11ff'Vll'l1UU'U1I!f)'U x 111:1::: y '9lllJ r.111'11J ~.:,jlll~ 2::.1~-(fl}nJlI~V{~'If)ciJ111:::ii'U'U1191 Iflfl
~ ,,~ ~ d '" ~ ~ u ~ -l ~i
fll'f>l t!1:1:::t'JlJ I'l ImV'Il1lJl rJU1flILl:'l:::I:1U IU'Ulll1'l1lJ'Vlff'Vl~'I'IJ()'I111~f) ff':iIUIlf)U.x ,11i:'l:::,, y 'I'I1)J'UlJ"lf)
26. I ' [
23
lUfl'iru.t1hJu'j~cimJhH!f)'W X ua:: y 'Jfl..:Ju'i~awfi'lJfl'lU'i'llu'i::tilul~tllnulOl'1 ffllJl'Hl '
'~fJtiflylu~tl
(2-1)
)' )'
----------~~----------x
(0) ('U) ,
)'
FJ FR '- . '
x
FRx
, (i'l)
'itl~ 2-16
~ "
lrim.h::tlo~1'li'fflJfll'iii'il::9lfllfhU'l()..:Jli'l~fl'l'f1lJltl'Ufl'lU'j'lrifltl~l'l '1 ' ~llJ!!UlUf)U X 1m:: y• q
ill'iliifhdJu1nf)'f1~mlU fflUU'i'lawi~lnl9l'il::9lCl'lI;UtluluVifl"'I'11'l~!'f1lJl::fflJ~llJUUlUf)U x ua::
y ~I~U~ 2 - 16 (fl) ;'UU1Ol'UCl'l FR 'f1119l'illf)'I'1flH~'Wlil1m~tlu (Pythagorean Theorem) JUfiCl
e =tan-l IFRy 1
FRx '
l _~
27. 24
"
y y
'------- x x
F'b' = 200 sin 600
N
FJ = lOON
I (n) ('I)
'jtJ~ 2-17
"
= ....
• li'Yll
UtlJ~flllrua!mn1 (Scalar Notation) l~e'l'Jlfl F m:;'I'111'mJHflU y Yid'Ju(j1J U(j:;'JlJl~u 1
'IJe'l F fie 100 N UJ'ltitltJ1:l'llJl'Hll~tJu'l'U'H.h:1'lmnl1~il1 v
d ..... OJ d ,
'YI,)'1Hlfl'UtJ'YIWnl
lHIU
1~tJfl~~tl~!'YI~tJ'IJ~lU'lJlJl'U F2 'J:;u~fll~d'J'UuJ..:JvmJ x U(j:; y ~..:J~tlrl2-'-17 ('J) 'IJ'Ul~
'IJtI'III9iCl::UJ..:JVtltJ'J::'VI1Mi~tJ~11muii~ 1~t1'1'Jlf1 F m:;'Vh'lUYlf1''V11'l -x 1m:; F m~'I'h'lu
a ~
F2x
= -200 sin 60' N = -173 N =, 173 N ~
F2y = 200 cos 60' N = 100 N = ' 100 Ni
lHI'U
liIelU
iltlJinllru!1fl!~HI~1'U'j:::'U'Ui'ln~Hllfl (Cartesian Vector Notation) fllml'IJ'Ul~'IJtI..:J
ll,)'1VtltJ'lJtI'I F2 ~'I~tlrl 2 - 17 ('II) allJ1Jml1:l'~'I'l'U~tlllfll~t1fl'UJ~uuVlfi~mf1il '
FI = Oi+ lOON (-j) "
= {-100j} N
F2 = 200 sin 60' N(-i) + 200 cos 60' N (j)
= H73i + 100j} N
liIiI'U
liIiI'U
28. I .
I
I
I '
J-
25
~~aB10n2-~ --------------------------______________________________~
.. - 'iI'lvnu'j'lcitl(J x un.:; y 'Utl'l~~'j'l¥ ~'lH""~N1'W~u~ 2-18 (n)
y y
F= 260N
(n) ('11)
'jui! 2- 18
"
='" 0
llim
. U'j'l'il:;~L~mlJ'WLL'jl~tltJ x un:; y ~I~U~ 2 - 18 ; ('U) fl11lJ'lI'W'Utl'lU'W1Lff'WU'i-:Jf)'J::;'Vll
""llJl'jmL""~'l'h)'illn""llJL'I1~(JlJfl"lTlJ'lI'W 1~(J evnM'illfl e = tan-' C~) un:;'I11'U'Ul~'Utl'lu'j.:Jcitl(J
1~1'Uvil'Wtl.:J~~hnn'Uf11J F 1'W~1tlcil-:J~ 2-5 tlcil'lhn~llJlli~~l(JW,il ~tl Hff~ri1'W'Utl'llJlJ_ . 2 "Ii
'illn~U""llJm~[JlJfl"'1[J~1'i1'V16nl'l1'U~hi' ~I.J'W
(
' Fx )_(12)
260 N 13
F = 260 N(12) = 240 N 'x 13
Fy = 260 NC
5
3) = 100 N
1"jUil'U'Wl~'UtllH'j-:Jcitl[J1'Wu'W1'jlU F 'il:;11ii1~(Jm'j~tl!'U'Ul~H'j'l~1(JV~'iTri1'U'Utll'U1U'U1'il1J
'Utll ffUJm~[JlJ mllJ'lI'U~'I11'i~1[J ~l'U[Jl~~-q~'Utll~U""Ailm ~(JlJlJlJll.l n 1'W'U tl!:;~'U'Wl~'Utl-:J U'jl
citl(J1wL'W1~'1 F 'il:;1~1~(Jm'jfltl!'U;:n~'UtllLL'il~1[JV~'ilri1'U'lJtll'U1U'W1~lvn'i~1[J~1'U[Jll~ff~y <u i " "I
'Utll~U""llJm~(JlJlJlJll.l n 1'U~i1'il::;1'lifft1Jc)n'lJruffLfI nif
Fx = -240 N = 240 N (.,-
Fy =-100N = 100Nl
ill F H""~lLtJ'Wnm~tli1'U'J::;1J1JVin~ll.ln 'il:;Mil
F = {-240i-100j}N
,.,
mJ'lJ
17HJ1J
29. 6
• ~baEhJn 2-7
y y
FI =600N F2 =400N
,..--..
--------~~--~-------x
I.....-¥~-"---I-f....., --x
(Il)
~d 0 d
11i111I1UU'fI 1
y
582.8 N ;1--~FR
....".-:...,...,-----x
236.8 N
(ft)
('lJ)
tlUH:lfl1Hihumn1 (Scalar Notation) ifqj'VIldllm~(JHf)~lui'f!'l1~(Jmhu'1'l..!li!
mh.:JhfililllJ ll::;Hlilfllll'ii;l::;IlJ.:Jllhm'J.:Juu(J x lli;l::; y ~.:JlD~ 2- 19 ('1) mrnllJll'J.:JUU(J~.:Jf)ci11
'I'lJ--t~'liflWI'I fi'Tfl'u~YlI'I"Yll.:JUlf)'lJtl.:Jtl,:]rlU'J::;f)tlUll'J':] x lli;l::; y I'IllJ1:1':lJfll'JY1 2-1 ll::;Mil
~ FR =LFx ; FRx =600 cos 30° N - 400 sin 45° N
x "
= 236.8 N ~-7
. '
FRy =600 sin 30° N + 400 cos 45° N
= 582.8 N i
IlJ'll:1~TI~'lU1:1'~.:]l'UlUY1 2-19 (,fl) ii'1'Ul~ .
FR = ~(236.8 N)2 +(582.8 Nf
=629 N
e== tan-1
(582.8 N) =67.90
236.8 N
{;HlU .
I?HJ1J
30. . .,;
l~,hIl1J'lJfI 2
aruaflllrunfll~W~1u':i~'lJ'lJ-Wfl~Ulfl (Cartesian Vector Notation) 'Ulm'!J~ 2-1.9 e'IJ)v ~
LL~l:l::U'i.:luff~.:Ilu~'!Jn f1,LI9l{l'flu'i::uu'i'l n~mf1
FJ
= 6QOcos 30·i + 600 sin 30·j
F2 = -400 sin 4Yi + 400 cos 4Yj
FR = FJ
+ F2 = (600 cos 30· N- 400 sin 4Y N) i /
+ (600 sin 30· N+ 400 cos 45· N) j
= {236.8i + 582.8j} N /
'lJU1~ml::Vlfl'V11.:l'IJCl'l F 'I111~1'U'vhuCl'lI&itnnU'll1'lI'1U- R '
/
ImtiU lli tluffCl'llfid 'V'IU":h f11'l1i'-ff()j ~mHlr1.'Hf1~11ihh::ffVllif11'V0J1f1 f1il d'iCl'l'Ul f1 IImiCl tI
fflf1l:ll{ffll!l'Hllnl~~tI 19l'i.:l lli,}lIUU1'1Cl'l IIff~'1'l'!J'lJCl'l uvi l:l::u'l.:ll'I1IUun f1 II9lCl{uuulm::u1J'Vl n~~ .
111f1 nClUf11'l1JJ f1 11'l'lVCl {} Cl vl.:Jl'ln19l1l! f11'l1 Irrn::rfnf1 II9lClllm::uu'i'l n~lllf1li'!J'l::lt1'lfUClVl.:1l!lf1
l'Uf11'iIInif()j'l11ffll!iJ&i
~3af.hJn 2-8
'!Jcntll'1i~.:J 0 ll.n'!J~ 2- 20 ef1) f)f1m:::'IhI'1JtllI'i'l1'U'i:::'U1UI&i<r:Jtlwm:::~,)lJ'i)~I&itlJn'U[;fllJ!t'i'l<u 'J q 4
~ ~ ~
'i).:I'I11'IJ'U1 ~ 11l:l::V1fl'V11'l'UCl'lII'i.:li:l'V'l1l
y y
_r;, = 250 N
--~~~~-----------x
F;=400N
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= - 383.2 N = 383.2 N ~
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k 'Utl'l A UCl~ B ,yu~tl
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1I1muYi2-31 'IAIU1l ex ~ 60· !dV-3111fl F flv1uVlfl"I'm+x..., . x qJ
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== {100.~ f+Too:Oj + 141.4k} N .
, -- -...•- " ' .. ,/ .
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35
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l"~"f'l l .:;2
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y = cos-1(0.866) = 30.00
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l~fl~Jlf)lll'l'lvifunll 1t'J~~VHj Fii'U'WWI 800 NU R
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F2y
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o =-150 + Fzz ; Fzz = 150 N
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rilUm'l'lJrJ'IrJlflU'J::flrJui'l'ffl1JM r ,rU~rJ l~1J1Jlfl A lu B ilU'ff~'11U';Ju~ 2-37 ('lJ) BU!!'Jn
"
!~1J'illfl (x - x ) luVlfl''Vll'l +i, (y - y ) 'lUYiPl''Vll'l +j !!a:: (z - Z ) Vlfl''Vl}~ +kB A B A B A
z
ClIL- - - - - - - Y
x (n)
'JtJ~ 2-37'IJ
~bafi1Jn 2-14 -,
'il'lm'IJU1~!m::Vlp('Vll'l'lJrJ~nml9lrJf'J::1J9l1WI1:UI~iJVlf('illfl A hJv'l B lUlU~ 2- 3 (n)
x
x
('lI)
41
44. 42
=d.
111m
1'1111ffllf11'j~ r7"",13 wn~'IJ'fllri1'Ui111'A(1, 0, -3) !H't::;fJflCtU~1UWn~'IJ~lri1'U,r1 B.(-2,
2, 3) 'il::;1~11 - , ,'~~
( T , ': (-2m y m)I + (2m - O)j + [3m - (-3m)]k
~""') = ;~-3I j2j + 6k} m
'illfl~1J~ 2-38 ('IJ) U'jlri'flU~lffl11'IJ'fll r ffllJl'H)i111~~UOlJ'I lOltltfl~'fl'U'illfl A l1JrJ'l B
1'll1lUfl'U x={-3i}m; Oll11Ufl'U y={2j}m U(I::;1'11lJUfl'U z={6klm
'IJ'U1I'l'IJ'fl~~ ~::;ii-h
r = 1(-3)2 +(2)2+(6)2 =7m
fflJf11mfllOlf.}'{l1l1~Wii1uhj'Vifl''Vll'l'IJf.}'1 r 'il::;l~-:il
"C""" ~
r - 3. 2. 6 k
U= - =-l+-J+ -
r 7 7 7
11'j'lri'flU'IJ'fl'lI1f)IOl'flfl1l1'lmi1tJ'n'il::;MllllUff~.'lV]fl''Vll'l~l~'illf)'j:::uui'in~
VltllJ
a =cos-t~3) =115° VlfllJ
13 = cos-
1
(*)= 73.4
0
VlfllJ
y = cos-1
( %)= 31.0° I'ltllJ
lllll'l'lfl~l'.l'd'l9l'illflUfl'WUlfl'IJf.}'1'j::;U1Ji'inl'l~ri1'wi11'l'IJ'fl'l r 1'l'lllffl'l'll'W'j1J~ 2-38 (1'1), ~
2.8 l:lntVlEJSllSOnufinn10Vl1UllU:llaU (Force Vector Directed Along a Line) /
. l'Uutyi11"'(lOlm"'Ol{"'lllij~ V] ff'Vl1'l'IJiN U'j'l 'il:::J'::;1JlOl(J~l'lll'l"1 "'tl'l~I'l~i'lr-.il'WU'W1f11'jf)'j::;i'h(
:I9ll21J~ 2-39 lrimm F iHifl''Vll11'11llU'W1lff'U AB Cj}I"'llJ1'j(H~tJ'U F l'U21J'IJ'flll1flll'1'fl1l'U'j::;uu
i'inl'lmfl 1~Uffl'llfifl''Vlll~1tJl1fllOlf.}{'j::;1JllllUl1UI r 1I'ltJiiv]fl''illfl~~ A l1JrJI~~ B U'UU'W1Iff'W4~
l91U-vflLt.lVlff'Vll'l'il:;J':;1J1U'WI1fl!I'If.}{l1l1'l'l1Ul(J (Unit Vector) U = rlr l'l,nr'W ' ,
UJ''l F !tffl'l'll'W~1J 2-39 tU'Wl1UltJ'lJtllUJ''1 cB'IUl'lfll1i1'l'illfl r l11ili'in91 x, y !!(I:; z
Cj}liil1U1tJllJ'Wfl1111tJ11 I9llJ'W UJ''l F ~'lhjffllll'jm~(J'Wl'U21J'IJ'fl'lffIflCtU'UUf)'Ui'inI'l1~
45. F
.' • J ~
) - - - - - - - y
x
'Jtl~ 2-39'IJ
53n1Sa1V1Su51AS1::vI (Procedure for Analysis)
v
. IlJ{) F iJYifl'Y11':]ill~UmHiHnml1fl~9i A hJ~9i B 9i.:]'.!'U F ~l~l':itlJoi(J'.ll'.l~tlnmil{)f
i'.l'j::1J1J~n9imflM~.:]if
nflllltJ1'J:;1JVhmnl~' (Position Vector) rmhu'I1u'lnmil{)f r L9itJl'I':i'l'Jlfl A ltl B
. ,
mI1rll'.l1tU'11'U'.l19i'U{)':] r
<,,; • .,. d • d ~I •
nfll~~'J'I1'U.:.I'I1'U1£l (Unit Vec~or) '11nmil{)'j''I1'U':]'I1'U1CJ u = r/r 'li'llu'.lfl1'j'1J~1J{)fl
YiffYll.:]'U{),nl'l rIm:: F
' nflllltJ~I!H (Force Vector) '11 F 'JlflflTJ'j'J'IJ'U'Ul9i F u,,::Yifl'YIl'l u u'UiiitJ F = Fu
Pl::>a~.i1l1' 2-15
'liltJi'l'.l'l1i1'l'vju~i'.l~tl~ 2 - 40 (fl) ~'Hff'UI9i{)fllKltJU'j'.:] 70 Ib 'J'lU~9i'lU':i'l~'lm::'I'hn1JlIl'U
':iU':]1lJ A l'U1tlnmilt)'fl'.l':i::1J1J~n9imfl uCl::'11l?l1Url'll-:!'UU'lu'j''llKltJ
z
z'
r
. (
• B (12,-8, 6)
('I)
43
~ "
. "'
46. 44
"' . . 0
1lim
U)~ F tHjl'.mJ~ 2-40 ('lJ) 'i1fl''I'11~'lJtl~I1fl1~tl{d u ''nl~'illfl11fl1~tl{)::'lJ~1!m'll~ r ~~alfl" " q
'illfl A lU It 'i.::J~u~ 2-40 ('lJ) t1'h:Jt1'l.Ifll) F lU~UI1fl1~tlfh.j)::'lJ'lJ~fl~ll1fl 1~l'Ji~flTJi.::J
~tllud
I1fl1lnt&i:::'l!Ylurtnl-:J (Position Vector) ~fl~'lJfl-:J~~Uft1tJ'lJfl,:mrU!GJiflfl fitl A(o, 0, 30
ft) ua:: B(12 ft, -8 ft, 6 ft) t1"hmfl!~tl{'J::1J~lUl1'1l.:J1~1'J"'lJ~fl~~t1'tl~fl1i'tl.::J x, y u,,:; Z '1Jtl.:J A
flU B 'il::l~il
r = (12 ft - O)i + (-8 ft - O)j + (6 ft - 30 ft)k
= {12i - 8j - 24k} ft
lu~u~ 2-40 (fl) !;"'~'lfll'j!~tJU r 1~tJ~'j'l'illflfll'j!fl~flU~'illfl A{ 12i}ft, {-8j }ft !!t'!::
{-24k}ft lUtJ'l B
'1JU1~'1Jtl.:J r ~.:JU'I'1Ufl11l.1I'J11'1Jtl,:mrU!GJitlfl AB fitl
--I l1f)mel~11rtnnhtl (Unit Vector) "'flmfl!~elfl1d':I11'1l1tJ~iil'Jll.1'i1fl''Vl1'l'IJtl'l"f'l r !It'!: F
'il:Mil
u =E. =~i _ ~ j _ 24 k
r 28 28 28
l!flIlnel~II'J-:J (Force Vector) tiltl'l'illfl F ii'1JU1~ 70 Ib ua::iiVifl''I'11.:J'j:;1J1~£1 u i'l,ru
F=Fu=70 Ib(~i - ~j - 24k)
28 28 28
= {3Oi - 20j - 60k} Ib
U"'~'llu~u~ 2-40 ('J) lllJ!lt1'~'l'i1fl''Vl1'lVil~'illm:U'lJ~fl~t1'll.11)fll~'J:'1,dl'l r (l1~tl F)
"",-<vd..",. "":'v"'; , ~&.
u,,:ufnnnfl'IJtl,n:uu~fl~'VllJ~9l!'Jll9lU'Vl A'illflUl'ltJfltJ'lJtl'lllfl!9ltlW!U.::Jl1UltJ
a =COS-1G~) =64.6° .
~ =cos-
1
( ;!)= 107°
(
-24) .
Y= cos-
1
28 =149°
47. f1~afi1Jfi 2-16
ll~·h'!1J"*~l1d~fli:1l1lU~l1~ 2-41 efl) tJfl<Hl~r1JlJl-lriJ'U1~tJ!fI!Di:1 AB th!!~-l'1Jil-l!fI!DfI~fl'j":
yj~~tJYl:'Jf)~ A ~il F ; 500 N 'il~~~fI)l~X 1'U~l1nfliYlilll'U':i:1J1J~n~mfl
A (0, 0, 2)
~
I2m
ly
y
l cos 45° m
x
(0) ('I)
'JU~ 2- 41
" .
~'" .111m
'illO~U~ 2-41 ('J) F lHiffYll.:J!~(nn'Un1Jnfl!Yldm...jl'llU'YIU.:J r ~~i:11fl'illfl A 111 B
110IVl61'J~!vllllml-:l (Position Vecto~) ~n~'Uil-l~91U(I1tJ'Uf).:J!fI!Di:1 ~6 A (0, 0, 2 m)
. UfI: B (1.707 m, 0.707 m, 0) ~.:J,r'U
r = (1.707 m - O)i + (0.707 m - O)j + (0 - 2 m)k
= {1.707i + 0.707j - 2k} m
fl'llJl'Hl'YI1U~.:J~il(J.nl~tJfllfl A{ - 2k j' m" 1'11lJ!!fl'W Z, {1. 707i} m IilllJUfl'W x Ui:1:
{o.707j} m flllJUfl'U y l11cY~ B
'U'.ll91'Jf).:J r ~il
r = ~(1.707)2 + (0.707? +(_2)2 = 2.72m .'.
d d t
I1flIVl6'J'YI'U-:l'YI'U1£J (Unit Vector)
u=E. = 1.707 i+ 0.707 j - ~k
. r 2.72 2.72 2.72
= 0.627i + 0.260j - 0.735k "
I1fllvm11m (Force Vector) l~il.:J'illfl F = 500 N 1m: F iiVlff'V1l-l U 'il:ll9i'il
. -..)
F = Fu = 500 N (0.627i + 0.260j - 0.735k)
= {314i + 130j - 368k} N : ,i
'illfl!!~.:J~iltJ.n 'l'/lril'U<ul91'Uil~ F ~il 500 N 11'1(J~
F=~(314?+(130)2+(-368)2 =500 N
,
Vltl'U
VleJ'U
45
48. 46
fl'::>aEi1un 2-17
u'i~~tl~l'.Hfl!1J(l F.;.B = 10? N um: FAC
= 120 N 1Jm~!!'111'U~ A ~~~U~ 2-42 (n)
. 'ilJj1':!'J'U1~'Utl~u'i~~YnfVim::vlTVi~~ A
z
y )-----r--y
B t4, 0, 0) ./"-___--Y
x
(0) ('1/)
'j,j~ 2-42
'IJ
"'''' 0
Tlim
!!'i~~'I"nj F !!iY~I'i,jmlyJyjnl'U'i,j~ 2-42 ('U) iYltJ1'ibl!!iYfII!!';ildl'U';iUnfllfltlfl'U';i::1Ju'Vlnfl
R <u <u ,1" <u
mn lf1f.Ji~lJ!!miY~l1iYlJfl1'i F !!(l::: F !1I'Unfllfltlfl'U'i:::1J1J'Vln~mn!!allJ1fl1!';ilr.i'flfJ'iliYtllAB AC
Ylft'1'll1'Uill F U(l:: F flm:::1Jlf1ufl1';iiY111nn!fltlf"1~llnbu U U(l:: U flllJ!fl!1JCl
AB AC ~ • AB AC
nfllfltl111~lm,bud'il::M'illflllfl!fltl'h:::1J9hUl1U~~iYil~flaeN r tw::: r 51~t)~'iU~ 2-42 ('U)q AB AC <u
ffll1i'U F 'il::Mil
AB
rAB (4 m-0)i+(0-0)j+(0-4 m)k
{4i--:4k} m
fAB ~(4)2 +(---4)2 =5,66 mv
100 N (rAB) = 100 N (-.Li--.Lk)
fAB 5,66 5.66
{70.7i -70.7k} N
49. ' rlTHfu F AC ~~1~il
rAC = (4 m - O)i+(2 m-6)j+(O-4 m)k
= {4i+2j-4k} m
rAC ~(4)2 +(2)2+(-4)2 = 6 m
FAC = 120 N (rAC) =120 N (~i+~j-~k)'
rAC 6 6 6
{80i+40j-80k} N
FR = FAB + FAC
= (70.7i - 70.7k) N + (8Oi + 40j - 80k) N
= {150.7i + 40j - 150.7k} N
FR ~(150.7)2 +(40)2 +(-150.7)2
217 N
2;9 waJ;]rulBualna1S (Dot Product)
hnJl-:J flr-:Jl-Wffi'i ll f'flffll{1J::ii fll'l'l1llJlJ'J::'VIil-:J !ff'UffV-:J ny'U !'If'U n'l-:JrivtJ~'IJ'Ul'U'VI~V~-:Jll1fl t1U
n'Ul!ff'U rll'V1i'uifty'l1l ffV-:Ji] ~ffllJ1'lfl1ill11fl ruii ~ !deJ'l1Jlml~~ll!'li-:J!'l'Ulflrull1~~ltJ nvirll'V1fu
'h,,HJifty111ffllJii~1J~vll1~ellfl vll1t11'ltl-:J1i1~fll'l'l'11'l!1 mlleJ1'lfltJUf) l~fJthmJ'lJeJ'l fH'lf,] ru fltl 1ii
lll'Wl::-ffl'V1i'Ufll'lfl run fl !llV{ffVIn fl !llv{ 1irll11i'u nnifw'111'1l1-:J1'l'U~ u
J:-H'lflru'Uvmmllv{ A !I~:: B !~tJ'UM':h A· B 91'liiDtJllJil~H'flOl'IJtl-:J'IJ'Ul~ A !Ii:'!:: B !tTI~~ , ~
lfl'lflfJ"r'IJV'llJlJ e 'l::whlril'U'I1l'lJ'lfi~m.J~ 2 - 43 1~tJ!~fJ'U1'U'l1l'IJVlfflJfll'l 1J::M:i1
q " 'lI "
~' .~.'IV~'7'II't:~~~"",~~~",
".', rcA." !,.~B>= 'ARcos "!!.~_" ..,.....___,,;i
(2-14)
.d v d d , ..J, d'
!lJtl 00
~ e ~ 1800
f-l1:'lf,]OllJ.fl1J::!'ltJflVflVtJl'll1'U'lll f-l"f,]OlUUUff!fli:'!l'l (Scalar Pro-
duct) 'Uv-:Jnml'ltl{ !dVl1JlflJ:-.l~c1'Wi~-:Jflcill!1J'Uff!fla1fhn'lfnm~ltl{
nnms16nu (Laws of Operation)
1. fltl'ffc11J~ (Commutative Law)
A · B = B·A
.. B
'J1J~ 2-43
"
47
i,
!,
50. 48
2. I1T:i~tu~1t1tilmn{ (Multiplication by a Scalar)
a(A . B).= (aA) . B = A . (aB) = (A· B)a
3. 110m'jm::1l1tl (Distributive Law)
A . (B + D) = (A . B) + (A . D)
':itl~T:lJfll':il1fl1l'1tl11m::;'lJ1J'Vlflflillfl (Cartesian Vector Formulation) ti'IJm'j~ 2-14'
1il11~1:'l~tu'IJtlluii1:'l::l1fH(;ltl5'1'l'ct'l'H'li':HJlW'l::1J1TVnr~mf) ii'1tl~l1l'li'W i· i = (1)(1) cos 0' = 1
lm:: i· j = (1)(1) cos 90' = 0 1'W'Vh'WUlr~tnn'W
i . i = 1
i·.i = 0
j.j = 1
i· k = 0
k· k = 1
k· j = 0
'W1l1'ltu1 ~(1~ru'IJf)'Hlmflf){l~"l A U(1:: B 1'W~U'lJf)ll1mfltl{l'W'l::1J1J'Wnflml1 1l::1~11
A· B = (A) + Ayj + Azk) , ~B) + Byj + Bzk)
= AxBx(i . i) + AxByCi. j) + AxBJi . k)
+ AyBXG . i) + AyByG . j) + AyBzG . k)
+ AzBx(k . i) + AzBy(k . j) + AzBz(k . k)
(2-15)
ii'lJ'W m'll11 ~1:'l~tu'IJtll11f)1(;lf)ll'W'j::lJuYl«~'inf)titl'l11f)Ifltl5~run'Wfl1J.j fflljU,'l::!1~JJ ~-L...y
11(1:: z ~(1a'l'l1~M1l::liJ'W1(1'IJ-W'lfflru(1) ' Idil.:l1l1f)~(1a'l'l1IiJ'Wtilf)(11{ ~.:I~f).:I'J::;,r~'J::;l.:lhj"Hj ·
;~~I(;ltlf'H~'1'H'lbtl1'W~(1a'l'l1J'W
m1'ih::;f,!flvl1.jj(ApplicatioI!~2 ~(1~ru1'Wl'lflf)(1fYl'ffflfiJm'ju'l::~f)fl1i~ri1rltytlQtif)~11l-
, 'iI , r! <! ~ 'V dOJ tV
. n fll"Ji:'f11'-U;!:ln::;'I111'll1fl1l'1tl':iiHl'll1flll'ltl':i'l1':iellnnlll'U't1I'1f1fl'U (The angle formed
between two vectors or intersecting line.) l.l'IJ eoR'ItlQ'l::w.i1'1ffl'Wl11.:!'IJtl.:!l1fH(;ltl5 A U1:'l::
B ii'':!~U~ 2-43 tillJ1'ltl1111~1l1f)ti'IJm'l~ 2-14 hw
e=cos-l(~:) 0°:::; e :::; 180°
oR.:! A· B 1111~1l1I1ti'IJm'l~ 2-15 t11 ~ . B = 0 U(1:: e= COS-I 0 = 90' Uti~.:!11 A
v
(;l~I'in flfllJ B
®tl'lf'itl1::;fltl'lJ'Utl-3l1flll'ltl1'U'Ul'U!!(l::;Ill-3'inflfl1J!I'U1I1:l'U (The components of a vector
parallel and perpendicular to a .line.) tllrlu'j::l1tlU'lJtl,mmfltl5 A ~'IJ'Wl'U'I1jtllill'Wu'Wl
l~f.nnlJlff'W aa'ii'I~U~ 2-44 iltll'IJ11 All 'lJru::~ All =, A cos 8 1'W1J11flr-3tl'lrlU'l::l1tllJi1'utifllM
1~um'l'lmu'IJtll A lJ'Wlff'Wm-3 th¥iffl'l11'IJtllll'Wllffm::u1~ul1f)!(;ltl{'I1~.:!;"nb£J u ii'lJ'W I~f)
U = 1 tillJ1'Jfll11 AII1~Uil'j.:!1l1flt-l(1~ru (ti'IJm':i~ 2-14)' J'W~f
51. , !
All = A cos e= A· u
'·;~,fu fl1~mU1:1'lfHn{'lJtl'l A 9l1lJllU111:fU'Vll'1~'il1f11!-1f1t)ru'IJtl~ A llfl:::l1f1l9ltl{l1~'1l1lbU u
~~ij!mri11vU'i'lft'V11'1'IJtl'l1l'U111:f'U 'lltl:cr'l~f1Jl t11I!-1mlVl1l1V'UU1f1 All 'iI:::lJ'i'lft'V11~ll1iitl'Ufi'u u l'U'lJru:::
~r-ifltlVlilV'UflU A ll 'iI:::lJ'i'lft'V11'1I;)'i'l'llllJnU u tl.:]ftlh:::f1tlu All 111:1'~.:]l'U~tll1f1l9ltl{~'1d
All = A cos eu = (A · u)u
,j'V~.lf19ltl.:]fttl"i:::f1tlU A ~i~mf1nUllU111:f'U aa' ~.:]~tl~ 2 - 44 1~tl~'iI1f1 A = All + A.L
~~,f~-A.L ;= A - All iilTIf11"i1:1'tl.:]iTI~'iI:::'VIl A.L iTIll"if1'V1l ell1f11!-1f1t)ru e= cos-
1
(A· ulA)
~~"ru A.L = A sin e ril'Uflf)11i11~':] fitl t11'Vl"ilU A ll ~.:]"r'U ll1f)'V1qfJQ'lJtl':]'W1Jllf1l~u'U
~ v' I 2 2
(Pythagorean Theorem) 11:::1~11 A1. = j A - All
~ _al
AII=Acos8u
'jll~ 2-44
"
/
PlJaa10n 2-18
lm'ln·H)lJ~'1ltlYi 2 - 45 (n) lnm:::'I'11~lUll"i.:]lullU1"ilU F = {30oj} N lW:::l'hYil,JlJ
'lJv~lm'lmtlu 11'1'V1l'IJ'W19l'IJtl'lll"i'lciVU~'1'IJ'Ul'Ullfl:::i'l'nnnu;'Uril'U AB
B. F= rlaOj)N
I
x (a) x
(0)
49
'-'-'-- - - y
52. 50
""". 0
111m
'U'Ul¢l'Utl-lU'.i-lV'O!'J'Utl-l F OlllJ AB ~i'ilLl'hnmH'lfJru'Utl-l F u"::nf)LOl'Of'l1~-l'l1'.i1!'J U
B
~U!'J11J'Vii1'1'l1-l'Utl-l AB ~-l~U~ 2-45 ('1) Ldtl-l~lf)
r ~ + ~ + Th . .
"B =.J!. =~ =0.2861 + 0.857J + 0.429k
rB (2)2+(6)2+(3)2
FAB = F cos e= F ' "AB = (300j)· (0.286i + 0.857j + 0.429k)
= (0)(0.286) + (300)(0.857) + (0)(0.429)
1
= 257.1 N;f -r"I" )9l' "nn l: ,
rdtl-l~lfH,md'J'Ui:1'Lf)m{U1f) F iiVii1'l'lVH~!'Jlnu U ~mJ~ 2-45 ('I)
AS B ~
UC1'~-l F l'U1.unmOltlflm::uu~n~mf1 ~::hlilAB -
FAB = FAB"B = 257.1 N(0.286i + 0.857j +0.429k)
= {73.5i + 220j + lIOk} N
U'.i-lVtl!'J~-llllf)~-l~U~ 2-45 ('I) ~-lJ'U
F.L = F - FAB = 300j - (73.5i + 220j + llOk)
= {-73.5i + 80j - 1I0k} N
'I'U1~'il:;'I111~'illf)nm9ltl{d'l11tl~1f)l'lt]'H~~1i11ma!'J'U (Pythagorean Theorem) ~-l~U~ ~-
45 ('1)
F.L = ~F2_F2AB
~(300)2 -(257.1)2
155 N
53. viil1'U~1.l~ 2-46 (n) lnm:;'I'h~ltJ1L':i'l F = 80 Ib ~l.la1tJ'l'ifl B 1l'll1llJm:;'l1il'l F flU
~ri1'Uvifl BA <nlJvf'l'IJ'Ul~'IJfl'll!~'lriilV'lJfl'l F ~'IJ'Ul'Ul!a::~'lmflfl1J BA
z
..~~~==_2ft-::::,7' S77""/_'... Y ~~r-----Y
2ft
c x
x
F= 80 Ib B '
(n)
~tJ~ 2-46
"
"'...l1i'fl1
3;!:IJ (Angle 9) nflll'lflf'J"::1Jl'i'll!'I1,j'll'lllJ BA l!~:: Be 'I111~'illfl
r~A = {-2i - 2j + 1k} ft
r
Be
= {-3j+ 1k}ft
cos e rBA · rBe _ (- 2)(0) + (- 2)(- 3) + (1)(1)
fBA f Be - 3M
0.7379
e 42.5° I'HI1J
' ( v O".J ,
1I~'lUtlU'ltl'l F Components of F) 1:l''J"1'l1:l'lJfll'Hlfl1l'1fl'J'I1'U.:J'I1'U1Vl'lllJ BA U~:;l!'J.:J F
1U~U!1fl!l'I{)flm::1J1J~n~mfl
F
rBA = - 2i - 2j+lk = - ~i-~j+.!.k
~A 3 3 3 3
= SO Ib(rBC
) = SO( - 3
j
+ 1k) = - 75.S9j + 25.30k
fse .JfO
0 + 50.60 + 8.43
= 59.0 Ib
B
('I)
51
54. I
I
!
I
i
I
·f
I.:
, .
52
. FBA = 80 cos 42.5" lb = 59.01b
'lJU1~'lJCN!I'l'ltJUtJ~~'l'il,1f11:l'llJl'ltnn1.,n~tJ~'j'l'l'11'l~~1f1U!ii&l
Fol F sin e
80 sin 42S
54.0 lb
'Y!1u1~tJ'I'lflavhn1f1l~tlu (Pythagorean Throrem)
F.L ~F2 - F~A = ~(80)' - (59.0)'
54.0 lb
.
./
C;UI'IJ -
:)
55. Pi =600N
---'-.,--- x
·n.J~ 2-1/2-2
"
' 2-3 'il.:Jm'lJ'Ul~'lJtl.:JIl'l.Hl'V'l1r F = F + F 'l1lJ'I'l.:JVifl''Y1l.:J i
R 1 1 2
1~trr~1'UVifl'm'Ut4JlJ'UlWf)1 'illfHtfl'U X yjiil'i11J1fl
_2-4 'il..:Jm'J'Ul~'Jtl..:J1!'l·Hl'Wli F = F - F 'l1lJ"r..:JViff'l'n1
, -, '. R I 2
1~trr~1'UVifl'm'Ut4JlJ'U1Wf)1 'ill fl Ilfl'U X yjiiril1J1fl
y
F, =250 Ib
''-."
F2= 37S1b
.,
40lb
'j'll~ 2-5
"
. - -~,
2-6 'il.:J'1l'IJ'Ul~'lJtl.:Jtt'l.:Ja'Wli F = F +F TllJ"r.:JVifl''I'1l.:J. R 1, 2
1~Ul~l'UVifl'l91llJ t4JlJ'UlWf)1'ill fl Ilfl'U u yjiiril1J1 f)
2-7 'il..:Jbbl91f)1!'l'l F tl'OfHlh..!'O'lfhh:;fltl1J~mjm:;v1ll91llJllf)'U
" 1
u ttel:; V 'illJ'I'l.:J'1l'IJ'Ul~'lJtl.:Jtl.:Jrllh:;fltl1Ji.:Jflrill
2-8 'il.:JUl91flll'i..:J F tl'OfHtJ'Utl..:JrlU'j:;fl'01J~Oum:;'Yh91llJ1!fl'U
" 2
u Ilel:; V 'j1lJ'I'l..:Jm'IJ'U1~'Jtl..:Jtl..:JrlU~:;fltl1Ji.:Jflri11
. ,
, .
" I
'jU~ 2-6i2- 7/2-8 :1
2-9 t.~;H."'J;''i(V-Groovoo Wheel) onH'i,u",,, ,I
t1l'il..:Jd)~tml'Ut~'Ul~.:J 200 Ib m:;vlll9imi'tl ;..:Jmo.:Jrlu'l:; / .. . I
fltl1J~tlU'lJo.:JU'j..:Jm:;vll911lJllf)'U a Ilel:; b cJi..:J~.nnfln1Jil1'U~ f
ii~tl.:J i
I
1
56. 54
..
2-10 1JlU9lflU'Il 60 Ib tH)mlhHl'lrllh~fl{)1.l{jmJm~i'h
1'l1lJllfl'U u w''l::: v ':i1lJ~-:I'H1'IJ'U1~'IJ!)-:I!).:Jfi'U),::f1!)U~,:If)ciT1
v
'JtJ~ 2-10
"
60lb
2-11 "lJi'h'h1lii~u),'la'Vnf F = 110 Ib ~-:lmf1n~lui~B
'iJ-:I UI'l fl U),':I'd'B BflIU'UffB.:J tl.:J fi'lh~f1tlU citlU ('IJU1'UU"~~'lmf1
v '"
f1UIIf1'Um::~f1~I),tl aa)
v
* 2-12 1'l::'IJB),B':l'ruu)'':Hfllijml'lfftl.:J F = 500 N u,,:: F =v 1 2
300 N t111'J"a'Vnj'lJtl.:JII),.:J~'lflci11ilm~i'hl'Uiif1*".:J1uu'U1
~.:Jm'j~ii'lJ'Ul~ F R 750 N 'iJ..J'I11l,JlJ e IW~ 0 'lJtl..J!flIU"
~..Jflcil1
2-13 !!':i..Jl'U!!Ud~..J F = 60 Ib m::yhluiiftvi.:J".:J~'iJ~ A UU ~, ,
lrmmtlUfftl..J<1lurilu 1ll'l11'lUl~'ltNtllfhh~f1oU'vflfftN'ltll
F l'Uiiffl'lllJl!fl'U'UO..J;u~h'U AB u,,~ AC nl'11'Ul'lril e = 45
2-14 1!),ll'UU'U1~.:J F = 60 Ib m::yhl'Uiif1vi..J"..J~'iJ~ A, ,
u'Ulf14'..Jf1JtluffB..J;'Uri1'U 'iJ..J'I11l,JlJ e (0 :0; e :0; 90
0
)
'llOl;Uril'U AB rritll'11tllrllh::fltlU'lltl..J F m~Y]19t1lJUfl'U
AB iiril 80 -lb ),llJ~l'll'U1~'lltl..Jtllrl1.h~f1tluu),.:Jm::y]l
v
9l1lJl!m.j'llOl~uril'U AC
2-15 I!~UU1l~f1m::y]1~lUU),..Jfftl..JU),..JYl A !w:: B ~..J~t1
t11 e = 600 ' 'il..J'I11'IJ'U1~'Jtl.:J,:,,,,a'VHj'lltl..JU),..J~..Jfftlilif ':illJ-vr..J
iiff1'11.:J~1~l'lllH~lJ'U1Wm'iJlflufl'U X iiiirilulfl
- - -- - x-----y
FB =6kN
57. 50 Ib ililflltJ'Uil~rl1.h::m)'lJu~HJm::l'hI9l11J
1m:; y'
y
'j,j~ 2-16
"
2-17 tl1-lfl'j:;'Vl1lJ'UYf'UlliJil.:J F = 20 Ib 'il~U9lf1U1.:J'ifililf1
d'JUffV,W-lfllh::f1illJm::'I'i'119l1lJU'Ullff'U aa 1m:; bb
2-18 f.J-lflU'j'::f1f.JlJ'Uf.J~It'j''1 F m::'I'i'119l1lJltUllff'U aa !,l'htllJ
30 lb 'iJ.:J11l'U'Wl ~'Uil'l F It"::il'l rllh:: f1 illJ'Uil'l1t'J'I 9l1lJ UUl
I~U bb
b
F
v
2-19 U1'1vl'l'fff.J'Iii'UU1~ 10lb It,,:: 6Ib m::'I'i'1~il1'111'l11'U
fhUU1~lJlf1~'l'~'Uil.:JIt'J'I clYnr~l'1It'l11'U'ffllJl'jf)rlJi~ ~il 14
lb Jll1l~lJ e'J::wh'lIt'J.:JIil,:mcill
*2-20 'il'l'l11~lJ e (0' :::; e:::; 90') 'J::'I111'ltl1'1vY'I'ffil'l
.d d ' <V <I 0 I .0<:1' !I.I ..J
IYHl'YI'UUl ~'U il.:J II'J'I "'I'l1l m:;VI1 9l ill~ It'I11'UlJ fll'Uil tJ'Vl 'ff9l 'JllJ./' ,
'nJ~ 2 - 19/2-20
"
55
2 - 21 rt11lf1~'1'illf)«'U~'Ul9ltJHlff'Ut;'iilf)'ffil'llff'U A tI,,:: B
Iff'UI~ilf1 A tJf1m:;'I'i'l~lu U'J~ 600 lb tI,,::iiVifl' 60
0
'il1f1
U'U1'JllJ 'ill111U'JI T 1'Ulff'Ul;'iilf1 B f111'ffll~lJ~'UfIf1~~lrlil
e = ,20' rlll1r~ll1~f11'Jru'if U'J'I~'I'l{lJurt11'il::iiVl~Yj'l~'U1'U
..:... QJ 0 <V d'.J'
U'Ul ~'1 'Uilf1 'illf1'U'U 'il'l fllUlrul1l'U'Wl9l'Uil'lU'J'I"'I'l1iU
2-22 IJ:YltJf1~'1'illf1~'U~'U19ltJ1'lflffUI~flf1J:Yfl.:JlffU Au,,:; B
IffuI;'iilf1 A f)f1m::'I'i'l~ltJ 11'J.:J 600 Ib ua:;iiVlfl' 60' 'il1flll'U1
11lJ f11Umr~{m:;'I'i'llJ'Ut'ffl!'l'htllJ 1200 lb 1'UYifl'Yjl~'U1'U
lIUl~'1 'iJ'I111U1'1 T 'IJ'Ut-ff'Ul;'iilf1 B tm::lJlJ'ffil~rHlil'l e
600Ib
'j,j~ 2-2112- 22
"
2 - 23 fil'1'i'1111li)~u'JI 20 Ib lJ'U~il'Ui,r 'iJ'IIII9lf1u'JI'ifililf1l11u
fllrllh::f1illJUiltJm:;'I'i'l (f1) 9lllJLIf1'U n Uft:: t ('U) 9l1lJUf1'U
xu,,:; y
*2-24 fil'1'i'l111liiflU'JI 20 lb lJ'Ul'iilUi:U' 'iJlU9lf1U'JI'ifililf1
tll'Uillrlll'J::f1illJUil£Jm:;'I'i'l ef1) 9l1lJUf1'U n Uft:; y ('U) 9l11J
Uf1'U xU,,:: t
y
n
20Ib
58. 56
2-25 0'1 e = 20° lla:; 0 = 35° 'il~'I11'11'Ul~'IIeJ'l F _ua:: F
, I 1 . 2
IYieJh1ll'j'lEl'Y'nji'i'll'U1~ 20 lb lIa:;iiYli1I'nlJilf)'U X Viiifi1mf1
2-26 51 F = F = 30 lb 'il'l'l11lJlJ ella:; 0 IvieJ'll1lm
1 2 , q
ElVOjiiYli1>lllJllf)'U X Viii~lmf)lIa:;ii'IJ'U1~ F = 20 lbR
'jtl~ 2-25/2-26
"
2-27 'il~'I11'IJ'U1~lIa:;Yli1'Vl1~'lJeJ~YlaElvi1j F = F +F +F
v I R 1 2 3
'lJfl~II'j~vl~ffllJ l~tJI~lJu'jf)'I11YlaElv/11 F' F +F ml1'linJ
1 2 '"
llUU F = F'+F
R 3
lIuuF = F'+F
R 1
y
F~=20N
tid '
l l1Z-Z7IZ'-Z8
2-29 'il~'I11lJlJeJflf1LI1J1J e (o~ :s; e:s; 90·) thl1rU'JtJ~tJ
AB Ivitl'l11I1';j~'lull'U1'j11J 400 lb iieJ~rllh:;f)flUrifl(J 500
lb iiYli'fI'l1'l'illf) A iurr~ C ';jllJvf~fl1'Ulru111tl~rlU'j::f)flU
v
rifltJ'lJfl~II';j~f)';j:;'I'll>lllJ'ii'Uril'U AB fhl1'U~ <p = 40·
2- 30 'il~'I11lJlJtlflf1LIUU <p (0· :::; <p :s; 90·) 'j:;l1iWUfl~fl
AB 1m:: AC Ivifl111u'j'l'l'UII'Ul'J1U 400 Ib i'ifl~rlU'J:;flflU£ifl(J
600 Ib ~f)';j:;'I'l1~~iU'Vl1~~l'W'lfltJJjtl'l'UYli1m~'il1f) B lurr~ A
fhl1'U~ e = 30·
4001b
'jtl~ 2-29/2-30'tJ
2- 31 'Vitl'W'1!~~fla1fll~(J'jf)a1Mtl~r1'U A IW~ B 'il~'I11'IJ'UWI
'Utl~ll'J'lll~a1flvllfftll Fila:; F 5111'J~El'Y'njVili'f)lfll'Jii'IJ'Ul91, A B
F = 10 kN ua::iiVii1V11~~llJllf)'U x nll1'U~ e= 15°
R
v
*2- 32 51YlaElvnf F 'lJtl~II'J~vl~fffl~f)';j:;'I'll~f)'Vif)'U'1!~ii.Ylrl'., R
1'l1lJllf)'U x Viii~lmfllla:;ij'U'W1~ 10 kN 'il'll11lJlJ e 'lJf)~. -, q
Iflllia~ti~~~f)vU B Ivif)'ll1l1'J~ F '1'Ulfllliadiifi1UtltJ~ff~t.f B 'V q
'jllJvl'l'l11'IJ'U1~'IJfl'lll'J~'1'UII~a:;lflllia-ff1l1i'u Il1lPJ fll'jruU
'jtl~ 2-31/2- 32
"
59. 57
'UEl!U)! 800 lb ' *2-36 ~!!!ff~! F, F Uft:: F h'!'Jt1nfll~H)'fb.!':r::1J1JVln~mf)1 2 3 <u
<v.,. ~ dev c:: ..,.
2- 37 'il!'11l'll'Ul~'IIil'l !!'J'lft~l1 !!ft::Vl ffVll!Vl1~Vl1'U!'IIlJ'U1Wfl1
y 'ill flI!f)'U X vilhi11J1 f)
y
F3 =750 N
-------------~8Z------------ x
"!tJ~ 2-33
"
F2 =625N
QJ oS' "'" dv ~ "'"
2-34 ~'l'I'Il'll'Ul ~ 'IIil'l!!'J'lft~ 11!!ft::'Vl ffVl1.:J'Vl1 ~'Vl1'U!'IIlJ'U1Wm
'illf)Ufl'U X Viii~i11J1f)
"!tJ~ 2 - 36/2-37
"
y
800 N
----~~~----~~------ x
."
"'.. ,
'illfl!!fl'U x 'VllJfl11J1 fl
y
IV.,. """ dcv ~ 4=>.
2- 35 'il'1'111'11'Ul ~'IIil'l !!'J'l ft~1l!W::Vl ffVl1.:JVl1 ~ IllllJ!'IIlJ'U1Wm
d ", ,
'illflUfl'U X Vl:IJfl11J1f)
y
50 N
-----------~~~---~-------x
t./,,'._
- -- .....----x
70N
Fj = 30kN
65 N
~tJ~2-38/2-39
60. I.
III
l
I, .
I
I
I
58
Q,.' ~ """ dV' ~ .co.
2-41 1l.:J'Y1l'IJU1~'lJV.:JU'J;jft'V'l1iUft::'Vlfl''Vl1.:J'Vl1~'Vl1'WI'lJlJtnWfll
lllfHlf)'W X Viiifilmf)
y
45°
;
:n18----'----!.... FI =200 N
F2 =IS0N
x
'JtJ~ 2-40/2-41
"
2-42 lI;junifUJ'Yll'li'v~ 2-1 1~£Jfll'J'J1lJV;jrfU'J::f)VUUV£J X.u .
11('1:: y IIUU~l'Y1~£JlJ flw·rl~v.:J LL'J.:J,Ylv1'Y1'1~II'J·:Hrl'nr
2-43 ~.:Jllniff.1J'Yll'li't1~ 2-2 1~£JflTj'J1lJV;jrfU'J::flVUUV£J X
U('1:: y UUU~l'Y1~£JlJfl'Wr:hutl,:m'J.:JLYlvl'Y1'1~II'J.:Jtfl'ffi
*2-44 ~.:Jllniff.1J'Yll'li'v~ 2-3 1~£Jfll'J'J1lJtI.:Jr1U'J::flVUUV£J X
11('1:: y IIUU~l'Y1~£JlJ fl'W~l'Uv.:JLI'J.:JIYltll'Y1'1~LI'J'ltfl'ffi
2-45 ~.:JLlniff.1J'Y1l'li'v~ 2-15 1~(Jf)wnlJv.:Jrfu'J::f)VUUtI£J X
LW:: y LlUU~l'Y1~£JlJfl'W~1'UV.:JlmIYlvl'Y11~LI'J.:Jtf~li, .
2-46 ~~Llniff.1J'Yll'li't1~ 2-27 !l9Wfll'J'J1lJV.:Jr1U'J::flVUUeW X
lm:: Y-!lU1!fil'Y1~(JlJ fl'W ~l'JV'lu'J.:J!Ylv1'Y1'1~u'J'ltf~li
2-47 ll'l'Yllil.:Jr1U'J::flilUUil£J X Uft:: y 'Jv.:Ju~a:iLl'J.:Jf)'j::'I'11
U'Wll~'Wl'Y1~mh::nu (Gusset Plate) 'UtI.:Jlm'lt1m"::l'n'W 'J1lJ
Ij . IV d'.d ~ I I V' . ;. 0' v {.
'Vl.:JU~~'l !!'J'lft'V'ffi'VllJ fI1!'V1lflU ~'W£J ~n £J
/
F2=4001b
./
x
':nJ~ 2-47
"
- -~-
*2-48 tIl e.= 60· lIa:: I; = 20 .kN ~'l'Yll'IJ'W1~'lJtI.:J1l'J.:J-tf~li
, I 1 ;
ua::V1i'l''Vl1.:J~1~o/l~lJtnWf11~lm!f1'W X Viiirilmn '. .
2-49 ~'ll11'IJ'W1'~ F ua::V1fl''Vll'l e '1Hl'lU'J.:J F !VlvVi~::
'I'111li~ft tf~li'IJil.:JU'J.:Jvr'l ~lltlf)'j::'I'11U'W~::'IJt1~iifillyh nu ~'Wtr
r--------x
40 kl'!
'JtJ~ 2-48/2-49
"
61. v v
.>2i5l~)!':i'J'I'r.:)t11:IJm:::1111J'W!ll1!1'lJ'L6'1JthI1Ufl ll':)Ml'lJ'WJ~U~::
. fitYf11~ e'lltFl F, !viil~'il:::'Vhl11!!':i.:)i:l'Vnjii~fl''Vll':)lll:IJ!!fl'W x'
~~fh1J1fl!!~::ii'U'W119l 1 kN
*2-52 61 F = 300 N !t~:: 8 = 20° ll..:J'I11'U'WlI9lU~::'
du 1 ~...... ... QJ (J'
iifl''Y11..:J'Yl119l'VI1'W!'U:IJ'WlWfl11l1fl!!fl'W X 'U il.:) U'J..:J (I'I"l1l'Uil..:J !t.'J':)
y .J Q V QJ ':( <V
'tl..:Jt11:IJ'VI m:::'VI11J'W!'I'l1!!'U'W'J1J'Wl'l1'Wfl
45°
F3 =200 N
:ilI---;--I... - - x
Fl
'Jt1~ 2-51/2-52...
J>
. x'
59
2-54 ll':)'I11'U'WlI9lU(I::lifl''I'll..:J e 'iUil.:) F !vl8~1l::.yh111'!!':i':), A
rv ,(~ """ "'" d, I .".
(I'I"l1l:IJ'VIfl''I'll.:)lll:IJUfl'W X 'I'l:IJfllU1ntm::lJ'U'Wl19l 1250 N
2- 55 61 F = 750 N !w::: 8 = 45° 1l..:J'I11'U'WlI9I!!(I::iifl''VI1..:J
• A
iii'~l'11Ut~lJl..nWfll'ill fHLflU X Vijjrll1J1f1~fl-:J U'j~ a'Y4lif1~~vll
'Jt1~ 2-54/2-55
'II
* 2-56 11'J..:J-vr..:JmlJm::'l'l1U'Wt'Vl1U'U'W1mh'l1'lrn ll'l'l11'U'W1191!!(I::
Yifl''Vll..:J 8 'Uil':) F !vlil~1l::Vll1'11!!'J'Ifi''I''lTIiiYifl'~l:IJ!tn'W x'
· ,
viijfi11J1fH!t'l::ii'U'WlI9I 800 N
2-57 61 F = 300 N U(I:: 8 = 10° M'I11'U'WlI9I!!t'l:::Yifl''Vll'l
• 1 ,
..c:t <V "" Q. d.:::t I _ <V.I 0
'VI119l'VI1tH'U:IJ'W1Wmmfl!!fl'W X' 'I'l:IJfl1U1n'Uil..:J 1I'J..:Jt'l'l"lfifl'i::'I'll
v ~ v
2-53 !!'J':)'I'l':)t11:IJ m :::vl11J'W1..:J1I'111'W ll'l'l11'lh..:J'Uil..:J fllff1'1111J 1J'W!111!!'UU1mlTI1Ufl
'U'W1191 P ~rvitl~1l::vli111'U'W1I91'Uil..:J!!'J'Ifi''I''l1l1lili)'W 2500 N
1191(J~u'J..:J p lJYifl'1t1vm~i'1'W'U11iiil -
'Jt1~ 2-53...
y
I
F2 =200 N
x'
~________________ x
62. 60
2- 58' 'il'lll'ffmll~'1U~a:::ll~'1~m:::vll1Jtm11ll'IJ'Ufuth"T1rflll1ilri ' *2- 60 1l'l111V1ff e 'lJil'ltfHU~Ua:::flTJ~~ F tviilvll111ll':i'la'Wi. 'U I 1 .
'1 _I ~ """ <V &:j .... ""'" X ~ ~ .eI
1'U~Unfl1~il'J!m:::UU'Wfl~ll1fll'll'!Htfl'U X lltl::: y 'J1lJ'Vl'l'VI1 lJ'VlJJYj-ru'UI'Ull'U1~'1Utl::lJ'IJ'UW18illLN---
'IJ'Ul~Hta:::V1ffm'l e'lJil'l F tviil~1l:::vll111u'J'Ia'WiiiV1ffl'lllJUfl'U1
X' Yiiir111J1mttl::ii'IJ'U1~ F t'vilnu 600 N
R
x'
F3=100N ..
'JU~ 2-58OJ
2-59 U'J'Im:::vll~9lt~£J1n'U"f'l'ffllJm:::vllU'Ut,nvll111til~U'J'I
a'Wi F = 0 til F = 1. F ua::: F vlllJlJ 90° 1l1fl F
R , - 2 2 1 1 q 2
~,mJ 1l'l'VI1'IJ'U19lYi~il'lfl1'J F Uff9l'll'U!'VlillJ'lJil'l F tttl:::3J3J e'" J 1 "
y
OJ
2- 61 1l'll11'IJ'U19llttl:::V1ff'Vl1'l'IJil'lU'J'Ia'Wi'IJil'lU'J'I'I'1'1ffl3Jm:::vll
U'U1'1tt'l11'U A rll'VI'U9l F = 500 N lttl::: e= 20°
1
y
400N
~'-------'----x
';iU~ 2-60/2-61
"
2-62 1J'Il11'IJ'U19l'IJil'lU'J'I F tvlilvllll1'IJ'Ul9l'IJil'ly.",a'Wi F
v d ' ,,~
'IJ il'l U'J'I'I'1'1'ffllJiir1l'Uil £J'Vl ~9l ti'iTVi I1J'UltJl~ 'J1lJ"''1l11'IJ'Ul 9lYi
.. UtWYi~9l'IJil'l F R
.,..----i~5kN
4kN F
63. "
61
F = 250 Ib 'il'lbb'i.Y~'1 2-66 ~llJ,rU Su~~~nUbfl~tl'lna'llC1l'1::flnm::'I'h~11'J!!':i.:J
60 N ~'Hn~'illnuihnhnaI'J1 D 'il'll'lllllJ:I'i.YI'l'lVifl'l'm~il'l
'illm::Uurinl'l ~ UCI::Uff~'1h.!lllnml'!tlTI'.m~uurinl'l'illfl
F=2501b
1tl~ 2-63
"
* 2-64 bl':i'l F m::'I'hu'..!l'Il.,/l'll'lllfliiel'lffll'j::fltlurimJ 40 N
nm'hl'..!':i::'..!1U x-y i'llll 'il'lU'i.YI'l'l F 1Ulllnml'wTI'..!'j::UU
rinYllllfl
Q., dlV Q,IV
2-65 'il'll'll'U'..!lI'l UCI::l.llJ U'i.Y~'1'1'1 fl''I'1l'I'1'11I'l'illm:;UUVi fl~'Utl'l
U':i'l F m ::'I'11U'..!l'Il.jl'lmlfl
z
--~--y
x
1tl~ 2- 66
"
2-67 'il'lIt'i.Y~'1uI'iCl::u'j'll'..!llll1fll(OltlTI'..!':i::uurinml1flmhl'll
v ,
U'j'lilVili F 'jllJ'Vl'll'll'U'..!lI'lUCI::lJlJIWI'l'lVifl''I'1l'lV1il'l 'illflR " IV IV q
1::UUrin~ fl fl'Vl'l11 I'l n ml'!tl1ii1'..!1::UurinI'l'illfl
x
Fj =8kN
1tl~ 2-67
"
~ 2-68 'il'll'll'U'..!lI'l UCI::l.jlJU'i.YI'l'lVi fl''I'1l'lV1il'l 'illm::uurinl'l'Utl-l
U1'1ilVili flmf'l11I'lnm9lil1d1m::uurin~'illfl
z
::::;,t-----y
x
'Jtl~ 2-68/2-69
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j
I
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2-70 'il~Utll'l~U~~:;u'j'llu'jtlnf)ll'1tli'hn:;'IJ'lJYinl'llllf)..
.<::lo, d u ' ""'" IV
2 - 71 'il ~'I11'U'UlI'11W:;JJJJ 1Itl1'1'I'1'1 1'I'1'11::J'I'11 1'1'illm:;'IJ'lJWf)l'I'Utl'l
11'j~awi ~mf~111'111f) l~u1if1m:;uuYinI'lUlf)
z
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x
'nJ~ 2- 70/2-71
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*2-7 2 'il~'I11'U'Ull'1'UeJ.:IlJJJ I1tll'l'lill l'I'1'1l'lYill'1'ill m:;uuYi nl'l'UeJ.:I
u "
Im~W1i
z
75lb
y
55lb
'aU~ 2 - 72
"
2 - 73 m'Uflflm:;vh~11'J1I'j..:J"r..:Jtltl..:J~..:J'jtl ~..:Jtltll'l'll1l9i~:;!l~..:J
1'U~1In f) 11'1 ~fl'U'J":;'IJ'IJ'w n 1'1 m f) U~:;111~'U11'1'jlmr'1JJJJ 11'if1'1'1
" . .""'" '..... <U' """ QJ _ <S'
'1'11'1'1'11'1'1'111'1'illm:;u'IJwf) I'I'U tl'111'J"'1 ~W1i
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. 2-74 l'iflm:;ll'1..:Jf.' f) m:;Yll ~, £J tt'j'l"r..:J 'ifllJ~'l'J"tl ~..:J1111JJJ
" " ,""'" dlU'""cv .d
1l'if1'l'1'1'1rl'l'11~'I'111'1'illm:;uUWf)1'I a, ~ ml:; 'Y 'UeJ'1 F tWtl
1 1 1 1
Yh11111~'Hlwim:;Y1lu'Ut'iflm:;11'1'1 F = {350i} N
R
2 - 75 t'iflm:;ll'1'1nf)m:;yh~ll'J1l~.:I.J.:I'ifllJ~.:I~lI 'il'1mJJJJI1'ifI'l'1
" '"
iIlrl'l'1l'1Yill'1'illf):J:;uuYinl'l a, ~ IW:; 'Y 'UU~ F trieJY1l1'l1
1 1 1 1
tt'J".:jawim:;Y1lu'Ut'iflm:;ll'1'1iifill'vi1 nUrl'Uu
"
x
Fi =200 N
'aU~ 2-74/2-75'II
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1 2
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'il'1'I11'li'Ull'1 tW:;lJ JJ ll'if1'1'1ill1'I'1'11'lYill'1'ill f)
~:;1JuYinl'l'IJeJ.:j F
2
2-77 'il.:j'l11lJlJll'ifI'l'1i1lrl'l'11'1Yill'1'illm:;1JUWnl'l'UeJ.:jtt~.:j F, 1
11~:;tt'ifI'l.:j1'U~1I1'l1£J
B
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x
65. . . .l.. "'.1 ' •
Lff.l1flm::Y1119l1tJU1'l F 'If'llHl'lfllJ1:;fltlUtltltlm:;'V11
~l1JLLflU;; k, y LL~:; z ~'l~1l 51'UU19l'lHl'l F i!iv 3 kN U~::
p,: 3D· 1l11vf.:J Y = 75· 'il'l'YI1'UUll9l'UV'lV'l1l1l'J::flVUVmJvf'l
2-79 Lff1t1flm:;vlll91ltJU'J'l F 91'liiv'lllllm1vUVVtJ F = 1.5~ x
kN LLCl:: F ,: 1.25 kN 51 ~ = 75· 'il'l'Yll'UU19l'UV'l F U~::
z 1
Fy
z
'JtJ~ 2-78/2-79
"
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* 2-80 U'J'l F t1flm::vll'ViriluUU'UV~'YIVfltltJff'lYi A 51U'J'l- ~ ~
m::vl11uVlfl'Vm~.:J~1l tl.:Jlllh'::nvuvcltJvYlu'J::U1UH'Jl.:Jl y-z
.d, : """.d !IV
'IJ'IJ'Ull'l 80 Ib 'il~'YIl'IJ'Ull'l'Hl~ F !tCl::1J1H!ff9l~'Vlfl'Vl1-!l'Vll9l
.'il1m::uuVln9l a, /3 UCl:: 'Y .. '~
A
- - - y
x
801b
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"
63
• ... F .J... 0'.1 '
2-81 fffl~1flfl'J:;'V1119l1 tlU'J'I 'b''IllMfllJ'J:;fltlUtltl Jfl'J:;
vl1fl111UflU x, y UCl:; z ~~~1l 51'U'U119l'UV'l F iifhL'yhnu
80 N ll~:: a ,: 60· 'JlllYl'l Y = 45· 'il~'YI1'UU19l'UV'IV'I1l
ll'J::fltlUriVJ~'lfl all
2-82 ffmt1flm::vl11'l1tlH'J'I F 91'1iitl~llll'J::m)1J(jvtJ F ,:~ ~ x
20 N HCl:: F
z
= 20 N 51 ~ = 120· 'il~'YIl'IJU19l'IJV~ F HCl::
F
y
'JtJ~ 2-81/2-82
"
...
2-83 U'J~Yl~ffv~F UCl:; F m::vll?itlfffl~ 51U'J~t1'V'lTI F
1 2 . R
ii'UU19l 50 Ib U~:;l.JJJ!!ffl9l~Yifl''V11~Yil9l'illm::uuVln9l a =
110· U~:: B,: 80· ~~21l 'il-l'Yll'UU19l'UV.:J F2 UCl::'l,PJUff9l.:J
VlflVl1.:JYill9l'illm::uuVln9l
z
lWH--r----y
FI =201b I
'nJ~ 2-83
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66. ·64
b)'il_lIl~CfI_lnfll9lvf'j:;'4phm11l~ r 1~l~llfllCflVTI'U2:;'yD
VlflCflmfl mr:I'Hl'IJ'U1Cf1 LLi:l:;~lJ m,"CfI_l'Vl fI'Vl1_l'Vl1 ~'ill m:;DDVI fl~
z
v----cr------r--,;j-m- y
x
~tJ~ 2-84'II
x
2-86 'il_lUff~_lnfllPHlfDVf)Phu'YIll_l r lwpJnfll9lVTI'U'j:;DD
Wn~ll.lflU51'YI1'IJ'U1~Lm:;~llLm~_liifl'Vl1_lYil~'illm:;DDwn~
1--- - 8 ft - - --I
A
,;n.'~ 2-86'II
2-87 'il_l'Yl1ml11U11'lJV_l'1fmfl'U AB 'lJV_l1fm«f)1mH~mr~
~mflL9Ivf'j:;'4i11LL'YIll_l1'U'j:;DDwn~mf)'il1f) A 'lufk B U51
'YI1'IJ'U1~~lU
y
T
1.5 m
I~~~-L_ _ _L--x
~tJ~ 2-87
v ,
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m 1m:; y = 2 m 'il_l'Yl1wn~ z 'lu«_l~~1'_l~~'lJ'fl_lfl1'j1i~~~
9I11l1ff1
2-89 IrHUi:lU11 8 m fJf)'(jCfl~CfIf)uD~'U&'W'yj A 0'1 z = 5 m
'il_l'YI1i1111'Y11l_l +x Lli:l::; +y 'IJ'fl_l~Cf1 A 1~£JI~vmh~ x = y
z
67. Ul1'IJfl~~'I"Hn'li'flm~u~ AB 1~H.II~lJI11f)
. 1ImUlhn::1J1JVin~'il1f)1l1fl A ltluI B
~--x
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"
.J d QJ ~I tI 0 ,
2-91 'VI 'i.::U::11 I)1'Yi'U-l ~-l JU 11 fllfl fl1'i::! fl1 Ul1'U~ flllJ ll'U'U
ri'UU'U1'f1l1fl 0 ltlV-l Bill):: B 'rtlv~ A fio r ={ looi+• OB
300j+4ook} mm IW:: r = {350i+225j-640k} mm 9ll'lJ
. BA ,
cililJ 1Jll1l'i::u::mnnfl 0 ltlu~Yi,r1J A
• 2-92 61 r = (o.5i+4j+O.25k) m UI):: r = {o.3i+
OA OB
2j+2k} m 1JlU(1'I'1..:J rBA 1'UJtll1fll9l0~'U1::1J1JVinl'1'illfl
x
y
~1J~ 2-92
"
65
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2-93 Yl'i::u::mnl1m 9l111'l1'U..:J'UO..:Jlfl'HHiil.!ij A 1ll):m11vJij
IV ILl IV ,fv ",..,:
B jfl11'11:YlJ'V'lYlllfllJ!1:Yll'il'lll1Yl 0 1Jll1l'i::u::Yl1~ d'i:::l1'h'l A
Ill):: B ~1:::!J::mmr'U ff111flJfll'illf)'Urul1l;1f1l'i,rI'1'itll1fH9l0{
'i::!~llmU'l~iHif11Jlfl A ltlu'I B ~!ti';'Yil'U'U11'1~1~
x
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z
0.5
x
68. 66
2-95 1J-3!!j,Y~-3 F hllllnfl!Plflf1U'J::UUWn~Ulflllal'I111PJ
l!j,Y~,'JVii'l'VIl,'Jii1~nl1m:::UUWn~']lU
':ilJ~ 2-95'II
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2- 98 1),'J'I11'lJt!119lua:::lJ1JUt'1'I9l'li1 fl'VIl-li11 ~1l1 m:::U1J''1 fl ~'lJtl,'J
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2-9 9 'iJlIlt'1'~-lU';i-l..r-lt'1'tlllU~lll1flIIPWflu'J:::uUW n~'illfl
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x
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69. ;,
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2-103 !!'l~ F lJ_'IJ'Ul~ 8~::;m::;VI1V1~~f)~f)'11~ "C 'lHJ~
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----~~~~----~~--~--------y
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67
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l'in~ll1 f) mITrlllJlJ uff~~Vi~V11~Vil~'ill m::;1J1Jl'in~
y
x
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2-105 IfHii'1lf)u~~~n1J~fI~ B lfi~u'j~ .350 Ib 1J'U1m~
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:----- --;r-- y
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z A
- - - - y
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2- 107 11,:) Ua~~tt~a::tr:l.:)l'U~tln f1 tl'1 eJTIm::uuwk~'il1f) U":;
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'jtl~ 2-108/2- 109
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2-110 "nr1~1-:)lmil~1~liJ1CJi AB 1l-:)'VIlf111lJ(J11'IJtl~lCJiua::
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. tll~H)'fbj'j::'IJ'IJ~t1~mflUa::'I11I1'l~~'YHf~11:J
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y
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I4 m
6m
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69
2-113 'il'llli.1~'1Ul~ F 1'U'jtlrjm9Hl{1'U'l~'IJ'IJ~«~'il1f1t11'il~
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lflliia m::vll'IJ'Ul1fl fl fl 1:J~'1~tl M'I11l'lllll1'111 (x,y) tYll1~'IJ
lflliiCl~ij~«'IJ~ DA lviflvllhi'll'Jlft'V'li'lfi ~~'U1'Um)fl()l:JilVif(
'Vlll~llJlln'U'U()ll1()flfll:J'Illn D ltlrJ-J 0
2-115 11()flfltJtJn£j~f-J«'IJ~1~l:JlflliiClyfli.11lJ t111l'Jll'UuI'iCl::
lfllii a m::vll'IJ'Ul1flflfl tI~'1'Jtl 'Il-J'I11'lJ'Ul ~ ua::lJlJ 1!i.1~-JVi ff'Vll'l• ~ q
Vil~'Illm::'IJ'lJVl«~ a, ~ Ull:: y 'UtJ'III'J'Ift'V'li' nll1'U~ril x =
20 m UCl:: y = 15 m
x
'j1l~ 2-114/2-~15
"
I
'I
72. 1
70
o ~ ~
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A· (B+D) = (A·B) + (A·D)
v
2-117 'iJ-ll1111lJ e 'J::l1iWffl'U111-l'Utl-ll1fHl9ltl1vi'-l1:Ytl-l
2-118 'iJ-l111'U'U1W1'Utl-lfll'l~1l1tJ'Utl-l r IPlllJ r Ha::tl-l~th::fH)1J
tltltlfll'VHntl r IPlllJ r
2 1
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3m
-<':~--r--:::::x<:
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x
1 2
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2-119 'iJ-l111l,llJ e 'J:::'YI11-l1:Y1'U111-l'Utl-ll1fHlPltl'J'V-l1:Ytl-l
*2-120 'il-l'YI1'U'U1W1'Utl-ltl-l~th::f)tl1JV{)tlfl1'V1Ultl'lJ{)-l r IPlllJ
1
r tm:::fl1'V1111tl'Utl-l r IPlllJ r
2 2 1
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'j,j~ 2-119/2- 120
"
2-121 'iJ-ll11tl-l~lh::f)tl1JVtltlvf-l1:Ytl-l!Jtl-lH'J-l F IPlllJH'Ult'ff'U
Oa Ha:: Ob tVhl'l'h111 F = F +F 'JllJvf-l'YIltl-l~lh::m)1JA B
Vtltlfl1'V1111tl'Utl-l F IPlllJ Oa Ha:: Ob lla::ff11-l{)-l~lh::f){)1J
citltl tta:::fl1'V1"ul tl1'Ut~-l mlvJy.J f) ~1 tl
b
O~----~------------a
'j,j~ 2-121
"
x
y
2-123 'iJl111'U'U1W1'Utlltll ~lh::f) tl1J titl tlfl1'V1111 tl'U tll t1 f) tlil tl1
'J:::t.l~hH'YI1j,:j r 19l1lJtif)'U Oa
z
2m
r r
6m
OV<"'-----------:::;r-~"------- }'
x
73. BA 1If1~ Be
y
x
~'ll~ 2-124/2-125
"
2-126 H'5'.:I F m~'i'h~um£J A 'Uil'l'viil.yjU'J::fH)lJ~'W 1)'1'111
'IJ'Ul~'Uil'lil'H'lu'J::flillJciil£J F IItI:: F Yim~'l'h~TlJHfl'U AB
1 2
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x
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"
71
2-127 t111l':i'l1'Ul!'Ul~'1m::'l'illJ'Ufffll F = {-500 ~} N 1).:1
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OA LLel::i'l'inflnlJLLfl'U~'::Jflcil1
* 2-128 1)'1'111l,J'lJ e 'l::'Hil'lll'ln nl'U'Utl'lfll':im::'l'il'IJtll F Lm::
LLfl'U OA
x
F = [-SOOk} N
~'ll~ 2-127/2-128
y
2-129 LflLlJClLflI9lU':i'l 400 N lJ'ULffl 'iJI'I11'U'Wll9l'Utlltllrl
lh~flf)lJcimJm'VHl1(J'lJtll F ~1'lJU'U1LtY'U'IJ()'1fll'lfl'l::'l'il'U()I F
1 2
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74. 72
2,..131 lI'l'l11'fmhh:;f)v1JUtHJ'UtH F ~m:;VhlPlllJLLvi'l AC 2-135 1I'l111lJlJ e iiLrUua OA VIlr11Jfll'W OC
Ua:;J~ulflr11HLvi~ 1~Wll.9l B VtJ..·~~~fla1~'Uv~Uvi'l '" 0 v
* 2-136 ll~'I11lJlJ 0 'VlLflLUa OA 'Vllfl1JflTW OD
2-13211~'I11V'Irflh:;f)v1JumJ'U1l'l F ~m:;vh9l1lJuvi'l AC
ua:;J.:J'inf)r11Juvi'l 19ltl~9l B V~~ 3 m IPIllJUvi'l1l1fltlaltl C
x
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r11.1 AB ua:; AC 1'11lJr:i'1~1.I
2-134 Lfl LuarhtJuvr'l'ff1l'lLf)9l U';i'l ~'l~tl 'il'l'l11V'Irftl';i:;flV1J
UVtlmv/'intl'UV'IU~a:;U';i'lm:;vlllPlllJUflU OA 'UV'lI'ffl
x
y
'JV~ 2-133/2-134
"
y
x
-'JV~ 2-135/2-136
"
2-137 'il~m'UUl 9l'U 1l'l V'I rftl';i:: fl V1J UVtI fl1 v/Ul tI'U V'I LIN
100 Ib m::vlllPlllJUflU BC 'UV'IviV
v
2-138 ll'l'l11lJlJ e ';i:;w.h'l~uridUvi1l BA ua:: BC
z
- ~8ft
x 4ft
~D Y
'JV~ 2-137/2-138
"
75. ,_ ~~""lf1~'m""m',oli'fftl,mftll;'itlf) 'il~111'U'Ull'l'Utl~U'j~
rl'j:;l'il1ti(l~n:aff'U!;'itlm~v'I'hlr1'lnl'lu'j~Kl'nj 80 lb,
. aa i~iU fll'l1'U1'l e ~ 40·
O 1~"OflCllflt'Utr~il'loli'fftl~lff'Ul;'itlf) t:1111'j~Kvnj 80 Ib
*2-14 .U"
"-""""111U'U11ff'U aa i--li'll 'il--l111'U'Ull'l'Utl~II'j--l T IICl:; P1111T1T' v ,
m:;~hhi!l~Cl:;lff'Ul;'itlf) 'j,1lJvl--l11111lJ e,'UV--l P lVltl'l'h1r1''U'U11'l
'litH" P i1filUilO~,,!1'l diil T m::'I'lTVilllJ 30
0
'illf)U'U11ff'U
Yl-3flth1
':iU~ 2-139/2-140
"
II
70°
v
250 N
':iU~ 2-141
"
73
2-142 'il~111'U'UlI'lIICl:;lllJUffl'l~iiff'l'11~Vill'l'ill m:;1JlJ'Wnl'l'Uil~
F3 l~ill'il1r1'F,mKv'l1f'Uv-lI!'j-lvf'Hn:JJm::'I'h~11J1If)'U y Vii1fil
mflun::ii'U'Ull'l 600 Ib
2-143 'il~111'U'UlI'lIICl:;lJ:JJ llff9l--lii ff'l'11--lVil9l'ill m:;1JlJ'wnl'l'Utl--l
F I~V'I'h1r1'~ClK'I"nf'Utl--lu'j--lvf--lffl:JJiirill'l'iln1Jff'UV3 ..
F1
F2 =300 1b
1U~ 2-142/2-143
"
76. 74
!-145 'I'mff~N F Uft~ F l'U'jll!1nL~H)'n'U'j~uu~rl~mt1 * 2-148 1J~'I11'IJ'U1~'lJtl'H)~rlll'j~t1tlUritlUfllVHnt'J'lJtl~tI'j~1 2 "
!-1461J~'Hl'IJ'U1~'lJtJ~Uml'j!uiuft~Viflvn~~1~1'UViflYl1'U!~1l F = {60i+12j-40k} N l'UViflvn~'lJtJ~!fl!iift AB !!ft,: AC
.nWt1l'Olt1!!t1'U x Yiii,ilU1t1
y
---jl£--- - - - - - - X
F2 =351b
'nJ~ 2-145/2-146
"
v
2-147 'O.,'Jl11lJll e !!il~ 0 'j~'H';h~'lf'Ui,'h'U!ffW11~
z
O.6m~C
x
x
F
'itl~ 2-148
"
2-149 tI'j~ 23 kN !n~~'Ul~t'Jluvr~llll'U'UtJ~!flitJ.,'J!u~,
fl tJll!1'! tJflwu ill~~!flitJ~ii'Uill'1l1.,'JllUl 'O~til'! t1 tIl~i1!lJ'UtJ.,'J rl
lll:;t1tJUVtlt'J x!!!;):; y 11JJ'vr.,'JtlliU1tJ Nftm:;'VlU~tltflitl.,'J!ui!
fl tlll!I'!tlfvi!n ~'01t1!l~!;):;tl-l rll.h:;t1tlUcitl tJ~.,'Jf) rilTn
