Download Problems for Chapter 5 Statics and more Lecture notes Statics in PDF only on Docsity!
('*),+.-0/213 546).'7 8/9:),; =<?>A@B =<?C
DAEGF HJILKMON?PQSRUTOVQ.MOWXQYTOZ[V\IL]0TOVQ^,I_XLa"bcQZYRdLK"QLEefLWLQgh] RiQSQBjkalIAP"mnPNcLopRdX^ IX]!TOVQ6^qILaNcb?QrZSROLKQLEs6VQ6tuVQSQYbcMvLROQ6w2]xTyLz{XRiTyLKPgTdV"Q|ZYQSK&TdQYRvIX]8opRO}_ANGTkm N?MrV{LbG]xtr}mqa!Q~TktJQYQSKTdVQtuVQYQSb?MSE0UMiMO^,QTdVQ2aLbcbcLMiTJNcM6LKQB TdQSRiK{Lb8] ILROZSQ XZYTdN?KoIpK"Q*] IAILTa!QYVNcK"PTdVQb?QY]xTg Ab?QLKPTOV{XTTOVQ*tJQYNcopV&TgV{XKopNcK"oIL TOVQUZYRdLK"QXTvz!ILNcK&TrNcMvLbcMiITdRiQ}XTOQSPXMrLKqQ~ TdQYROK{Lbl] IpROZYQLE0ROtTdVQ|] ROQSQ alI P"m PNXopRdL^{bXa!QYbXbcb=TdV"Q] IpRiZSQSMULKPP"Nc^,QSKMiNcIpKMYE|JQMiROQ(TdIhN?KZSb?PQ .ZYIAIpRiPNcKXTdQ` AN?MSE
W
5 ft
3 ft
Ballast weight WB
c.g. 1000 lb
B
( D E?F
Ipbc"TONcIpK8
3ft^
5ft^
1000 lb^ 3ft^
x
y
WB^ ¡
W W ¢
¢ ¢W
2ft 2ft
(^1 )
cg
( D E?F
£Lw ¤
DAE¥¤5¦Mi^hXbcblaRON?PopQIpKtJLbcW NcK"oz{XTOVVLM|zNcK XTuILKQ2QSKP8LKP .ROIpb?bcQYRrXT TOVQUIXTdVQYRSE QYz{LRd TdQUTOVQaRiNcPopQu] ROIL^§NGTdMvMOzzlIpRTdM6LK"P^hLWXQ] RiQSQalI P"m P"NLopROL^Es6VQ2ZYQSK&TdQYR6IL]¨opRd}_ N?TkmqIL]TdVQ2a"RONcP"opQNcMJXT6NGTdMropQYIp^,QYTdRiNcZZSQSK&TOQSRS ^,NcPAtr}m*alQYTktvQSQYKfTdV"Q(MizzlIpRiTOMSE
A (^) B
10 ft ( D E©¤
Ipbc"TONcIpK8
R W^ R
5 ft (^) 5 ft
A
B^ B
cg¬
y
® x
U| DAE©¤
£Lw&£
DAE³w´RO}t3h] RiQSQalI P"mPNcLopROL^μIL]²TdVQgX"TdIp^,IpaN?bcQ(MON?PQ^,NcRORiIpR|zNcZ~TdRiQSP=¶a&m N?MOIpbcXTdN?KoTdV"Qn^,NcRiROIpR] RiIp^·TdVQZ}XRqalIAPAmpE KZYbcPQ TdV"Qf^,NcRORiIpROMtvQSN?opV&T}E s6V"Q(^,NcRiROIpRv] IpRO^,M6.¸"AQSPfZYIpKKQYZYTONcIpKtuN?TOVTdVQZ}`XR|alI P"mpE
( D E¯w
Ipbc"TONcIpK8s¨ROQ}T|TOVQz!ILNcK&TuIL]XTOTdLZ[V^,QSK&TuTdI.TdVQalIAPAm LMr¸"AQSP
cg
R
R
wº
M
x
y
x
y
o
U| DAE¯w
£Lw D
DAE¥DenLWLQ5¼] ROQSQ alI P"m¦PNcLopRdX^ IL],TdV"Q5alQ}X^ MOQYPTOI½V"IpbcP¦z¾TdV"Q5MiNcopK N?bcb?MiTORdXTOQSP=E¿s6V"Q\MiNcopK½V{LMtJQYNcopV&TnIL]qFÀ5b?a½LKPÁTdVQÂKNG] IpRO^ a!QSL^ tvQSN?opVMDbca=E
x
y
z
4 ft.
(0,-2,3)
(0,0,3) (0,2,3)
Ã
( D E©D
Ipbc"TONcIpK8
T (^1) T 2
10 lb
FBD of Sign
Ä
T
T
T
T T
A
A
A
1
2
y
® x zÅ
5
Æ
3 4 3ft
Ç
y
x
z
1 ft 1.5 ft
.5 ft
1.5 ft
2 ft
È
FBD of Beam
Ä
2 ft
U| DAE©D
£Lw&É
DAE¥×5Ø"TdN?bcN?TkmÙzlIpbcQhNcMMia °iQSZ~TgTdIÙftuNcKPÊb?I&LP ÚgE HJIpK"MiTdRiZYTgTOVQ*] ROQYQ~jkalI P"m P"NLopROL^E
F
( D E©×
Ipbc"TONcIpK8
F x^ Û
y^ Ü
Fx
Fy U| DAE©×
£Lw&Ý
DAE¯ÝKIpb?PNcZYQalIfNcMzbXZSQSPfIpKÏhROL^qzfV{}AN?KohMibcIpzlQIX]uFDLÞSEs6V"Qa!I}fNcM E³wh^ ß¾F^μNcKnZSRiIpMOMMiQSZ~TdNcILKntuN?TOVN?TOMZYQSK&TdQYRIL]²oLRd} N?TkmXTUN?TdM|opQYIp^qQ~TdRiNcZ ZYQSK&TdQYRSEs6VQalInN?MUVQYbcPfN?KzbcLZSQ(a&mhMi^hXbcb¶RON?antuVN?Z[VZ}XKÏa!Q^qI PQSb?QSPXMLzz"b?m NcKoh,] IpRiZSQLbcIpK"oqTdV"QRdX^qz=ERd}tàq] RiQSQa!I P"mPNXopRdL^áIX]âTdVQ alI}tuVN?Z[VnV{XM.^q`LMOMuIL]âDLÀ.W oE
15 °
c.g.
( D E¥Ý
Ipbc"TONcIpK8\s6VN?MNcMopI I P´TdNc^,QnTOIÊz!IpN?K&TIp"T*TOV{XTTOVQÏQ~"LZ~Tnb?IAZSXTdN?IpK IX]yTOVQgKIpRi^hLb¨] IpROZYQgã7NcMKIXTW K"ItuK\K&TdN?bTdVQ.QYä {XTdN?IpKÂIL]vQSä Ncb?NcaRiNc^ P"QYTdQYRO^,NcKQYM6N?TSE
x
y^ Ü
.
F^ N (50)(9.81)kg
U| DAE¥Ý
£Lw&å
T (^1) T 2
FBD of Sign
T
T
T
T T
1
2 ë
5
Æ
4 ì 3 0.4m í
y
® x
Å z
0.2m í 0.3m í
0.2m
0.3m í
0.3m
FBD of Beam 0.3m
î
100 N
.2mï .2mï
U| DAE¥å
£&DAF
DAEGFÀRO}tæ] ROQSQ,alIAP"mÂP"NLopROL^ðIX]JTdV"Qqb?N?]xTdN?Ko^,QSZ[V{LK"NcMO^ðNcbcb?MiTORdXTOQSPÏtuVN?Z[V VLM|g^q`LMiM6IL]rFÀ.W oE
b (^) B
c
1000 N
Motor
20 °
a
c.g.
,
( D E?FÀ
Ipbc"TONcIpK8
A
A W^
M F
x
y ¬c
añ
b ò
y
x
20 o^20
ó oó
U| D E?FÀ
£&Dp¤
tuV"NcZ[VNcM6MON?^qz"b?m
Ú
F
F
é ¤
LÝpÀÊw&ÀpÀD
w&À&ê FÀAF
Ép× FÀ&¤bca
ç|Q~ T|MO^,^,NcKoTOVQ2] IpROZYQSMuNcKTdV"QhPNcRiQSZYTONcIpK*m N?QSbcP"M
þ Ú
Ú ×LÀ DXÀ ÉpÀ½FÀ&¤ À
ILR
Ú
FÝpÀ F}À&¤ ×LÝ.bca
£&DXw
DAEGF¤5¾Mi^hLb?b=zlQSPQYMiTdRiNLKnaRON?PopQNcMuMizzlIpRiTOQSPfa&mgROI Z[WLQYRXTLKQSKPé .ê6LK"P zNcK TJTdV"QILTdV"QSRé Ë2ê~E² ¤LÀpÀ jbcaqz!QYROMOILKNcMJMT[LK"PNcKow]xT6Ip"Tv] ROIp^ zlIpNcK&T ËEus6VQaRiNcPoLQV{XM,tvQSN?opV&TUIX]yDLÀpÀ,bca=E6MOMO"^qN?KoqTOVQZYQSK&TdQYRIL]²opRO}_ANGTkm N?M2NcKÏTdV"Q,^,NcP"PbcQIL]vTOVQgaRON?PopQX¨ZSLbcZYb TdQTOVQgROQ}XZYTdN?IpKÙXT(z!ILNcK&TdM2Ë `LK"P qE
A B
20 ft
U| D E?F¤
Ipbc"TONcIpK8 N?ROMiTPROtæTOVQq] RiQSQ*alI P"mÂPNXopRdL^EsLW NcKo^,Ip^,QSK&TdM`LalIp"T zlIpN?K Tr˾m N?QSbcP"M þ
r1 éF}À&êSé DLÀpÀ&ê éw êSé ¤LÀpÀ&ê ¤LÀL
ILR
F
¤LÀ
é D
LÀpÀpÀ5ÝpÀpÀ&ê ¤LåpÀ.bca
A
A
200 lb 500 lb
Æ
4 ft
10 ft 10 ft
x
y By
U| D E?F¤
ç|Q~ T|MO^±TOVQ2] IpROZYQSMuNcKTOVQ hPN?ROQSZ~TdN?IpKmAN?QSb?PM
þ Ú À
ILR
À
Ë
LÀpÀ DLÀpÀ¤LåpÀ
ILR
Ë
w F}Àgb?a
ç|ILTdQ2Ë À.MiNcKZYQ(NGTuNcMrTOVQIpKb?mq] IpROZYQNcKTdVQ fPNcRiQSZYTONcIpK8E
£&DpD
DAEGF}wK¿LN?RÂZSIpKP"N?TdN?IpKN?KoÁKN?T\V{}_ NcKo ^qLMOMÙIL]¤XÀpÀ½W o MON?TOMõIpK3MiVQSbG] MizzlIpRiTOQSPa&mfqzN?KLK"PZ}La"bcQLROROLKopQY^qQYK TULMNcbcb?MiTORdXTOQSP=E6MOMi^qQ(TdVQ oLQSIp^,QYTORONcZ(ZSQYK&TdQSRXKPÏZSQYK TOQSRIX]0opRd}_ N?TkmnZSIpN?KZSN?PQXKPTdV{ TUTdV"QzbTO] IpRi^ VLM|g^qLMiM6IL]0¤pDW oEyHrLb?ZSbcXTdQTOVQROQSLZYTONcIpKMu T˾`XKPfqE
6m 8m
A
B
cg
( D E?F}w
Ipbc"TONcIpK8s6VQ] ROQYQ(alI P"m*PNcLopROL^ØN?M
4m ì 2m ë 2m
ë
245N ë y^ (200 9.81)
x®
B
A
A
T
. U| D E?F}w
þ6ÿ, À é%w êYé ¤Xw&Dpê é%É&êSé ¤LÀpÀ&êYé å
Ý"Fê é%Ý&ê.-
ILR
é
F
Ý
ê
Sé åLÝ"F&½FpF×L×p¤pê FDLåLw F¤pD FDLåLwgç
ç|ILTdQ/- NcMu.Z}La"bcQ`LKP^MT|z!IpN?K&T6zõé0/*PN?ROQSZ~TdN?IpKê~EâçIt
þ Ú À.MOIgTdV`XT|À Ë ¤
w D ¤LÀpÀ{é%å
Ý"Fê1½FDLåLw
£&Dp×
ILR
Ë
É
"F£
¤LÉ É"F}£,ç
o&`LN?K þ Ú
2* À 43 Ë* À
£&DLÝ
ILR
Ú
H
J Ú I
ç|Q~ T þ
r1 H L
G
H J
G
Ú
I
À
ILR G
H
GNM
Ú
I
J
PO
G
é
QE Q}`LRdê
R KZYQ
G
H NcM6W KItuK=
G
I
G
G
H tuVNcZ[VNcMrTdLabcXTdQYP NcKTdVQ2] Ipb?bcItuNcK"o
Hr`LR
G
H é%N?Kê
G
I éNcKê
D NcKZYIpbcK w&À"E¯åpÝ ÉpÝ"E¯À&¤
6e; DAFpE¯ÉpÉ DXwE¯ÉLw
ILROMOZ[V"Q w&å"E¥× wpwE¥×
Jbc`:9SQYR w ×AE¯ÀpÝ DLå"E¯å&¤
£pÉpÀ
DAEGFɽMON?opKh¸" TOROQZSIpKMiNcMTdMrIL]¶w&À jW oa!QSL^æzN?KKQSPXTrzlIpNcK&TJöØLK"Ph¸"AQSPa&m ZSLab?Q2XT6zlIpNcK&TJËE²s6VQKNG] IpRO^ alQ}L^ÍNcMF2^§bcILKotuN?TOVZSQYK TOQSRuIL]¨^qLMOM TgN?TdM.oLQSIp^,QYTORONcZhZSQSK&TOQSRSE5s6VQMON?opKÊNcM.ZSQYK&TdQSRiQSP¼XKPN?MgÀ"E¯ÝÂ^,QYTOQSRiM,b?IpKo V_ N?Ko^qLMOMvIL]²FÀ(W otuN?TOVhZSQYK&TdQSRJIL]¶^qLMOMJXTJNGTdMyopQSIL^qQ~TdRON?ZuZSQSK&TOQSR6LK"PNcM V"QSbcPTOI,TOVQMOzzlIpRTalQ}X^±a&m*TktJIqZ}La"bcQSM|XTuzlIpN?K TOMuÍXKPfÎgEvHrLbcZYb TdQ TOVQROQSLZYTONcIpKXT|öμLKP TdV"QTOQSKMiNcIpK N?K TOVQZ}La"bcQ`XT|zlIpNcK&T6ËE
3 S 0 o
T
0 U .8 m U 0 .1m
0 U.1m
D
A^ V
DOCTOR'S OFFICE
( D E?FÉ
Ipbc"TONcIpK8 KTdVN?MâZ}LMiQJTdV"QSROQuXROQvTktvI rгMTOItJIpRiWLalIp"TâLKPTOVQJ] IpRiZSQSM XROQZSIpz"bLK{XR6a"T|KILTLb?b8z{LROLbcb?QSb E0HJIpKMiNcPQYR|TOVQMONcoLKNGTdMiQSb?]èE ä Ncb?NcaRiNc^ m N?QSbcP"MS þ
6ÿXWY À é
Ýpê.-1Z é%À
w êSé%åpÝ
Fê ILR
[Z
å
pÝ F
w
på ÀpDgç
\ Ú
À - W K-1Z åpÝ
F
À
ILR
W
# åpÝ
F w&å
À&D w&å
À&Dç tuV"NcZ[VZSIpK"¸RO^,MuTOVQIpa&_ NcIpMYE
ç|Q~ T|ZSIpK"MONcP"QSR| r¾IL]TOVQa!QSL^
þ Ú 2* À43]-^* ö<* À.IpR_-ZYIpM£pÀ ö<*
þ6ÿ`badc4 e éèFê.- é
åpêSéf- W êg éDpêSé J ê1 é
Fêh-[Zé> ZSIL^qzlIpKQYK T[ê
£pÉ"F
