d,
AB and BC
e ld ld e
ge er at
an
,.,
(a) rod AB (b rod Be.
oa ed
ow
no
AB and BC e ra ra g or al
ed
ge er at an x. ee d, and
AB and BC
ed
ge er at
ha
an
rod Be.
(a) rod
75
l 1
ra
Fig. Fig. P1.3 P1.3
ns
------1.1
AB
es
rod BC. 1. h ig ig hh- st st re re ng ng t
ac t ee ee l b o t s i t i n a ce ce r
os
co om ca
de nd
he og er e an an s n ug ug l i n i d c yl yl in in dr dr ic ic a b ra ra s ne
he ou
d ia ia m
of
e te te r p ac ac e s . K no no w pa er
y ie ie ld ld s
es n.
Fig. P1.5
indica cate te AB indi
1200N
Fig. P1.6
18
25
er
that that
he
Problems
19
Fig. Fig. P1.
BD h a BD
u n f or or m c ro ro ss ss -
MPa.. Fig. Fig. P1.8 P1.8 3 66- m
points ts Band Band (a) poin
u ni ni fo fo r
r ec ec ta ta nn- : 12mm
E.
20
Fig. Fig. P1.10 P1.10
Fig. Fig. P1.9 P1.9 of th asse assemb mbly ly ax
va
of
e s (a) i n l in in k AB
a ve ve r g e
b) in
link Be.
EFG
pp
by
ys
O.gm
wn
l_j[~< l_j [~
CG
m in in e t h c ro ro s - se se ct ct io io na na l
MFa.
;"
up or EFG a re re a o f m em em be be r
ys
. De De t
~l=~~===S~
,Luml,'m+,~.J
Fig. Pt.t
and PU2
20
introduction--Concept of Stress
ABC. a me te r n d a p h e a ve ra .g e n or ma l s tr es s i n (a) member AE (b member DO.
boti
ar
e ac h h av e
0m
Fig. P1.13 60mm
Fig. P1.14
15mm\
E sg ~ ~l + d~ 0m
ng ne or os h e e ng in e y st e nectin ro BC,
e qu il ib ri um ,
(a)
u ni fo r
ar al ng ea
de er (b)
nd on
c ro s
s ec t o n
as ed
at
ve ag
at and
Fig. PU5
al
ow
2SkN
Fig. P1,1
ng
if t h a ve ra g
h ea r
Problem.
1.17
40
10 nu
by
er
a,
magnitude
15mm~
Fig. Pl.17
Fig. P1,1
1.19
is
75 leN. D e e r i n
th
al es
a ll o a bl e
e ng t
(a) the m ax im u
b ea r n g
t re s o n h e c on c e t
f oo ti ng , (b)
Fig. P1.2
1.21
c ro s s ec ti on a ar
a re a
7 56 0
rr an
d is t i bu te d t o
c on cr e
f ou nd a i o
. P
mm-+)
21
22
! nl ro du ct lo n- Co nc ep t
1.22
o f S tr es s
nk
al
ow
ou
am
a sh -
1.23
Fig. P1.22 18mm
4 .5 0 o N
AO.l2-mm-diamete stee rodAB CD. F o t h l oa d n g h ow n d et er m n e (a) t h m ax (b) th distance ve ea ng ac nd ed da he es ea ng es on he d. (c) h e v e CF
h ic h
ar al
c on t
he po
on of
BD nd
co ne ed
ve
al
(a)
(b) BD.
Fig. P1.23
45mm
Fig. P1.24
1.25 K no wi n
ha
500.N determine (a) h e a v
ge ar es (c) h e n om in a b ea ri n
p in , t re s
1.26 shown determine (a)
(b) t h c o r es po nd in g
b ea ri n
t re s i n h e p ed a
(c) Fig. PU5
and P1.26
1.27 a ve ra g s he ar in g t re s i n h e p i a t B , b ) h e a ve ra g b ea r n g t re s a t ber a ve ra g ar in member ABC, n o
1.28 F o h ea r ber Be, (c)
as ve ge
bl
an
ea ng
oa
P ro b 1 0 e te r es (b) h e a v g e b ea r at in member Be.
(a) the in mem at hi
(a)
av em
11 kN, e te r
he
an
ea ng
P1.
l ow ab l
h ea ri n
es
ed
nd P1
s tr es s i n t h g lu e
p li c (b)
is 62 or
! cP a d e e rm in e (a) th larges nd en he
splice.
er
he
nd
ar
ce
ea ng
F ig . P 1. 3 a n
P1.32
1.
1.
ed
n.
ab
ns
es
(a
safely supported, 1 .3 3
ap
ed ct 1 .3 4
nd he
(b) t h c o r e p on d n g
h ea r n g s t e s
h e p li ce .
t ee l p ip e o f 3 00 -m m o ut e d ia me te r i s f a b i ca te d
e, al
no
ne he ng nt
nd e ld .
t ee l p ip e o f 3 00 -m m o ut e d ia me te r
ng (J'
es es .5.0MPa an
ea
es
a br ic at e
ro
6 -m m t hi c
di
f ro m 6 -m m- th ic k
pe or ng nt 3 0 M Pa , d e e rm in e t h m ag n t ud e of an
33
34
tntrocucuon=-Oonoept of Stress
35 9 60 -1 cN l oa d pp ed h e g ra n b lo c o w D e e rm in e h e r es ul ti n m a xi m u v al u o f (a) t h n o rm a l s tr es s (b) t h s h ea ri n s tr e ss . S p e c f y h e o r e n a t o n o f h e p la n o n w h e a o f h e m ax im u m v a u e o c u r
34
35 9 60 -1 cN l oa d pp ed h e g ra n b lo c o w D e e rm in e h e r es ul ti n m a xi m u v al u o f (a) t h n o rm a l s tr es s (b) t h s h ea ri n s tr e ss . S p e c f y h e o r e n a t o n o f h e p la n o n w h e a o f h e m ax im u m v a u e o c u r
tntrocucuon=-Oonoept of Stress
ed wn h a h e r es u n g m ax im u v a u e o f h e s he ar in g es h e b lo c 17 M P a , (b) h e o r e n a t o n o f h e u rf a determine (a) ma on wh h e m ax im u h ea ri n e s o cc u s , (c) h e n o m a e s e xe r e d o n ur face, (d) ma mu ma k. es or of
ma 4 5 M P a D e e rm in e h e r os s e c i on a et wi 3. 0. As me ha B.
ma ma a re a f o AB f o w hi c h e f ac w i b e d eq ua te l ei fo ed
r240mm~ Fig. P1.37
F ig . P 1. 3
80mm
an
mm
t.
ma
MP -i
P 1. 3
mm Wh
ma ed
180mm
4 50 -M P a u l m a if ac
et
s t e ng t wn e qu a
BC ma i n e ns io n W ha t h ou l b e h e w id t es
of he in
lO-rnm d ia m e te r i s p la ce d s te e l l oo p A B C D en 1.40 a s h ow n a ro un d 2 4 m m ·d ia me te r a lu m in u o d C . C a bl e BE an F, each Q. K no w n g h a h e u l m a me er ed e ng t o f h e e e ed or o p a n h e a b e s 4 8 M P a d e e rm i l ar ge s t l oa d ha an a pp l e d a n o ve r fa a fe t o f de ed
Fig. P1.40
, : , r : --=:1___
r!'·~J~·
M em b an ma me k n w n a t 2 0 m - q ua r b a he me wa es ed ma wa e d If 3. b e a ch ie ve d f o b o b a s , d e e rm in e h e e qu ir e r os s s ec t o na l a re a of (a) ba AB (b ba AC.
1.1
~kN
F ig . P 1. 4
an
P 1. 4
oy
M em b an ma me al oy k no w h a 2 0 m m - q ua r b a o f h e a m e a l o y w a e s e d f a l ur e a n h a a n u l m a t o a o f 1 2 le w a s r e co r de d . Ifba h a s c r os s -s e c ti o n a ac of e t o r a r AB t h c ro ss mrrr', determine (a) if e c i on a a re a o f b a me et B.
Problarns
ul
ea es ed
.3
he
c to r
es de
or
a, he
a fe t
qu ed
de
ha
ac
of af
he
n.
""
Fig. P1.45
1 4 m m u n f or m r ec ta ng ul a ow
ar
ed
52
c ro s
a, de
140mm
Fig. P1.46
1.47
by
40 mm, of
de
at d ia m he pi 1.48 F o t h u pp o o fP ro b 1.47, k n is "" 2 0 k N d et er m n e ac o f safety-for th pin, (b) (a) t o o f a fe t f o t h w oo de n m em be r h e a m a s h a f ou n i n p a r
P1.47
35
36
Introduction-Concept
01Stress
h e h ol e in K no wi n t ha t f ac to r of es en o f t h p la te , (b) h e i n m u d ep t (a) th required widt es
nd
1 0 k N determine at
at
1.50 12 kN
when
k no wi n
"" 1 9 m m
t ha t
AC u pp o
at
an
4 50 ·M P
m em be r BC
at
no in
stee with t ha t
no ma
t re s
by 10-mm-diameter pins whil member di all at he an es et at AC is notreinforced around
BC s he ar . load th pi
u l i ma t
et D.
ho es
1.52
ol di
Pr
ng
at
ct
as
esgn an
nd
Fig. P1.49
1.53 1 2- m - d a me te r in stress is load
p in s a r
A, and he
used at Band
3.0 is desired.
if
Fig. P1.5
12 mm
Front view 53
54
A. ha
et d.
'::":[""r= Side view
s su m n g
t ha t a l o th e al
p ec if ic a i on s
Problems
O·
er
no
p in s
at
an
ct
D. de
nk
he d , e te r o t e in fo rc e
50 BD. oa at ho
he ar un
mill
Sid vie
Fig. P1.5S
1.56
Solve Prob, 1 .5 5 a ss um in g t ha t t h
t ru ct ur e h a b ee n e de s g ne d
*1.57
(a) Assuming factor ed
1. an c ab le . (b)
at
resistance
he co ve
al
ac
y f r t
*1.58
40
or
ch
he
AB, d . (a)
at
(b
6, et at
ar es or
on
Lo
ad ha an be co ve na ac
and by an es
en er el nc ac ed or
BC
Be es 25 an
~t~=
37
·k 2 0 O Pa , d e e rm in e (a) th smallest (b) t h c o r es po nd in g n o m a s t e s c au se d
ng
ee
u b c te d
en
that (a) ding normal stress
rn t ha t t h m ax im u
ce
no
(b) the correspon-
a ll ow ab l
2.4 d ia me te r a lu m n u
t re s i s 2 2 M Pa , d et er m n e (a) th smallmaximu (b) th correspondin
n or ma l
o d w it h
is applied, determin
(a)
(b) t h f ac to r o f s af et y
determine he
e te r
that 69 Pa determine (a)
h e h re a
ha
bl
ch ng en 02 ni um al (b) h e
11 (b)
ha 20 e sp o d in g n o
(a)
ad
(b)
e te r
is applied
P,
(a)
al
1.4 it is ec ad Kn ab en il t re ng t i s 1 2 M Pa , d e e rm in e (a) t h m ax im u a ll ow ab l l en gt h of he e , (b) h e e qu i di en ns he cr e c o n if h e t en si l l oa d
with Pa
at
c re a
65
66
S tr es s a n
S tr ai n- Ax ia l
L oa di n
""
which
to
axia load Knowin
that
70
P a d et er m n e t h
e qu i e d d ia me te r o f t h
3 -k N od
2. rn
that I% 3.5
In
r eq ui re d d ia me te r o f t h t hr ea d
2.13
Th 4·mm-diame!e
cabl
ee
if
at
"" 20 GPa.
Fig. P2.13
cylindrical quire
portions
and
diameter
no
xc
if the allowable
no
I!OkN
300nlln-
kN
38mm
50mrn
;",.""'.,,, " " " . " ; , , •.. ;,.,""'"
Fig. P2.14 vinyl (E de or
(a)
portion
on
ci
n,
(b)
Be. D im e ns io n
Fig. P2.15
in mm
at
en
Problems
of portio BC fo
A B C . Knowin tha
10 GPa, determin th diameter hich th deflection of poin wi be mm
Fig. P2.16
Bot pojrion of th ro AB ar made of an aluminum fo whic (a) the ng gn that he deflection at is zero (b) the correspondin deflec
2.17
valu of tion of B.
20·mm diameter
.41l1
0.5m
"
ifj .....
SO·m
iamete
8kN
Fig. P2.17 and P2.18
Fig. P2.19
E.= 70 Pa 42 kN determin th deflection of (a) point
AB
Knowin tha point B.
2.19 wo olid ylindrical rods ar jo ne at an loaded as shown. Rod AB is made of stee (E 20 GPa) an ro of bras (E 105 GPa). Determine (a) th tota deformatio of th composit ro A BC , the deflec tion of poin B. 2.20
3·mm-thick hollow polystyren cylinder
:3.2kN
Fig. P2.20
(E
250-mm-Ion stee ro oa applie at IJ determine (a) th elongation of ro tion of poin B, (e) th averag norma stress in ro AB 0=
the deflec
67
68
Stress an Strain-Axia
Loadin
20 a) an oa n, de ne (E of member AB and AD. k no w n g t ha t h ei r c ro ss -s ec ti on a a re a an 8 0 mm", respectively.
deformations
20
~==~=~~U
"T.~
Fig. P2.2
41ll
2.5m
~L ~i BD
of 20 mm", D et er m n e t h em er
ar gt
a rg es t a ll ow ab l 1.5 mm.
AB and BE of th trus show stee rods (a) rod AB
1-<---1.5
l oa d
i f t h c ha ng e
consis of 25-mm·diarnete
rod BE.
-
15
Fig. P2.22
Fig. P2.23
ec on member BC,
AB and CD of 25
ad ow ng o in t E.
at he
(E pp
75 OP
CO IS0mm
260mrn
Fig. P2.2 ==*A.L:"'",,'c
kN
Fig. P2.2
I-240 mr
L~ _~
ABC and DEF a r j oi ne d w it h t ee l l in k (E sma 3 5 m m p la te s D et er mi n (a) member BE (b member CF.
2000Pa). t h c ha ng e
Problems
Fig. P2.26 h a b ee n a dj us te d rigi
beam
betwee
nd
n ta c p o
E. K no w n g t ha t
GPa determine
Band
2.27
and CD
Members
bers BC and
2-
er
e ne d t h d ia go na l m em be r d et er mi n t h l ar ge s a l o wa b bers AB and CD
ee
he
u r b uc k
ht 00
t en si o
de
at ns
Fig. P2.27
2.28 F o t h t ru ct ur e i n P ro b 2 .2 7 d et er m n e (a) th distanc h e d ef or ma ti on s i n m em be r and ar equal, (b th p on d n g t en si o i n m em be r AC.
vo on w ei gh t
ts ow
a, em
h t h, density p, a n
of m od ul u
om en ou o f e la s i ci t E,
t ha t corre-
a ra b
Fig, P2.29
2.30
h om og en eo u (a)
c ab l ot du (b)
o f l en g by
he
nd ni ns
ec pe he
vo
e)
n ga t
tained if
2.31
Denoting by E,
32
h e o lu m on cc d,
e ng in e 1n(1 en he ni
en
ec
n,
ho
E)
pe
en es nt ns nt h i p la s e te r o f ci en d.. h o In(dl/d)
69
C om p e s en 2.33 he as em h ow n b y m ea n 7 0 G P a d e te rm i n (a) m i nu m s he ll , (b) h e d ef o m a ti o
es gi e s K no w n g h a E, ma es es el o f h e a ss em b l
en OP
2_34 em ea es mm wh fo pp ed by me ns gi en e s D e e rm in e (a) the m ag n u d t h a pp li e f or ce , (b) h e o r e sp on d n g s tr es s h e e e c or e
A n a xi a e n i c f or c o f m a gn i u d 2.35 o m po s b lo c s ho w b y m e an s o f i gi d e n p la te . K no w n g h a d e e rm in e h e n or ma l s tr es s i n (a) h e b ra s o re , (b) h e a lu m in u 2.36 Fo mp v al u o f he po on of he ad p or ti o o f h e o a a rr ie d by h e b ra s MP
2.37
28 mm he no ma
Th 5on et po m e e r K no w n g h a es es he ee an
of
Fig. P2.33
10mm, p la te s
w n in P r o b , 2 .3 5 , d e te r m in e (a) th ed by he um nu p l e s is half the o re , (b) h e o ta l o a if h e es in e in fo r e d w i he on et
ee ba ea wi 2 5 G P a d e te rm i n 1 55 0 k N a x en
w he n
Bras cor (E
105 GPa)
mm
6mm
Stee core
QO
B r as s s he l 105 GP
Fig. P2.34
Fig. P2.35
Fig. P2_37
79
Stressand Strain-Axia Dimensions
2.38
Loadin in
mm
18
Prob, 2 . 7 , he on
e te r
x i u m c en t
Stressand Strain-Axia Dimensions
2.38
Loadin in
mm
Prob, 2 . 7 ,
18
e te r
x i u m c en t
he on 2.39
at k no wi n and
Tw cy nd ca
od
el nd o th e and E. t ha t E, E~"" 10 GPa, determin (a) h e e ac ti on s a t d e e c o n o f o in t
AC
steel.
CE Fig. P2.39
(E t h o d AB and CD has 625·rnm cross-sectiona area Determin
EF (a)
EF,
(b) 250-rnm-long aluminum tube single-threade screw-on covers gh ol o d (E an he o n c ov e c re w ce he t ub e i t i s o b e rv e t ha t t h c ov e m us t b e f o c e a ga in s t h Fig. P2.41
ht o ng e he o d b y o ta ti n i t o n e (a) th averag
(b)
t h r od . 36mm
2Smm
Fig. P2.42
2.43
(E,
a dj us te d
d ec re as e t h d is ta nc e b e w ee n i t a w and th portion BC he ub
b y 0 . m m D e e rm in e (a) the
Fig. P2.43
2.44
ob
.4
as
at
o rc e
ha
b ee n a pp l d ,
2.45
16 mm
BE and CD
20
(E
Problems
pitch of 2. i gh te ne d o n o d CD (b t h d ef le ct io n o f p oi n
on
ul
u rn , d et er m n e (a) the gi em ABC.
00 mo
FIg. P2.45
30
mr
30
Fig. P2.46
diameter (E were initiall
90
ha (a)
load
2.47 core (a,
2.48 23.6
as th
20 taut determin
t h c or re sp on d n g T h b ra s h e (a 11.7 1O-6/"C).
Th
20.9
1 O 6 /" C a rg e
er
bl
on
d ef le ct io n o f p oi n D. u ll y b on de d t o t h ow c re a 55 MPa. h e (E (E,
1O-6/"C)
Stee core
20 CPa
70 OPa, 20
OPa,
20°C. Consider-
1O-6(QC)
on de at ns e te r temperatur reache 180°C.
he
a lu m n u
6m.m
t ee l em
el
en
Bras shel 10 CPa
Fig. P2.47
Fig. P2.48
OPa,
2.49
Solve Prob. 2.48, a ss um in g t ha t t h c or e is m ad e o f b ra s (Eb
20.9
1O-6(QC).
E,
25
go
20
OPa, a,
11.7
10
1 O 6 /" C a n
9. 27°C.
Fig. P2.50
mm
81
u b c te d ns OPa, determine (a)
o rc e o f ng
30
Knowin that od 15
0. ag
nd "" 70 g th , (b) the
1 .6 -m m f la t t ee l p la t 200 OPa,) 0.30). Determin th resultin change g ag e g th , (b) po (a) AB o f h e t e c ou po n (c) i n t h t hi ck ne s o f p or ti o AB, (d) i n h e c ro s - se ct io na l a re a o f p or ti o AB.
20-mm diameter
mm
p'
Fig. P2.61
I2mm
Fig. P2_62
25mm
ne
he
od
ci
du
y, an
lfi-mm diameter
n'
of th material
0.29, determine !Lm. Fig. P2.63
Fig_ P 2 _ 6 4
iO h a b ee n s cr ib e
de
ne 0 ·k N e n
op ax
on
c o d -r ol le d y e l ow -b ra s 2 0 0m--l
ad
Fig. P2.65
99
10
S tr es s a n
S tr ai n- Ax ia l
2.66
L oa di n
ne of
ed asa
leN. K no wi n
ar ce ax al 0.33, determin (a th chang t s o u e r d ia me te r (e)
ha (b
h e c ha ng e
wal thickness.
(J"y
80 MP
Fig. P2.66
el er en Fig. P2.67
er pr
za n, av ab pe of
ch ge
es en na
nd
qu al
ue
at
of he
vessel.
in
2. t ha t r e u lt s i n n or ma l
a te d t re s e s
dO'y
0'-,
16
Ca) side AB (b side BC
e) di-
agonal AC.
Fig. P2.68 AD pr in
pl Fig. P2.69
od AD
00.36 determine (a
ha
en r em a
and ze
BC ch
(a) if t h a x a l s tr ai n
a s t h h yd ro s a ti c p re s u r ha ed
he
d. al
gt
p or ti o Be i s a pp li ed , (b) if th tota length
2]1
Problems
h e hypothenuses Fig. 2.54 whic represen respectively an e m be tion, (b) he va es of or nd es
101
axial strain e., by (a) c om pa ri n
Fig. 1040, a n
he
en
0"1
(T.n
p la t ABeD 0"0
.€,.
an
by
(b) th rati
Poisson'
0.
ratio, determin
no ng (a) t h e qu ir e
ny ua on ys al co ec on or am e, d in a em nt he pr en p er pe nd ic u a r t o t h o ng it ud in a a x r em ai n p la n E,.,
and
Ey
m ag n t ud e of
O'O/E,.
2.73
0""
nd af de and "x
o ke '
2.72 T h h om og en eo u the e la s
(T
ve
o cc u
ve o in t P la n ct ns a n t h s am e d i t an c a pa rt . plalje strain w e c a e xp re s
/~~.--, ;?>-P»Sh~(7,
Fig. P2.72
as follows (T,
v(O",
0").)
r})O"
.r
1[ (1
ll(l
0"
v)O'yJ v)O",]
Fig. P2.73
2.74 ec on
xa
', '"
plan
stress
ho
t ha t if th
strain
Ex
and
O"
follows:
Fig. P2.74
102
Stress an Strain-Axia
Loadin
tica plat to whic 240-kN load is pp ied. Knowin ha fo used 1050 MPa, determin th deflection of th plate.
duce
L5-m
he plas ic
deflection?
bonded to plat AB an to rigi supports as shown. Knowin that forc of magnitude 24 kN causes deflection 1. nu of plat AB, determine th modulu of rigidity of th rubber used
D im en si on s
in mm
Fig. P2.75
F ig .
77
2.
2.78 vibratio isolatio unitconsistsof tw blocks of hard rubber with modulu of rigidity 19MP bonded to pl te AB an to rigi supports as shown. Denoting by th magnitud of th forc applie th plat an by th correspondin deflection determin th effectiv spring constant P I S , of th system 2.79 Anelastomeri bear ng (G 0. MPa)is us upport bridge girder as show to provid flexibilit during earthquakes. Th beam must no di kN Knowin that th maximu allowabl shearing stress is 42 kPa, determin the smallest required thickness a. (a) the smallest allowable dimension
Fig. P2.79
ea ng Pr b. 2. 2.80 F o h e e l o me r 3 0 m m , d e e rm in e h e h ea r m o u lu s an m ax im u m a te ra l o a kN ma mu
2.81 an
wo
ks
he
ea
ea e me n
es mm
er wi
'= 40 k N , d e e rm in e
ks
Problems
wi
es
ec
m o du lu s o f r ig id i AB. K no w n g h a h e m a l e s a l o wa b d im e ns io n an h e u bb e ot e x e e 1.4 M P ea mm,
2.82 wo ks gi u pp o are o nd e an 12 mm, d e e rm in e l o w ab l e t h ic k n e s MP
MP 10
mm
of th de-
er wi m o du lu s o f r ig id i MP n d ro plate AB. K no w n g h a mm h e a rg e a l o wa bl e l oa d a n h e m a e s ks es er mm,
Fig. P2.81 an
P2.82
*2.83 D e m i me mm en eg m e n t AB P r b . 2 .6 2 (a) b y c om p u i n h e d il a a t o n o f h e m a e r a l (b by s ub tr ac ti n h e o ri gi na l v ol um e o f p or ti o AB f ro m f in a v ol um e . *2.84 mm
D e e rm in e (b)
h e d i a ta t o n wn (a) h e o d is m ad e o f ma mi
ee wi 73
20
"" 0,35.
2 5. mI U 45kN
-='~~
d ia me te r
~4-5kN
~-200Jl1m~
Fig. P2.B4 Fig. P2.8S
"2.85 s um in g h a
(a) F o
h e x ia l o a o wn , e te rm in e h e a n he gh me w n (b) S o v e p a a, as 0', -70 M P a . h e o ad in g h yd ro s a ti c w i 0', 0'),
"2.86 SO mm di me er ol e e p he r o we re d n t h e o ce a p o n t w he r p re s u r S O MP a b ou t km b e lo w h e s ur fa ce ) . K n ow in ha OP 0 . 30 , d e te r m i n e (a) h e d e r ea s i n d ia m e e r o f t h s ph e re , (b) h e d e e a vo um h e h e e , (c) t h p e rc en t i nc re as e de p he re . *2.87 v ib ra t o n s o a t o n s up po r o n i s o f od ub o nd e 0 -m m - n g h o wi m od u u s o f g id i 0 .9 3 M P a D e e rm in e t h r at i R/RI mm
o f r ad iu s RI an b be r de e qu i e d v a of A.
*2.88 0mm o f i nn e r ad iu s 2 S r o b on de d a n 8 0- m m -I on g h o o w b be r de wi m od u o f g id i 1 2 M P a D e e rm in e h e e s a l w ab l or e-P ha ma be pp ed o d if d ef le c o n no ex ee 50 m.
Fig. P 2. B a n
P 2 .8 B
103
A ns we r p r~ b ~ m s w i n um b e s e n um b e r s e rn i ta li c a r n o t l is te d ,
1.1 1.2 1.3 1.7
1.9 1.10 1.13 1.14 1.15 1.16 1.18
1.19 1.20 1.21 1.23 1.24 1.27 1.28 1.29 1.30 1.31
1.33
y p a r g iv e o n h i a n
M P a . (b) 42.4 M P a . 25.2 nun; 16.5 nun. (a) 81.5 M P a . (b) 18.1 M P a .
(a) 35.7 d,
kN 62 kN. MPa. (a) 1 0 1. 6 M P a . (b) -21,7 M P a . (a) 94.7 M P a . (b) -64.4 M P a . (a) 12.73 M P a . (b) -4.77 M P a . (a 17.86 kN (b) -41.4 M P a . 5.93 M P a . 304 nun. 9.22 kN 178.6 nun. (a) 3.33 M P a . 525 nun. 275 nun. (a) 3.97 M P a . (b) 202 n un . ( e 20.9 M P a . (a) 61 M P a . (b) 29.9 M P a . (a) 80.8 M P a . (b) 127.0 M P a . (e) 203 M P a . (a) 55.4 M P a . (b) 145 M P el MP 0' 498 kPa; 489 kP al 13.95 kN (b) 620 !cPa. 0' 498 !cPa; 288 kPa. -37.1 M P a ; 17.28 M P a .
1.34 1.35
33 kN
1.38 1.39 1041 1.42 1.43 1,44
2.34. 30.8 nun. (a) 181.3 mnr', (b) 213 nu (a) 3.97. (b) :265rom'. 20.8 nun. 2.50. 2.16. 2039 kN (a) 38 nun. (b) 196 nun. 800N. 3.72 kN 3.97 kN 1.683 kN 2.06 kN (a) 2.78 kN .6
1.45 1.46 1.49 1.51 1.53 1.54 1.55 1.56 1.57
a ig h
( te ns il e a t 90°; 42.7 M P a ( c o m p re s s iv e ) .. 0·. (b) 21.3 M P (! 45°.
(a)
1.58 1.59 1.62 1.63 1.65 1.67 1.68 1.69 1.C2 1.C3
h e f o o w n g p ag e
36 kg
p ro b e m s w i
,7
60, MPa. rum. (c 25.2 rnm, (b) 227.8 M P a . 69 0 .6 9 2.42.
40.6 m ; XF
Xl
dl4
0',11
mi
27.9°. (e)
1',11'
(d) 18 nu :5 :5 22 rum. 27.5 nun. d:5 31.25 mm, 38.66", ta 0.8; BD is perpendicular
:5
(e) 17.5 mm (b)
1 .4 3
.2
mm
(d)
l.C4
An wer
Fo to Be.
:5 22
d:5
3.58 fo
(e) F.S.
c<
i s p e rp e nd ic ul a
26.6°;
line AC. 1.C5
(b (I) 490
1.31, 60°: kPa; (2) 282.90 kPa; (3 2.143; (4 5.295;
(5) 2.143. 60·: 1.31, for €X (1 49 !cPa; (2 28 kPa; (3 2.14 (4 5.30 (5 2.l4
1.C6
Fall
5.79 k N ; s tr es s i n l in k i s c ri ti ca l
~HAPTE nun. (b) 125 M P a . (b) 1 60 . M P a . (a) 4.3 nun. (b) 1.43 (a) 81.8 M P a . (a) 17.25 M P a ( b 2.82 nun. (a) 81 nun. (b) 15.28 nun. 10.70 nun.
2.1
(a)
2.2
(a) 6.91
2.3 2.4 2.6 2.8
2.9 2.10 2.12 2.15 2.16 2.19 2.20
160.0 0.603 nun. 29mm. (a) 0.794 rum. (b) 0,48 mm 16.52 mm, (b) (a) 0.308 ru (a) 0.1415 mm (b) 0 .2 1 m m (e) 113.2 M P a .
in AB; 1 .7 8 n u 2.22 2.23
t.
1.
i n AD.
164.4 kN (a) 1.222 nun. (b) 1.910 nun.
2.25
nu .J.. Ca -0.0302
2.26
92.6
kN. (b) 0.01783
nun.
2.95
2.96 2.99
(4E
2.33
2.39
Ca -116.3 MPa ; 0' -40.7 MPa . Cb -0.145 mm 101.6 kN (b) 100 MPa . 140.6 MPa . (b) 93.75 MPa . 15.00 mm, (b) 288 kN. (a) 62.8 kN +- at point A; .37.2 at point E. (b) 46.3 tun. -7 45.5 kN +- at point A; 54.5 kN +- a t p oi n E. (b) 48.8 p' -7 0.0762 nun. Cb
O 'e D 30.5 MPa ; O ' e F 38,1 MPa . tube, 67,9 M P MF (b) tube, 0,2425 m m ; r od , -0.1325 nun. 21.14 kN (b) 0.947 rom. in BE; 931 in 838 1.78 UAS
MPa , MF
2.49
2.50
2.54
2.60 2.61 2,62
2.75
steel, -8.0 MPa ; concrete, 0.2 MFa . Pa in AB; -100.0 Pa in Be. -44.4 (b) 0.500 tube, 63.0 MFa ; rod, -51.6 MFa. -116.2 M P a . (h) 0.363 mm. (a) 94.1°C. (b) 0.45027 172.8 kN (b) 0.236 ( z z ) -122.8 M P a . (b) 108.5 M F a . (al 0.205 (h) -0.00905 (b) -0.00258 (a) 0.0358 (e) 0.0003437 rom. (d) -0.00825 MFa; 0.433; 62.7 M P a .
0.0754 0."1220 (b 0.1028 m m 0.13 nun. (b) -0.0146 rom. 34.3 k N c o m pr e ss io n . (b 102.9 kN compression. 1.091 ro
kN MPa.
2.79
2.86
2.94
2.100
(a
0,0303
(b)
0',
(b
40.6 M F a ; 'y 0', .6 M P a ; (Iy -0.Of29 rom.
kN 3.75
mID.
t.
-49 MPa. (b) -3.15 10~. 100.644 2.131 FA 397 N; Pc 105.3 N. -57.7°e. (b) 0.0329 nu -+ at A; 0.0263 mID -7 2.135 a ) A O 'y l/ Lg . (b EAIL 2.C1 Prob. 2,]9: (a) 0.3112 rom (b) 0.4534 2.C3 Prob. 2.52: (a) (FAB -76.844 MPa; (Isc -23,719 MPa ; (b) 0.0529 mID. Prob. 2.57: (a) 172.835 kN (b) 0.236 nun. 2.C5 16.023 kN 18 n un ; 1 1. 72 1 k N . 2.C6 (a) -0.40083. (b) -0.10100. (c) -0,00405. (e) 110.25
H AP TE R
3,4 3.
3.10
70.52 M F a . (b) 55.8 mID. kN m. 89.7 M F a , 117.9 MPa. (b) 69.8 (b 181.4 kN m, MPa . (al 61.6 M P a . 75.5 MPa. (b) 63.7 MPa. 81.2 MPa. (b) 64.5 MPa. (c) 2 3. 0 M P a (a) 125.7
3.15 5.48 MPa. 3.45 MPa . 0; u, 0'
(b) 176.
495.9 kN (b) 572.4 M P a . (e) 0.23 (e) 0.104 2.110 Ca 0.8 rom. (b) 0.7 310 M P a . (b) 6.20 t. (e) O. e) 2.20 t. 310 MFa . (b) 6.20 -250 MPa. (b) 108 MFa. +-. -250 MPa. (b) 0.0930 +-. 2.115 Ca 30.8 MPa. (b) 0.0462 nu 2.116 (a AD, 250 MPa ; BE, 124.3 MFa. (b) 0.622 233 MFa; 8E, 250 M P a . !. (b 1.322 493°C. (b) 965"C. 2,120 (a) 0.1042 rom. (b) -65.2 MPa. (b) -6.06 MPa. 0.00788 2.12 4.67"C
kN 2.91
(c)
176. kN 0.75 kN 3.39
t.
9N (a) 262 mID. (b) 21.4 rom. 1.080 MFa ; 'T 43 kPa. 184.35 18,1 10- m~. (b) 376.7 1036.98 '. (a) 15 (b) 530 '. (e) 0.03%.
MPa. (b) 92.2 M F a . 69.5 MFa. (b) 66.7 MFa. (a) 58.7 kN. (b) 69.75 kN (a) 12 rom. (b) 62.1 kN (a) 134.7 MFa. (0) 135.3 M P a . (b) 6.88 4,69 (a) 70.7
3.17
(a)
42.0 rom; 1.473
3.20
(ti)
35.8
33.3 (b) 43.7 mID.
(b) 42.4
rom.
76
