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Unformatted text preview: 10 l. A beam is made by bolting two identical angles to a web plate as shown in Fig. lb. The moment of inertia about the centroidal axis. for the builtup crosssection. is l,‘ =22‘5l><1()‘5 mm“. The beam must support a 200 kN load as shown in Fig. la. [f the allowable shear stress in each bolt is
280 MPa, determine 5, the maximum longitudinal spacing of the bolts. typical bolt
spacing s llS dimensions in mm 285 20 lx=229x106 mm“ Bantu]: I I 2m 2m 0
m
m
m 0
WM 0 mm Q: ——Iljtos+ss ﬁgsl/Iﬂ, .. (too 000 N)(3lf2_ ooo mmz') = [(moXaoﬂrros) .+ [( wastes) m M»
3 = 34.2 000 mm = l‘f?3N/mm_
FBM = “mar 93.” ‘3 = FB_§l'_
= [.1230 HP.)(3eTr)
. 15,ng 3 F305”. _ 31667. 3 N
" 3l667.3 N T}  W SW = 21:. mm pasez Marks
2. The bar shown in Fig. 2 is ﬁxed the left end and has three forces acting at the right end. The uniform rectangular crosssection is 50 mm x 100 mm . The x axis passes through the centroid of
the rectangular crosssection. 6 a) Find the normal stress at points A, B, and C.
4 b) Find the z coordinate of the point where the neutral axis crosses line BC. CID My £78.22 KIA/5mg? £73. D. l 500”
2—717? :0 + C?
M; + [490 “am“lﬂeéﬂﬁyeo £0”!
W=+Z5Nm . SOON 4am
/
EM; ‘0 {ﬂ 2
if? r 400+m—54yépsjso (SOON ﬂ: [0.09.535]
_ —3 2
M2 = /0 MM  5719 m
400N = .L , m 3
2:5:0 17311, F. I; {L/ﬂﬂfli‘é)‘
P+4ooééwwm =0 M = 4/9200 M 5 m4
P: keep/V 2': “715/90” 05ft.  /,042xwm
0"" i ‘ Mi}. ﬁg: 252: ,_, (/0!
X A I? =5£A€ég AMZM“ 4.16 FWD—é
= {0350 25.992 4.4.905) We
(a) A: = 0.360 25 99Aaozsj— 24w/M60)  —0 #98 Met
.( H) (" My 0259— (” ) (+4. oer») " 1?. stiﬂe/14,04
_( ..) —( )(—a 025)‘( " )(+o.a5o)= +9 5395 Mp“
05) ﬁlm/Z? 36} ﬁat(9460M a; : o..;29 Man a; _= 4369 M19:
03 = mama MP4 9" a; = @3é0)— 23.992 _ zwoéaas)
= 0.240... 13. 99? WHEN (Zie'b Z: #23:: /0.00xxp3m 
W ‘ —
313' hid : 'mgm . warm/L £5175 M7EZS¢Z73 36 47] 7:7:an mm]
3  c
Raw/35.. d.£40+a34 a 0. 66
$134 "“ W— "' 24 on 5': 5—4." = (90/5 Z: Z€/5=/&mm Marks
10 3. A uniform bar with a crosssection area of 400 mm 2 carries an axial load P as shown in Fig. 3. The state of stress on an element on the face of the bar and which is oriented 34'" from the vertical,
is given in the expanded View in Fig. 3. Use Mohr‘s circle to determine the magnitude of P. MUSI' ROTRTE ELEMENT
2(3L+D> 5: 68° 5 C = 206.1 ”3.3
(_, o) _ 2
“ (ISO Jr(:3) 12" ([5010) ml”.
R = (56.2)1 +031")
R: ISO ”Pa;
= mm
ltd/n 269 — ’36,
56.2.
6P: 34.) 0.. 0:}: "' C+R
= ISO 1*!50
= 300 MPe
0": _F’_
H Marks
4. The propane storage tank shown in Fig. 4 is formed by welding two hemispherical end caps to a
circular cylinder. The inner diameter of the cylinder is l m and the maximum internal gage pressure in the tank is 1200 kPa. If the allowable stress in the wall is 80 MPa and the allowable
stress in the weld is 50 MPa determine 3 a) the minimum allowable wall thickness, tc , for the cylinder,
3 b) the minimum allowable wall thickness , ts , for the end caps,
4 c) the minimum allowable thickness, tW , of the weld. weld weld Figye 4 @ CVL/N3EKJ #00? 57155 éﬂuﬁ'ﬁtﬁ 3
0/7“ 1% 1:" ’54 " cam/w = 00075 M 1755: ¥5mﬂ Q 5/5545 : O": Pf
2t is: éé; :: 520 rT' a/[yrgd z": ﬂ.003#5m
(ﬂaxm‘) If : 3,75M/ﬂl
@ M565 ‘ 7/7' éiVéZN/ﬂé 571555 Ar 7%: Mﬂé/WD/ﬂﬂé
521535
0:; ’3‘;— iw'; ‘53 :: [/ZoW/er600) :_ &006m
2 [50x06 lzﬁw: émml Marks 5 5. a) The three columns in Fig. 53 are each 5 m long and have the same crosssection. If column 1
has an elastic buckling load of 130 kN. what are the buckling loads for columns 2 and 3? Both ends of column 3 are constrained against rotation. As part of your answer. sketch the buckled
shape of all three columns. 1 k=o.s
G) Pa“: IT 51 P ___,_._—— ( )t
tr‘cl = ﬁrm):
1r2£I =(t300oo)(o.?9°°) " I. 5?:25 gram
2 5 m 5 [11
® Pa, 2 a" 5%15 wel
(24: 500 c5)"
= :59 15
@ per; 1.5125 mu. (D G)
5 50.0 2 (I) (2) (3) _ 
_C°‘ "" ) Pcr=15.1m Pcr‘QS‘LBkN
" 2 5"} 5‘30 Figm 5a 5 b) The 10 m tall column shown in Fig. 5b is laterally supported at its top by links in the y and z
coordinate directions. It is braced at midheight by a link in the z coordinate direction. If the
column is to carry an axial load of 100 EN with a factor of safety of 3.0 against buckling, what
are the minimum required moments of inertia I), and 1,“? Assume the column remains fully
elastic with E = 200 GPa. P ' Tr? E]: x 3:
Cr '
L61
2.
I "2 _Pc___rL 6
1T 1 E Le."
Le‘ l0!“
crosssection
z axis View y axis View /_
2. ' 2
1:: “7°90" (‘°°°°) Emit 17 = (loooooXSooo)
’ _.
1T (ZOC‘°°°) Ti:L (2.00 coo)
6 '4
5,0 7 7K to mom i.
F. 5. = 3 I2 = 3(S.O7X(OG> I), = 3(.27m‘o‘> = ts.2>uo‘ mg 3.30 xroémm‘i page 10 Marks 6. The beam shown below has a pinned support at A and a roller support at B. It is loaded with a
couple at the free end C. The bending rigidity is 2E1 between A and B and is El between B and C.
Using the moment area method, ﬁnd expressions for the following. 3 a) the rotation at end A 57 g
3 b) the rotation at end C PET)”
4 c) the deﬂection at end C. C D
”a 3y
2742 .— 3‘0
2E] . EI . DMD M0 ...
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 Spring '09
 EDDIE

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