This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering
Mechanics of Materials (CE130—II) The First Mid—term Examination (Spring 2004) Problem 1. Consider the following statically indeterminate system (Fig. 1). Find the reactions forces R1
and R2. Hint: The ﬂexibility is deﬁned as L and relationship between internal force and elongation of a two force bar is P = f A. Figure 1: A Statically Indeterminate System Problem 2
Consider the following two shaft system. Both shafts have circular cross section. Find the
maximum shear stress in the system. Assuming T3 = T and To 2 2T. The radius of shaft AB is
given as R = C; and the radius of shaft BC is given as R 2 2C. Hints: torsion formula
Tp 7d?“ 7' = 1—, for shafts with circular cross section , II) = 2 . (2)
p Figure 2: Torsion of a two—shaft system Problem 3
A planar circular threehinge arch consists of two segments as shown in Fig. Determine the
reaction forces at A and B caused by the application of a vertical force F. Problem 4
Consider a long ( 1000 meters in zdirection) concrete block with its both ends ﬁxed. The cross section of the concrete block (section in xy plane) is a 5 meter square. Suppose that in xy plane, Figure 3: A twobar truss system the block is subjected biaxial tensile stress load7 namely, anc = 5MPa and cry = 10MPa. This is a typical plane strain state. Let E 2 100MB; and Poisson’s ratio 1/ = 0.3. Find 02, cm, and cy. Hint:
The generalized Hooke’s law is e — Lava '7 _ E E E
_ _0_z ﬂ_ 2
6y — VE+E 11E
(TE 01, 02
: 711......1/4. _
‘2 E E+E Problem 5.
Consider a rectangular block with the dimension dw >< dy >< dz. Uniform shear stress, any, is acting
on the surfaces normal to (+/ A) xaxis and uniform shear stress7 Tyz, is acting on the surfaces normal to (+/*) yaxis as shown in Figure 4. Show my 2 Tym. Hint: use moment equilibrium equation
about the z—axis M2 = 0). Figure 4: Inﬁnitesimal element in pure shear 4m
" + rk +z~l H1 .
(15¢ git r Gs,‘+.'un le‘u‘; 3:: iik ,5 ._ﬁHM .
fwd“
?noH¢m 1. X
15 / L 6') i
’P $ ~ )( + 2L (27C) V X P $ L (f) H/ (R2 SYJJ'ZMI 72:2» — x
A”: H +2¥>< ﬁx ~ 47‘
A‘” = O '24? r}? = ~3—FP a») H 0 + 0'3CP='9CP
=0
3)” ' P
A AU)+ AU’) + — 4 Xszﬁl 7mb’em Z
We 4??”1‘ 4th M‘Fﬁi‘m‘vo
® ©
@ l T I 2T
/ i
2 l
@ , @
2T
Tooé’f J
I
1‘ 2T 45);?!» 2 Alia NM ' M2 T62): 3T " ‘4 y 5 L’
/
/7 / /+
/ / /
2
@337: BT'C : ,4]: :: 2T. 20 "" T g
(‘rrC‘U/a WT C3 / 17(2cf/2. 27f C ‘7’}: WNWM slum» 34m; [‘5 ?a blew 3 “Al .
' Jabboel‘f allagrmu of #154: join+ I'; ( wafe brf'k ACQBC Gré "l‘wo— n1 MmLevs )
{if PB EV srwuurl‘vr ; 1%, FE
ZF = o P r ‘5‘ €o$4f°+ ﬁg Gséfo— P z: 0 ASP; =t> => IFA=F5=NE§ m
U!
ml— ’9 7 r '3
: C'ngfklo' xix‘tf) xw  I m
= o_o7 [admin
Rosie“:
Kite a Womanf ahaand ?aw‘$
2M0? = o r‘ <4 3‘ . __ r\
Mr vii. W #7“
FT 0m am
(ET: {FT}: ...
View
Full Document
 Spring '10
 Gilman
 Force, Shear Stress, maximum shear stress, circular cross section

Click to edit the document details