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Unformatted text preview: 2.16 The specimen shown is made from a l—in.—diameter cylindrical steel
rod with two l.5in.—outer—diameter sleeves bonded to the rod as shown. Know
ing that E = 29 X l06 psi, determine (a) the load P so that the total deforma—
tion is 0.002 in, (b) the corresponding deformation of the central portion BC. 2.17 Two solid cylindrical rods are joined at B and loaded as shown.
Rod AB is made of steel (E = 200 GPa) and rod BC of brass (E = 105 GPa).
Determine (a) the total deformation of the composite rod ABC. (/7) the deﬂec
tion of point B. P I 30 kN —> <—3() mm
250 mm 300 mm Fig. P2.17 2.18 For the composite rod of Prob. 2.17, determine (a) the load P for
which the total deformation of the rod is —0.2 mm, (b) the corresponding de—
ﬂection of point B. 2.19 Both portions of the rod ABC are made of an aluminum for which
E = 70 GPa. Knowing that the magnitude of P is 4 kN, determine (a) the value
on so that the deﬂection at A is zero. (/7) the corresponding deﬂection of B. 2.20 The rod ABC is made of an aluminum for which E = 70 GPa.
Knowing that P = 6 kN and Q = 42 kN. determine the deﬂection of (a) point
A, (17) point B. 2.21 For the steel truss (E = 200 GPa) and loading shown. determine
the deformations of the members AB and AD. knowing that their cross—sectional
areas are 2400 mm2 and 1800 mml. respectively. 225 l< N <ill) mg» l<——4.()HI—> Fig. P221 Problems l%—in. (liamett‘r )7 
l A /
l—in. diameter 0.4 m 0.5
m 60min diameter Fig. P2.19 and P220 80 Stress and Strain—Axial Loading 2.37 The 1.5m concrete post is reinforced with six steel bars, each with ,
a 28mm diameter. Knowing that E. = 200 GPa and E(. = 25 GPa, determine me
p the normal stresses in the steel and in the concrete when a 1550kN axial
L centric force P is applied to the post. I
2.38 For the post of Prob. 2.37, determine the maximum centric force me
‘ which can be applied if the allowable normal stress is 160 MPa in the steel and If?“
i 450 '“m 18 MPa in the concrete. 110‘
;._ 2.39 Three steel rods (E = 200 GPa) support a 36—kN load P. Each of
‘ 1.5 m ~_;‘  ‘ the rods AB and CD has a 200mm2 crosssectional area and rod EF has a 625
’ mm2 cross—sectional area. Neglecting the deformation of rod BED. determine
‘ (a) the change in length of rod EF, (1)) the stress in each rod.
1
‘ 2.40 Three wires are used to suspend the plate shown. Aluminum
1 wires are used at A and B with a diameter ofﬁ in. and a steel wire is used
at C with a diameter of}: in. Knowing that the allowable stress for aluminum
(E = 10.4 X 106 psi) is 14 ksi and that the allowable stress for steel (E =
29 X 106 psi) is 18 ksi, determine the maximum load P that can be applied.
Fig p2_37 2.41 Two cylindrical rods, one of steel and the other of brass, are joined
at C and restrained by rigid supports at A and E. For the loading shown and
knowing that E‘ = 200 GPa and E,, = 105 GPa, determine (a) the reactions at
A and E, (b) the deflection of point C.
term
Dimensions in mm
, ‘ l()() 100 Semi
i‘ W) N 120 T >i matii
I C D . 1959
200 i
40—min diam. 30—min diam. 3. .
Fig. 132.39 Fig. P2.40 Fi . P2.41 I‘m ‘
9 3.6 >
2.42 Solve Prob. 2.41. assuming that rod AC is made of brass and rod m th'
CE is made of steel.
‘ a 2.43 A steel tube (E = 29 X 10‘1 psi) with a ljin. outer diameter and a
ﬁin. thickness is placed in a vise that is adjusted so that its jaws just touch the ends
‘ of the tube without exerting any pressure on them. The two forces shown are then
i ' applied to the tube. After these forces are applied. the vise is adjusted to decrease
the distance between its jaws by 0.008 in. Determine (a) the forces exerted by the
vise on the tube at A and D, (b) the change in length of the portion BC of the tube.
‘«—3 in.‘<73 in.4>‘«3 in.—>l
‘ 2
_ core ((
Fig. P2.43 Imam] 2.44 Solve Prob. 2.43, assuming that after the forces have been applied.
the vise is adjusted to increase the distance between its jaws by 0.004 in. 2.45 Links BC and DE are both made of steel (E = 29 X 10“ psi) and
are% in, wide andﬁ in. thick. Determine (u) the force in each link when a 600lb
force P is applied to the rigid member AF shown. (/7) the corresponding deﬂec
tion of point A. 4—— 4 male :3 in. ai FMJQM 2.46 The rigid bar ABCD is suspended from four identical wires. De—
termine the tension in each wire caused by the load P shown. 2.47 The aluminum shell is fully bonded to the brass core and the as—
sembly is unstressed at a temperature of l5°C. Considering only axial defor mations. determine the stress in the aluminum when the temperature reaches
195°C. 2.48 Solve Prob. 2.47. assuming that the core is made of steel (E =
200 GPa. a = 11.7 X lO"“/°C) instead of brass. 2.49 A 4ft concrete post is reinforced by four steel bars. each of
31—111. diameter. Knowing that E. = 29 X 10“ psi. a“. = 6.5 X 10’(‘/°F and E. =
3.6 X lOr7 psi and 01‘. = 5.5 X 10 "‘/°F. determine the normal stresses induced
in the steel and in the concrete by a temperature rise of 80°F. \ J. ft FMJQ“ 2.50 The brass shell (01,, = 20.9 X lO"’/°C) is fully bonded to the steel
core (ax = l 1.7 X l()"’/°F). Determine the largest allowable increase in tem—
perature if the stress in the steel core is not to exceed 55 MPa. Problems ngzm 25min Brass core
E = 105 (11)..
a : 20,9 x “Hi/‘1: Aluminum sllt'll
E = 70 CPU
a = 223.6 x 10"“/°(I i4—60 nun—>i Fig. P247
5 mm 5 null .70 mm
20 mm d
\\ \ SinilI—\ “\K 2/Q /5nun Stool core
If : 200 (Il’a Brass shell Ii = 105 (am 35" “1‘” ngzm 81 2.56 Determine the maximum load P that may be applied to the brass
bar of Prob. 2.55 if the allowable stress in the steel bars is 30 MPa and the
allowable stress in the brass bar is 25 MPa. 2.57 A brass link (E,, = [05 GPa. 01,, : 20.9 X l()"‘/°C) and a steel rod
(Es.= 200 GPa. oz‘, = ll.7 X l() (7°C.) have the dimensions shown at a teln—
perature of 20°C. The steel rod is cooled until it ﬁts freely into the link. The
temperature of the whole assembly is then raised to 45°C. Determine (a) the
ﬁnal stress in the steel rod. (1)) the final length of the steel rod. 3” null 012 I'll“ —" ‘63)” “1'” id Sll—nnn (lltllllt‘U‘I‘ Setlion .\—;\
Fig. P257 2.58 Knowing that a 0.02—in. gap exists when the temperature is 75°F.
determine (a) the temperature at which the normal stress in the aluminum bar will
be equal to —l l ksi. (/7) the corresponding exact length of the aluminum bar. (L02 in. _,H<i [1 in. Ari IS in. ’l Bronze Alnniininn .\ : 2.4 in? _\ : 2‘s in? Ia‘ : 13 X new 1‘: : nus >< new
a : 12 x It) W? a : lit) >< to "WI? Fig. P258 and P2.59 2.59 Determine (a) the compressive force in the bars shown after a tem
perature rise of 180°F. (/7) the corresponding change in length of the bronze bar. 2.60 At room temperature (20°C) a 0.5—mm gap exists between the ends
of the rods shown. At a later time when the temperature has reached 140°C.
determine (a) the normal stress in the aluminum rod. (/7) the change in length
of the aluminum rod. 0.3 nun #7 Sill) IIIlII H! lei30 Hull" ‘ :\lnlninlnn Stainless steel
.\ : goon nnnl .\ = son mm2
[C : T5 (il’tl 1’3: l9“ (il’il
a : 2:3 x In “M: (r T_:3 X In “M: Fig. P260 Problems 83 PROBLEMS 2.61 In a standard tensile test. an aluminum rod of 20—mm diameter is P
subjected to a tension force of P = 30 kN. Knowing that v = 035 and E =
70 GPa. determine (a) the elongation of the rod in a ISO—mm gage length.
(b) the change in diameter of the rod. 2.62 A 20mmdiameter rod made of an experimental plastic is sub i W l" i H
jected to a tensile force of magnitude P = 6 kN. Knowing that an elongation 150 mm ‘ Hm” ( "mum
, of 14 mm and a decrease in diameter of 0.85 mm are observed in a ISOmm
' length. determine the modulus of elasticity. the modulus of rigidity and t
Poisson‘s ratio for the material. ’_ 2.63 A 600—lb tensile load is applied to a test coupon made from ﬁin.
ﬂat steel plate (E = 29 X 10" psi and v = 0.30). Determine the resulting change 1,,
(a) in the 2—in. gage length. (/7) in the width of portion A8 of the test coupon.
(c) in the thickness of portion AB. ((1) in the crosssectional area of portion AB. Fig. P2.61 l ’4— 2.() in.——> 300 kips 6001b 600 Hi Fig. P2.63 2.64 A 6ft length of a steel pipe of lZ—in. outer diameter and %in. wall
thickness is used as a short column to carry a 300kip centric axial load. Know
ing that E = 29 X 106 psi and t' = 0.30. determine (a) the change in length of
the pipe, ([9) the change in its outer diameter. (c) the change in its wall thickness. 2.65 The change in diameter of a large steel bolt is carefully measured
as the nut is tightened. Knowing that E = 200 GPa and v = 0.29. determine
the internal force in the bolt. if the diameter is observed to decrease by 13 um. Fig. P2.64 60 mm Fig. P2.65 2.66 An aluminum plate (E = 74 GPa and v = 0.33) is subjected to a (r
centric axial load that causes a normal stress 0. Knowing that, before loading, aline of slope 2:1 is scribed on the plate. determine the slope of the line when
0 = 125 MPa. Fig. P266 99 ...
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