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Unformatted text preview: :30!) min 250 mm Fig. P1.3 and P1.4 1:20” X I‘ll)“ N
Fig. 91.5 18 PROBLEMS 1.1 Two solid cylindrical rods AB and BC are welded together at B and
loaded as shown. Determine the magnitude of the force F for which the tensile
stress in rod AB is twice the magnitude of the compressive stress in rod BC. ill] k lps 1.2 In Prob. l. l. knowing that P = 40 kips. determine the average nor
mal stress at the midsection of {a} rod AB. (b) rod BC. 1.3 Two solid cylindrical rods .43 and BC are welded together at B and
loaded as shown. Knowing that the average normal streSs must not exceed
175 MPa in rod AB and 150 MPa in rod BC. determine the smallest allowable
values of a" and d2. 1.4 Two solid cylindrical rods AB and BC are welded together at B and
loaded as shown. Knowing that d, = 50 mm and d2 = 30 mm. ﬁnd the aver
age norlnal stress at the midsection of (a) rod AB. (b) rod BC. 1.5 A strain gage located at C on the surface of bone AB indicates that
the average normal stress in the bone is 3.80 MPa when the bone is subjected
to two IZODN forces as shown. Assuming the cross section of the bone at C
to be annular and knowing that its outer diameter is 25 mm, determine the in—
ner diameter of the home‘s cross section at C. 1.6 Two steel plates are to be held together by means of l6rnmdiameter
high—strength steel bolts ﬁtting snugly inside Cylindrical brass spacers. Knows
ing that the average normal stress must not exceed 200 MPa in the bolts and
130 MPa in the spacers. determine the outer diameter of the spacers that yields
the most economical and safe design. 1.7 Each of the four vertical links has an 8 X 36mm uniform rectan Problems 19
'_'.H 1 cross section and each of the four pins has a lﬁmm diameter. Determine 35 maximum value of the average normal stress in the links connecting
it) points 3 and D, (b) points C and E. 0.4 In 0.56 In Fig. P13 1.8 Knowing that the central portion of the link BD has a uniform cross
Es ’onal area of 800 mmz, determine the magnitude of the load P for which
.‘.. normal stress in that portion of ED is 50 MPa. 1.9 Knowing that the link DE is Si in. thick and l in. wide, determine the
w a] stress in the central portion of that link when (a) B = 0, (b) 3 = 90°. ‘ 1.10 Link AC has a uniform rectangular cross section 116 in. thick and
_;_in. wide. Determine the normal stress in the central portion of the link. Fig. Pi. 1‘0 1.11 The rigid bar EFG is supported by the truss system shown. Know
I':: that the member CG is a solid circular rod of 0.75in. diameter, determine
5‘. normal stress in CG. 1.12 The rigid bar EFG is supported by the truss system shown. Deter
lu ' the crosssectional area of member A5 for which the normal stress in the ii" II a I' is 15 kSi. Fig. P1.11 and PLTZ 1.17 Two wooden planks, each % in. thick and 9 in. wide, are joined by Mb'am‘ 21
dry mortise joint shown. Knowing that the wood used shears off along its ..5:_' when the average shearing stress reaches 1.20 ksi, determine the magni ii  P of the axial load that will cause the joint to fail. I)! Fig. P'l'J‘? Fig. P1.18 1.13 A load P is applied to a steel rod supported as shown by an alu
''umu plate into which a l2mmdiameter hole has been drilled. Knowing that r shearing stress must not exceed ISO MPa in the steel rod and 70 MPa in
r aluminum plate, determine the largest load P that can be applied to the rod. 1.19 The axial force in the column supporting the timber beam shown
P = 20 trips. Determine the smallest allowable length L of the bearing plate
1 the bearing stress in the timber is not to exceed 400 psi. 1.20 The load P applied to a steel rod is distributed to a timber support
5.;2. an annular washer. The diameter of the rod is 22 mm and the inner diameA Fig. pug
as of the washer is 25 mm. which is slightly larger than the diameter of the .le. Determine the smallest allowable outer diameter d of the washer. know— . that the axial normal stress in the steel rod is 35 MPa and that the average ng stress between the washer and the timber must not exceed 5 MPa. “ .
120mm . I _ 100mm Fig. P1.20 1.21 A 40kN axial load is applied to a short wooden post that is sup <
'4 u m by a concrete footing resting on undisturbed soil. Determine (a) the
. = imum bearing stress on the concrete footing, (b) the size of the footing for
 hieh the average bearing stress in the soil is I45 kPa. Flg. P121 22 Introduction—Concept of Stress Fig. P122 Fig. 91.23 1.22 An axial load P is supported by a short W8 X 40 column of cros
sectional area A = 11.7:Ir in.2 and is distributed to a concrete feundation by
square plate as shown. Knowing that the average normal stress in the colu _
must not exceed 30 ksi and that the bearing stress on the concrete foundatio'
must not exceed 3.0 ksi, determine the side a of the plate that will provide the
most economical and safe design. 1.23 A 6mmdiameter pin is used at connection C of the pedal shown.
Knowing that P = 500 N, determine (a) the average shearing stress in the pin.
(b) the nominal bearing stress in the pedal at C, (c) the nominal bearing stress
in each support bracket at C. 1.24 Knowing that a force P of magnitude 750 N is applied to the pedal
shown. determine (a) the diameter of the pin at C for which the average shear—
ing stress in the pin is 40 MPa, (b) the corresponding bearing stress in the pedal
at C, (c) the corresponding bearing stress in each support bracket at C. 1.25 A 3in.diameter steel rod AB is ﬁtted to a round hole near end C
of the wooden member CD. For the loading shown, determine (a) the maxi
mum average normal stress in the wood. ((3) the distance b for which the av
erage shearing stress is 100 psi on the surfaces indicated by the dashed lines,
(c) the average bearing stress on the wood. 1.26 Two identical linkageandhydrauliccylinder systems control the
position of the forks of a forklift truck. The load supported by the one system
shown is 1500 lb. Knowing that the thickness of member 30 is E in., deter
mine (a) the average shearing stress in the %—in.diameter pin at B, (b) the bear
ing stress at B in member 30. Fig. was 1.27 For the assembly and loading of Prob. If}, determine (a) the aver
age shearing stress in the pin at B, (b) the average bearing stress at B in mem
ber BD, (c) the average bearing stress at B in member ABC, knowing that this
member has a 10 x 50min uniform rectangular cross section. 1.28 Link AB. of width b = 50 mm and thickness r = 6 mm, is used to
support the end of a horizontal beam. Knowing that the average normal stress
in the link is —140 MPa, and that the average shearing stress in each of the
two pins is 80 MPa, determine (a) the diameter d of the pins, (b) the average
bearing stress in the link. PROBLEMS  1.29 The 1.4kip load P is supported by two wooden members of uni
form cross section that are joined by the simple glued scarf splice shown. De
tennine the normal and shearing stresses in the glued splice. P!
Fig. P129 and 91.30 .30 Two wooden members of uniform cross section are joined by the
scarf splice shown. Knowing that the maximum allowable shearing in the glued splice is 60 psi, determine (a) the largest load P that can be
_r; supported. (b) the corresponding tensile stress in the splice. " 31 Two wooden members of uniform rectangular cross section are
the simple glued scarf splice shown. Knowing that P = l 1 kN, de
tri the normal and shearing stresses in the glued splice. 'I‘wo wooden members of uniform rectangular cross section arejoined ' pie glued scarf splice shown. Knowing that the maximum allowable
ss in the glued splice is 560 kPa, determine (a) the largest load P
:1: be safely applied. (b) the corresponding shearing stress in the splice.  A centric load P is applied to the granite block shown. Knowing
ultiag maximum value of the shearing stress in the block is 2.5 ksi,
'll" ((1) the magnitude of P. (b) the orientation of the surface on which '  A 240kip load P is applied to the granite block shown. Determine
"u . maximum value of (a) the normal stress. (b) the shearing stress. Spec r.....tauon of the plane on which each of these maximum values occurs. 6 in.
Fig. P133 and 131.34 33 34 Introduction—Concept of Stress 10 mm ‘W Weld /§ Flg. P135 and P136 Fig. P137 Fig. P1.40 and P1.41 1.35 A steel pipe of 400—mm outer diameter is fabricated from
thick plate by welding along a helix that forms an angle of 20" wi :.
perpendicular to the axis of the pipe. Knowing that the maximum it.
normal and shearing stresses in the directions respectively normal e l  .
tial to the weld are a = 60 MPa and 1' = 36 MPa, determine the
of the largest axial force that can be applied to the pipe. 1.36 A steel pipe of 400—mm outer diameter is fabricated from
thick plate by welding along a helix that forms an angle of 20° with :1
perpendicular to the axis of the pipe. Knowing that a 300kN axial 1 '1;
applied to the pipe, determine the normal and shearing stresses in d'
respectively normal and tangential to the weld. ' 1.37 A steel loop ABCD of length 1.2 m and of lO—mm di
placed as shown around a 2A—mmdiameter aluminum rod AC. Cables 3
BF, each of 12min diameter. are used to apply the load Q. Knowing "
ultimate strength of the steel used for the loop and the cables is 480 .
that the ultimate strength of the aluminum used for the rod is 260 j of 3 is desired. cable SD, was designed to support the l6kN load P as shown. Knowing .:
the ultimate load for cable 30 is 100 kN, determine the factor of safety "' respect to cable failure. 1.39 Knowing that the ultimate load for cable 30 is 100 RN and that.
factor of safety of 3.2 with respect to cable failure is required, determine a.
magnitude of the largest force P that can be safely applied as shown to men
ber ABC. 1.40 The horizontal link BC is 13 in. thick, has a width w = 1.25 in.. .
is made of a steel with a 65ksi ultimate strength in tension. What is the f: .
of safety if the structure shown is designed to support a load of P = 10 kips. 1.41 The horizontal link BC is i in. thick and is made of a steel with a
65ksi ultimate strength in tension. What should be the width w of the linki
the structure shown is to be designed to support a load P = 8 kips with a factor
of safety equal to 3'? 1.49 Each of the two vertical links CF connecting the two horizontal
members AD and EG has a uniform rectangular cross section :5, in. thick an
1 in. wide, and is made of a steel with an ultimate strength in tension of
60 ksi. The pins at C and F each have a %in. diameter and are made of a
steel with an ultimate strength in shear of 25 ksi. Determine the overall factor of safety for the links CF and the pins connecting them to the horizontal
members. 1.50 Solve Prob. 1.49, assuming that the pins at C and F have been re
placed by pins with a ﬁin. diameter. 1.51 Each of the steel links AB and CD is connected to a support and
to member BCE by Lindiameter steel pins acting in single shear. Knowing
that the ultimate shearing stress is 30 ksi for the steel used in the pins and that
the ultimate normal stress is 70 ksi for the steel used in the links, determine the
allowable load P if an overall factor of safety of 3.0 is desired. (Note that the links are not reinforced around the pin holes.) 1.52 An alternative design is being considered to support member BCE
of Prob. 1.51, in which link CD will be replaced by two links, each ofl X 2in.
cross section, causing the pins at C and D to be in double shear. Assuming that
all other speciﬁcations remain unchanged, determine the allowable load P if an overall factor of safety of 3.0 is desired. 1.53 In the steel structure shown, a 6mmdiameter pin is used at C and
lO—mmdiameter pins are used at B and D. The ultimate shearing stress is
150 MPa at all connections, and the ultimate normal stress is 400 MP3 in link
BD. Knowing that a factor of safety of 3.0 is desired, determine the largest
load P that can be applied at A. Note that link ED is not reinforced around the pin holes. 1.54 Solve Prob. 1.53, assuming that the structure has been redesigned
to use lZmmdiameter pins at B and D and no other change has been made. ...
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 Fall '08
 LINDASCHADLERFEIST

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