- A steel Rod is 2,2 m long and must not strecth more than 1,2 mm when a 8,5 kN load is applied to it. Knowing that
*E*= 200 Gpa, determine (a) the smallest diameter rod which should be used, (b) the corresponding normal stress caused bya the load.__Solution__ - A
4,8-ft-long steel wire od 1/4 – in diameter steel wire is subjected to a 750 - lb
tensile load. Knowing that
*E = 29 x 10*determine (a) the elongation of the wire, (b) the corresponding normal stress.^{6}psi,__Solution__ - Two
gage marks are placed exactly 10 inches apart in a ½ -in-diameter aluminium rod
with
*E = 10,1 10*psi and an ultimate strenght of 16 ksi. Knowing that the distance between the gage marks is 10,009 in. after a load is applied, determine (a) the stress in the rod, (b) the factor of safety^{6}__Solution__ - A
control rod made of yellow brass must not strecht more than 3 mm when the
tension in the wire is 4 kN. Knowing
*that E = 105 Gpa*and that the maximum allowable normal stress is 180 Mpa, determine (a) the smallest diameter that can be selected for the rod, (b) the corresponding maximum length of the rod.__Solution__ - A
9-m length of 6-mm-diameter steel wire is to be used in a hanger. It is noted
that the wire stretches 18 mm when a tensile force P is applied. Knowing that
*E = 200 Gpa*, determine (a) the maginitude of the force P, (b) the corresponding normal stress in the wire.__Solution__ - A
4,5-ft aluminium pipe should not strecht more than 0,05 in. when it is
subjected to a tensile load. Knowing that
*E = 10,1 x 10*psi and that the allowable tensile strenght is 14 ksi., determine (a) the maximum allowable length of the pipe, (b) the required area of the pipe if the tensile load is 127,5 kips^{6}__Solution__ - A
nylon thread is subjected to a 8,5-N tension Force. Knowing
*that E = 3,3 GPa*and that the length of the thread increases by 1,1 %, determine (a) the diameter of the thread, (b) the stress in the thread.__Solution__ - A
cast-iron tube is used to support a compressive load. Knowing that
*E = 10 x 10*psi and the maximum allowable change in the length is 0,025 %, determine (a) the maximum normal stress in the tube, (b) the minimum wall thickness for a load of 1600 lb if the outside diemeter of the tube is 2,0 in^{6}__Solution__ - A
block of 10-in, length and 1,8 x 1,6 in. Cross section is to support a centric
compressive load P. The material to be used is a bronze for which
*E = 1,4 x 10*. Determine the largest load which can be applied, knowing that normal stress must not excedd 18 ksi and that the decrease in length of the block should be at most 0,12 % of its original length.^{6}psi__Solution__ - A
9-kN tensile load will be applied to a 50-m length of steel wire
*E = 200 GPa*. Detemine the smallest diameter wire which can be used, knowing that the normal stress must not excedd 150 Mpa and that the increase in the length of the wire should be at most 25 mm.__Solution__ - The
4-mm-diameter cable BC is made of a steel
*with E 200 GPa*. Knowing that maximum stress in the cable must not exceed 190 Mpa and that the elongation of the cable must not exceed 6 mm, find the maximum load P that can be applied as shown.__Solution__ - Rod
*BD*is made of steel*E = 29 x 10*^{6}*psi*and is used to brace the axially compressed member A*BC*. The maximum force that can be development in member*BD*is 0,02 P. If stress must not exceed 18 ksi and the maximum change in length of*BD*must not exceed 0,001 times the length of ABC, determine the smallest diameter rod that can be used for member*BD.*__Solution__ - A single axial load of magnitude
*P = 58 kN*is applied at end*C*of the brass rod*ABC*. Knowing that*E = 105 Gpa*, determine the diameter*d*of portion*BC*for which the deflection of point*C*will be 3 mm.__Solution__ - Both portion of the rod ABC are made of
an aluminium for which
*E = 73 Gpa*. Knowing that the diameter of portion*BC*is*d*= 20 mm, determine the largest force P that can be aplied if Ïƒ_{all }= 160 MPa and the corresponding deflection at point C is not to exceed 4 mm.__Solution__ - The specimen shown in made from a
1-in-diameter cylindrical steel rod with two 1,5-in-outer-diameter sleeves
bonded to the rod as shown. Knowing that
*E = 29 x 10*psi, determine (a) the load P so that the total deferomation is 0,002 in., (b) the corresponding deformation of the central portion BC.^{6}__Solution__ - Both portion of the rod ABC are made of
an aluminium for which E = 70 Gpa. Knowing that the magnitude of P is 4 kN,
determine (a) the value of Q so that the deflection at A is zero, (b) the
corresponding deflection of B.
__Solution__ - The rod
*ABC*is made of an aluminium for which*E = 70 Gpa*. Knowing that*P = 6 kN*and Q = 42 kN, determine the deflection of (a) point A, (b) point B.__Solution__ - The 36-mm-diameter steel rod
*ABC*and a brass Rod*CD*of the same diameter are joined at point*C*to form the 7,5-m rod*ABCD*. For the loading shown, and neglecting the weight of the rod, determine the deflection of (a) point C, (b) point D.__Solution__ - The brass tube
*AB (E = 15 x10*) has a cross-sectional area of 0,22 in^{6}^{2}and is fitted with a plug at A. The tube is attached at*B*to rigrid plate which is itself attached at*C*to the bottom of an aluminium cylinder*E = 104 x 10*with a cross-sectional area 0,40 in^{6}psi^{2}. The cylinder is then hung from a support at*D*. In order to close the cylinder, the plug must move down through 3/64 in. Determine the force P that must be applied to cylinder.__Solution__ - A 1,2-m Section of aluminium pipe of
cross-sectional area 1100 mm
^{2}rest on a fixed support at*A*. the 15-mm-diameter steel rod*BC*hangs from a rigid bar that rests on the top of the pipe at*B*. Knowing that the modulus of elasticity is 200 GPa for steel and 72 GPa for aluminium, determine the deflection of point C when a 60 kN force is applied at C.__Solution\__ - The steel
*frame E 200 GPa*shown has a diagonal brace*BD*with an area of 1920 mm^{2}. Determine the largest alllowable load P if the change in length of member*BD*is not to exceed 1,6 mm,__Solution__ - For the steel truss
*E = 200 GPa*and loading shown, determine the deformations of members*AB*and*AD*, knowing that their cross-sectional areas are 2400 mm^{2}and 1800 mm^{2}, respectively.__Solution__ - Member
*AB*and*BC*are made of steel*E = 29 x 10*psi with cross-sectional areas of 0,80 in^{6}^{2}and 0,64 in^{2}, respectively. Form the loading shown, determine the elongation of (a) member AB, (b) memebr BC.__Solution__ - Member
*AB*and*CD*are 1 1/8 –in-diameter steel rods, and members*BC*and*AD*are 2/8-in-diameter steel rods. When the tumbuckle is tightened,, the diagonal member*AC*is put in tension. Knowing that*E = 29 x 10*^{6}*psi*and*h*= 4 ft, determine the largest allowable tension in*AC*so that the deformations in member AB and CD do not exceed 0,04 in.__Solution__ - For the structure in Problem 2.24,
determine (a) the distance h so that the deformation is members
*AB, BC, CD*and*AD*are all equal to 0,04 in., (b) the corresponding tension in member*AC*__Solution__ - Member
*ABC*and*DEF*are joined with steel links*E = 200 GPa*. Each of the links in made of pair of 25 x 35-mm plates. Determine the change in length of (a) member BE, (b) member CF__Solutio__ - Each of the links
*AB*and*CD*is made of aluminium*E = 75 GPa*and has a cross-sectional area of 125 mm^{2}. Knowing that they support the rigid member BC, determine the deflection of point E.__Solution__ - Link BD is made of
*brass E = 15 x10*psi and has a cross-sectional area of 0,04 in^{6}^{2}. Link*CE*is made of aluminium*E = 10,4 x 10*psi and has a cross-sectional area of 0,05 in^{6}^{2}. Determine the maximum force P that can be applied vertically at point*A*if the deflection of A is not to exceed 0,014 in.__Solution__ - A homogeneous cable of length l and
uniform cross section is suspended from one end. (a) Denoting by
*r*the density (mass per unit volume) of the cable and by*E*its modulus of elasticity, determine the elongation of the cable due to its own weight. (b) assuming now the cable to be horizontal, determine the force that should be applied to each end of the cable to obtain the same elongation as in part a.__Solution__ - Determine the deflection of the apex A
of a homogeneous circular cone of height
*h,*density*r*, and modulus of elasticity*E*, due to its own weight.__Solution__ - The volume of a tensile specimen is
essentially constant while plastic deformation occurs, if the initial diameter
of the specimen is d
_{1}, shown that when the diameter is d, the true straisn is*ÃŽ*_{t}*=*2 in*d*._{1}/d)__Solution__ - Denoting by
*ÃŽ*the “engineering strain” in a tensile specimen, shown that the true strain is*ÃŽ*= In_{t }*(1 +**ÃŽ**).*__Solution__ - An axial force of 60 kN is applied to
the assembly shown by means of rigid end plates. Determine (a) the normal
stress in the brass shell, (by) the corresponding deformation of the assembly.
__Solutio__ - The length of the assemby decreases by
0,15 mm when an axial force applied by means of rigid end plates. Determine (
*a)*the magnitude of the applied force, (b) the corresponding stress in the steel core.__Solution__ - The 4.5-ft concrete post is reinforced
with six steel bars, each with a 1 1/8-in. diameter Knowing that E
_{s}= 29 x 10^{6}psi and E_{c }= 4,2 x 10^{6}psi, determine the normal stresses in the steel and in the concrete when a 350-kip axial centric force P is applied to the post.__Solution__ - An Axial centric force of magnitude
*P*= 450 kn is applied to the composite block shown by means of a rigid end plate. Knowing that h =10 mm, determine the normal stress in (a) the brass core, (b) the aluminium plates.__Solution__ - Form the composite block shown in
Problem 2.36, determine (a) the value of
*h*if the portion of the load carried by the aluminium plates is half the portion of the load carried by the brass core, (b) the total load if the stress in the brass is 80 Mpa.__Solution__ - For the post of problem 2.35, determine
the maximum centric force which may be applied if the allowable normal stress
is 20 ksi in the steel and 2,4 ksi in the concrete.
__Solution__ - Three steel rods
*(E = 200 Gpa)*support a 36-kN load P. Each of the rods*AB*and*CD*has a 200-mm^{2}cross-sectional area and rod*EF*has a 625-mm^{2}cross-sectional area. Determine the (a) the change in length of Rod*EF*, (b) the stress in each rod.__Solution__ - A brass bolt (E
_{b}= 15 x 10^{6}psi) with a 3/8-in. diameter is filted inside a steel tube (Et = 29 x 10^{6}psi) with a 7/8-in. outer diameter and 1/8-in wall thickness. After the nut has been fit snugly, it is tighened on quarter of a full turn. Knowing that the bolt is single-threaded with a 0,1-in. pitch, determine the normal stress (a) in the bolt, (b) in the tube.__Solution__ - Two cylindrical rods, CD made of
*steel (E = 29 x 10*and AC made of aluminium (^{6}psi)*E = 10,4 x 10*, are joined at B and restrained by rigid supports at A and D, determine (a) the reactions at A and D, (b) the defection of point C.^{6}psi)__Solution__ - A steel tub
*(E = 200 GPa)*with a 32-mm outer diameter and a 4-mm thickness is placed in a vise that adjusted so that its jaws just touch the ends of the tube without exerting any pressure on them. Two forces shown are then applied to the tube. After these forces are applied, the vise is adjusted to decrease the distance between its jaws by 0,2 mm. Determine(a) the forced exerted by the vise on the tube at A and*D*, (b) the charge in length of the portion*BC*of the tube.__Solution__ - Solve problem 2.42, assuming that after
the forces have been applied, the vise is adjusted to decrease the distance
between its jaws by 0,1 mm.
__Solution__ - Three wires are used to suspend the
plate shown. Aluminium wires are used at A and B with a diameter of 1/8 in. and
steel wire is used at C with a diameter of 1/12 in. Knowing that the allowable
stress for steel
*(E = 29 x 10*is 18 ksi, determine the maximum load P that may be applied^{6}psi)__Solution__ - The rigid Bar
*AD*is supporteed by two steel wires of 1/16 in. diameter*(E = 29 x 10*and a pin and bracket at^{6}psi)*D*. knowing that the wires were initially taught, determine (a) the additional tension in each wire when a 220-lb load P is applied at D, (b) the corresponding deflection of point D__Solution__

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