First Project Examples

7/30/2019 First Project Examples

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AutomaticDesignLaboratory

The First Project

Understand the problems and define the design problem

considering characteristic of a structure.

Perform the optimization using optimization algorithm in software

such as Excel


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Calculate the compressive stressc in the circular piston rod (see

figure) when a forceP = 10 lb is applied to the brake pedal.Assume that the line of action of the forceP is parallel to the piston

rod, which has diameter 0.22 in. Also, the other dimensions shown

in the figure (2.0 in. and 9.0 in.) are measured perpendicular to the

line of action of the forceP.

Example 1


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Example 2

A long retaining wall is braced by wood shores set at an angle of

30and supported by concrete thrust blocks, as shown in the first

part of the figure. The shores are evenly spaced, 10 ft apart.

For analysis purpose, the wall and shores are idealized as shown in

the second part of the figure. Note that the base of the wall and

both ends of the shores are assumed to be pinned. The pressure of

the soil against the wall is assumed to be triangularly distributed,

and the resultant force acting on a 10-ft length of the wall is F=45

k.

If each shore has a 6 in. 6 in. square cross section, what is thecompressive stressc in the shores?


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Example 3

A tie down on the deck of a sailboat consists of a bent bar bolted at

both ends, as shown in the figure. The diameter dB of the bar is 6mm, the diameter dWof the washers is 22 mm, and the thickness t

of the fiberglass deck is 10 mm.

If the allowable shear stress in the fiberglass is 2.1, and theallowable bearing pressure between the washer and the fiberglass

is 3.8, what is the allowable load Pallowon the tie-down?


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Example 4

A torqueT0 is transmitted between two flanged shafts by means of

four -in. bolts (see figure). The diameter of the bolt circle isd= 6in.

If the allowable shear stress in the bolts is 14 ksi, what is the

maximum permissible torque? (disregard friction between the

flanges.)


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Example 5

A lifeboat hangs from two ships davits, as shown in the figure. Apin of diameter d= 0.80 in. passes through each davit and supportstwo pulleys, one on each side of the davit.

Cables attached to the lifeboat pass over the pulleys and wind

around winches that raise and lower the lifeboat. The lower parts

of the cables are vertical and the upper parts make and angle =

15 with the horizontal. The allowable tensile force in each cable is1800 lb, and the allowable shear stress in the pins is 4000 psi.

If the lifeboat weights 1500 lb, what is the maximum weight that

should be carried in the lifeboat?


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Example 6

What is the maximum possible value of the clamping force in the

jaws of the pliers shown in the figure ifa= 90 mm, b= 40 mm, andthe ultimate shear stress in the 6-mm diameter pin is 320? Whatis the maximum permissible value of the applied load P if a factor

of safety of 3.5 with respect to failure of the pin is to be

maintained?


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Example 7

The piston in an engine is attached to a connecting rodAB, which

in turn is connected to a crank armBC (see figure). The pistonslides without friction in a cylinder and is subjected to a forceP

(assumed to be constant) while moving to the right in the figure.

The connecting rod, which has cross-sectional areaA and length L,

is attached at both ends by pins. The cranks arm rotates about the

axle atCwith the pin at Bmoving in a circle of radiusR. The axle

atC, which is supported by bearings, exerts a resisting moment M

against the crank arm.

(a) Obtain a formula for the maximum permissible forcePallow

based upon an allowable compressible stressC in the connecting

rod. (b) Calculate the forcePallow for the following data: C = 150,A= 63.62 andR= 0.28L.


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Example 8

A square steel tube of length L = 6.0 m and widthb2= 250 mm is

hoisted by a crane (see figure). The tube hangs from a pin ofdiameter d that is held by the cables at pointsA andB. The cross

section is a allowable shear stress in the pin is 60, and theallowable bearing stress the pin and the tube is 90.Determine the minimum diameter of the pin in order to support

the weight of the tube. (Note: Disregard the rounded corners of the

tube when calculating its weight.)


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Example 9

A tubular post of outer diameter d2 is guyed by two cables fitted

with turnbuckles (see figure). The cables are tightened by rotatingthe turnbuckles, thus producing tension in the cables and

compression in the post. Both cables are tightened to a tensile force

of 32 k. Also, the angle between the cables and the ground is 60,and the allowable compressive stress in the post is C = 6000 psi.

If the wall thickness of the post is 0.5 in., what is the minimum

permissible value of the outer diameter d2?


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Example 10

The main cables of a suspension bridge [see part (a) of the figure] follow acurve that is nearly parabolic bridge deck, which is uniform in intensity

along the horizontal. Therefore, let us represent the central regionAOB ofone of the main cables [see part (b) of the figure] as a parabolic cablesupported at pointsA andB and carrying a uniform load of intensityqalongthe horizontal. The span of the cable isL, the sag ish, the axial rigidity isEA,and the origin of coordinates is at midspan.(a) Derive the following formula for the elongation of cableAOB shown inpart (b) of the figure:

(b) Calculate the elongation of the central span of one of the main cables ofthe Golden Gate Bridge, for which the dimensions and properties areL =4200 ft,h= 470 ft, q = 12,700 lb/ft, and E = 28,800,000 psi. The cable consistsof 27,572 parallel wires of diameter 0.196 in.Hint: Determine the tensile force T at any point n the cable from a free-bodydiagram of part of the cable: then determine the elongation of an element of

the cable of lengthds; finally, integrate along the curve of the cable to obtainan equation for the elongation .

`3

16

18 2

23

+= L

h

hEA

qL


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Example 11

Three steel cables jointly support a load of 60 kN (see figure). The

diameter of the middle cable is 20 mm and the diameter of eachouter cable is 12 mm. The tensions in the cables are adjusted so

that each cable carries one-third of the load (i.e., 20 kN). Later, the

load is increased by 40 kN to a total load of 100 kN.

(a) What percent of the total load is now carried by the middle

cable? (b) What are the stressesM and 0 in the middle and outer

cables, respectively? (Note: See table 2-1 in Section 2.2 for

properties of cables.)


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Example 12

A bumping post at the end of a track in a railway yard has a spring

constant k = 6.1 MN/m (see figure). The maximum possibledisplacement dof the end of the striking plate is 460 mm.

What is the maximum velocity that a railway car of weightW=

470 kN can have without damaging the bumping post when it

strikes it?


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Example 13

A bungee jumper having a mass of 50 kg leaps from a bridge,

braking her fall with a long elastic shock cord having axial rigidityEA = 2.1 kN (see figure).

If the jump off point is 60 m above the water, and if it is desired to

maintain a clearance of 10 m between the jumper and the water,

what length L of cord should be used?


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Example 14

Under cruising conditions the distributed load acting on the wing

of small airplane has the idealized variation shown in the figure.Calculate the shear forceV and bending momentM at the inboard

end of the wing.


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Example 15

A fiberglass pipe is hoisted by a crane using a sling, as shown in the

figure. The outer diameter of the pipe is 150 mm, its thickness is 6mm, and its weight density is 18 kN/m3. The length of the pipe isL

= 13 m and the distance between lifting points is s= 4 m.

Determine the maximum bending stress in the pipe due to its own

weight.


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Example 16

A railroad tie (or sleeper) is subjected to two rail loads, each of

magnitudeP = 36 k, acting as shown in the figure. The reactionqof the ballast is assumed to be uniformly distributed over the

length of the tie, which has cross-sectional dimensionsb= 12 in.

andh= 10 in.

Calculate the maximum bending stressmax in the tie due to the

loadsP, assuming the wheel gageL = 57 in. and the overhang

length a= 19.5 in.


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Example 17

A stile crossing a pipeline at a chemical plant is supported by two

fiberglass frames as shown in part (a) of the figure. Each frame hasa span L = 5.46 m and height h= 0.82 m [see part (b) of the figure].

The slope of the inclined members of the frame is 2 on 3. The cross

section of the frame is I shaped with width 100 mm, height 150

mm, and thickness 10 mm [see part (c) of the figure].

Determine the maximum bending stress at the midsection of the

frame due to a uniform load q= 2.8 kN/m acting on the horizontal

part of the frame.


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Example 18

A small dam of height h= 6 ft is constructed of vertical wood

beamsAB, as shown in the figure. The wood beams, which havethickness t= 2.5 in., are simply supported by horizontal steel

beams atA andB.

Construct a graph showing the maximum bending stressmax in

the wood beams versus the depthdof the water above the lower

support atB. Plot the stressmax (psi) as the ordinate and the depth

d(ft) as the abscissa. (Note: the weight density of water equals

62.4 lb/ft3.)


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Example 19

A pontoon bridge (see figure) is constructed of two wood beams,

known as balks, that span between adjacent pontoons and supportthe transverse floor beams, which are called chesses. For purposes

of design, assume that a uniform floor load of 10 acts over thechesses. (this load includes an allowance for the weights of the

chesses and balks.) Also, assume that the chesses are 2.4 m long

and that the balks are simply supported with a span of 3.6 m. The

allowable bending stress in the wood is 17.5.If the balks have a square cross section, what is their minimum

required width bmin?


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Example 20

A small balcony constructed of wood is supported by three

identical cantilever beams (see figure). Each beam has length L1=2.1 m, widthb, and height h= 4b/3. The dimensions of the balcony

floor areL1 L2, with L2= 2.5 m. The design load is 5.5 actingover the entire floor area. (This load accounts for all loads except

the weights of the cantilever beams, which have a weight density

= 5.5 kN/m3.) The allowable bending stress in the cantilevers is 15

.Assuming that the middle cantilever supports 50 % of the load and

each outer cantilever supports 25% of the load, determine the

required dimensionsbandh.


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Example 21

A horizontal shelfAD of length L = 36 in., widthb= 12 in., and

thickness t= 0.75 in. is supported by brackets atB andC [see part(a) of the figure]. The brackets are adjustable and may be placed in

any desired positions between the ends of the shelf. A uniform load

of intensityq, which includes the weight of the shelf itself, acts on

the shelf [see part (b) of the figure].

Determine the maximum permissible value of the loadq if the

allowable bending stress in the shelf is allow= 750 psi and the

position of the supports is adjusted for maximum load-carrying

capacity.


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Example 22

Water pressure acts against an inclined panel ABC that serves as a

barrier (see figure). The panel is pivoted at pointB, which is heighth

above the base, and presses against the base atA when the water level is

not too much high (note that the panel will rotate about the pin at B if the

depth d of the water exceeds a certain maximum depth dmax). The panel

has thicknesstand is inclined at an angle to horizontal. The allowable

bending stress in the panel isallow.

Derive the following formula for the minimum allowable thickness of the

panel:

(Note: To aid in deriving the formula, observe that the maximum stress in

the panel occurs when the depth of the water reaches the maximum depth

dmax. Also, consider only the effects of bending in the panel, disregard the

weight of the panel itself, and let be the weight density of water.)

( )

2

3

minsin

8

allow

ht =


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Example 23

A retaining wall 5 ft high is constructed of horizontal wood planks 3 in. thick

(actual dimension) that are supported by vertical wood piles of 12 in.

diameter (actual dimension), as shown in the figure. The lateral earth

pressure isp1= 100 lb/ft2 at the top of the wall and the top of the wall and p2

= 400 lb/ft2at the bottom.

Assuming that the allowable stress in the wood is 1200 psi, calculate the

maximum permissible spacing s of the piles.

(Hint: Observe that the spacing of the piles may be governed by the load carrying capacity of either the planks or the piles. Consider the piles to act

as cantilever beams subjected to a trapezoidal distribution of load, and

consider the planks to act as simple beams between the piles. To be on the

safe side, assume that the pressure on the bottom plank is uniform and equal

to the maximum pressure.)


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Example 24

A tall signboard is supported by two vertical beams consisting of thin-walled,

tapered circular tubes (see figure). For purposes of analysis, each beam may

be represented as a cantilever AB of lengthL = 25 ft subjected to a lateral

load P = 550 lb at the free end. The tubes have constant thicknesst= 0.375

in. and average diametersdA = 3.5 in. anddB = 10.5 in. at endsA andB,

respectively.

Because the thickness is small compared to the diameters, the moment of

inertia at any cross section may be obtained from the formula I =d3t/8 (see

Case 22, Appendix D), and therefore the section modulus may be obtained

from the formulaS=d2t/4.

At what distancex from the free end does the maximum bending stress

occur? What is the magnitudemax of the maximum bending stress? What

is the ratio of the maximum stress to the largest stressB at the support?


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Example 25

A square wood platform, 8 ft 8 ft in area, rests on masonry walls (seefigure). The deck of the platform is constructed of 2 in. nominal thickness

tongue-and-groove planks (actual thickness 1.5 in.; see Appendix F)

supported on two 8-ft long beams. The beams have 4 in. 6 in. nominaldimensions (actual dimensions 3.5 in. 5.5 in.)The planks are designed to support a uniformly distributed load w (lb/ft2)

acting over the entire top surface of the platform. The allowable bending

stress for the planks is 2400 psi and the allowable shear stress is 100 psi.

When analyzing the planks, disregard their weights and assume that their

reactions are uniformly distributed over the top surfaces of the supporting

beams.

(a) Determine the allowable platform loadw1 (lb/ft2) based upon the bending

stress in the planks. (b) Determine the allowable platform loadw2 (lb/ft2)

based upon the shear stress in the planks. (c) Which of the preceding values

becomes the allowable load wallow on the platform?

(Hints: Use care in constructing the loading diagram for the planks, noting

especially that the reactions are distributed loads instead of concentrated

loads. Also, note that the maximum shear forces occur at the inside faces of

the supporting beams.)


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Example 26

A simple log bridge in a remote area consists of two parallel logs with planks

across them (see figure). The logs are Douglas fir with average diameter 300

mm. A truck moves slowly across the bridge, which spans 2.5 m. Assume

that the weight of the truck is equally distributed between the two logs.

Because the wheelbase of the truck is greater than 2.5 m, only one set of

wheels is on the bridge at a time. Thus, the wheel load on one log is

equivalent to a concentrated load W acting at any position along the span. In

addition, the weight of one log and the planks it supports is equivalent to a

uniform load of 850 N/m acting on the log.

Determine the maximum permissible wheel loadWbased upon (a) and

allowable bending stress of 7.5, and (b) an allowable shear stress of 0.8.


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Example 27

An aluminum pole for a street light weighs 2300 N and supports an arm that

weight 330 N (see figure). The center of gravity of the arm is 1.2 m from the

axis of the pole. The outside diameter of the pole (at its base) is 225 mm and

its thickness is 18 m.

Determine the maximum tensile and compressive stressestandc,

respectively, in the pole (at its base) due to the weighs.


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Example 28

A cylindrical brick chimney of height H weightsw= 825 lb/ft of height (see

figure). The inner and outer diameters ared1= 3 ft andd2= 4 ft,

respectively. The wind pressure against the side of the chimney isp= 10

lb/ft2of projected area.

Determine the maximum heightH if there is to be no tension in the

brickwork.


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Example 29

A plain concrete wall (i.e., a wall with no steel reinforcement) rests on a

secure foundation and serves as a small dam (see figure). The height of the

wall ish= 2 m and the thickness of the wall is t= 0.3 m.

(a) Determine the maximum tensile and compressive stressestandc,

respectively, at the base of the wall when the water level reaches the top (d=

h). Assume plain concrete has weight density c= 23 kN/m3.

(b) Determine the maximum permissible depthdmaxof the water if there is to

be no tension in the concrete.


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Example 30

A temporary wood flume serving as a channel for irrigation water is shown

in the figure. The vertical boards forming the sides of the flume are sunk in

the ground, which provides a fixed support. The top of the flume is held by

tie rods that are tightened so that there is no deflection of the boards at that

point. Thus, the vertical boards may be modeled as a beamAB, supported

and loaded as shown in the last part of the figure.

Assuming that the thickness tof the boards is 1.5 in., the depthdof the water

is 40 in., and the heighth to the tie rods is 50 in., what is the maximum

bending stressin the boards? (Hint: The numerically largest bending

moment occurs at the fixed support.


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Example 31

A simple beam on a 12 ft span supports a uniform load of intensity 600 lb/ft

(see figure). The beam consists of a wood member ( 4 in. 11.5 in. in crosssection) that is reinforced by 0.25 in. thick steel plates on top and bottom.

The moduli of elasticity for the steel and wood areEs= 30 106 psi andEw= 1.5 106 psi, respectively.Calculate the maximum bending stressess in the steel plates and w in the

wood member due to the uniform load.


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Example 32

A spherical steel pressure vessel (diameter 600 mm, thickness 10 mm) is

coated with brittle lacquer that cracks when the strain exceeds 200 10-6

(see figure).

What internal pressure p will cause the lacquer to develop cracks?

(AssumeE = 205 and = 0.30.)


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Example 33

A cylinder filled with oil is under pressure from a piston, as shown in the

figure. The diameter dof the piston is 1.91 in and the compressive forceF is

3600 lb. The maximum allowable shear stressallow in the wall of the cylinder

is 6000 psi.

What is the minimum permissible thickness tminof the cylinder wall?


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Example 34

A gondola on a ski lift is supported by two bent arms, as shown in the figure.

Each arm is offset by the distanceb= 7.0 in. from the line of action of the

weight forceW. The allowable stresses in the arms are 15,000 psi in tension

and 7,500 psi in shear.

If the loaded gondola weighs 1300 lb, what is the required diameter dof the

arms?


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Example 35

A sign is supported by a pipe (see figure) having outer diameter 100 mm

and inner diameter 80 mm. The dimension of the sign are 2.0 m 0.75 m,and its lower edge is 3.2 m above the base. The wind pressure against the

sign is 1.8.Determine the maximum in-plane shear stresses due to he wind pressure

on the sign at pointsA,B, andC, located on the outer surface at the base

of the pipe.


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Example 37

The members of the truss are assumed to be pin connected. If member BD is

an A-36 steel rod of radius 2 in, determine the maximum load P that can be

supported by the truss without causing the member to buckle.

Assume that each members have a different radius.


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Example 38

The acrobat has a weight of 150 lb, and suspends himself uniformly from the

center of the high bar. Determine the maximum bending stress in the pipe

(bar) and its maximum deflection.

The pipe is made of L2 steel and has an outer diameter 1 in. and a wall

thickness of 0.125 in.


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Example 39

The A-36 steel pipe has an outer diameter of 2 in. If it is held in place by a

guywire, determine the pipes required inner diameter to the nearest 1/8 in.,

so that it can support a maximum horizontal load of P=4 kip without causing

the pipe to buckle.

Assume the ends of the pipe are pin connected.


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Example 40

The two pulleys attached to the shaft are loaded as shown. If the bearings at

A and B exert only vertical forces on the shaft, determine the required

diameter of the shaft to the nearest 1/8 in. using the maximum-shear stress

theory and maximum-distortion-energy theory.

.ksi12ksi,67 allowableallowable ==


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Example 41

The steel beam has an allowable bending stress and an

allowable shear stress of .

Determine the maximum load that can safely be supported.

MPa140allowable =

MPa90allowable =


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Example 42

The boat has a weight of 2300 lb and a center of gravity atG. If it rests on

the trailer at the smooth contactA and can be considered pinned atB,

determine the absolute maximum bending stress developed in the main strut

of the trailer.

Consider the strut to be a box-beam having the dimensions shown and

pinned atC.


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Example 43

The chair is supported by an arm that is hinged so it rotates about the

vertical axis atA.

If the load on the chair is 180 lb and the arm is a hollow tube section having

the dimensions shown, determine the maximum bending stress at section a-a.


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Example 44

Determine the smallest allowable diameter of the shaft which is subjected to

the concentrated forces.

The sleeve bearings atA andB support only vertical forces, and the

allowable bending stress is ksi.22allowable =


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Example 45

The A-36 steel posts are drilled at constant angular speed into the soil

using the rotary installer. If the post has an inner diameter of 200 mm and

an outer diameter of 225 mm, determine the relative angle of twist of endA

of the post with respect to end B when the post reaches the depth indicated.

Due to soil friction, assume the torque along the post varies linearly as

shown, and a concentrated torque of 80 kNmacts at the bit.


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Example 46

The device shown is used to mix soils in order to provide in-situ stabilization.

If the mixer is connected to an A-36 steel tubular shaft that has an inner

diameter of 3 in. and an outer diameter of 4.5 in. determine the angle of twist

of the shaft ofA relative toB and the absolute maximum shear stress in the

shaft if each mixing blade is subjected to the torques shown.


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Example 47

The steel shaft has an diameter of 1 in. and is screwed into the wall using a

wrench.

Determine the maximum shear stress in the shaft if the couple forces have a

magnitude ofF=30 lb.


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Example 48

The 50-lb lamp is supported by three steel rods connected by a ring atA.

Determine the angle of orientationOofAC such that the average normal

stress in rodAC is twice the average normal stress in rodAD.

What is the magnitude of stress in each rod? The diameter of each rod is

given in the figure.

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First Project Examples