Tutorial Questions 4523

7/23/2019 Tutorial Questions 4523

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epar men oMechanicalEngineering &MathematicalSciences

Faculty of Technology,

Design andEnvironment

Engineering Undergraduate

U04523 Stress Analysis I

Tutorial Questions Semester 1 & 2, 2013-14

[email protected]

o u e ea er:Dr JG Broughton


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Department of Mechanical Engineering & Mathematical Sciences Page 2of 29

Topic 1: Bending Moments and Shear Force Diagrams

For the following beams draw the bending moment and shear force diagrams stating the maximum

bending moment and shear force.

Figure 1

Figure 2

Figure 3


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Faculty of Technology, Design & EnvironmentOxford Brookes University____________________________________________________________________________


Figure 4

Figure 5

In figure 5 the logger weighs 102 kg and the log is 4.878m

Figure 6


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Answers:

1. Max moment = -13kNm, Max Shear Force = -7kN

2. Max moment = 10.5kNm, Max Shear Force = 7kN

3. Max moment = -8kNm, Max Shear Force = -8kN

4. Max moment = Pa, Max Shear Force = P or2aP/b5. Max moment = 610Nm, Max Shear Force = 500N

6. Max moment = 45kNm, Max Shear Force = -65kN


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Topic 2: Stress Profiles

1. The 20mm diameter bar shown in Fig. Q1 is carried on simple supports and is subjected to lateral and

longitudinal forces. It is made from steel, for which the Young's Modulus is 200 GPa.

Determine an expression for the longitudinal stress at points in the critical cross-section, and draw the

corresponding stress profile. Ignore the stress concentrations at the point of contact of the forces.

If a strain gauge were positioned at Point A to measure the longitudinal strain, what value would be

indicated when the loads are applied?

]750x10=(MPa),1050.[ -64 yAns

2. A torsion bar is made from titanium tube having an outside diameter of 50 mm and a wall thickness of5 mm. Youngs modulus for titanium is 110 GPa; Poissions ration is 0.33.

Determine:

(a) the radial profile of the shear stress when the bar carries a torsional movement of 5000 Nm,

giving maximum and minimum values.

(b) the corresponding stress profiles for a steel torsion bar of the same dimensions if the steel has a

yield stress in shear of 400 MPa, ensuring the bar does not yield.

(c) the torsional load that can be carried by the titanium bar if the maximum shear strain is notto exceed 7000 microstrain.

(Ans. (A) 345, 276 MPa (c) 4200 Nm)

3. A cylindrical pipe having an inside diameter of 100 mm and an outside diameter of 101 mm carries a

fluid at a pressure of 50 bar.

(a) Draw the state of stress at the inner surface.

(b) What effect would a fluctuation in pressure of 5 bar have on the stress?

(Ans (a) -5, 500, 250 MPa (b) 0.5, 50, 25 MPa)

4. The bar shown in Fig. Q4 is subjected to a compressive force of 20kN acting through pins positioned

4mm above the centroidal axis. It is made from a plastic for which Young's Modulus is 20 GPa.

Determine an expression for the longitudinal stress at any point in the cross-section, and draw the

corresponding stress profile.

What values of strain will be indicated by strain gauges positioned longitudinally on the top and

bottom surfaces?[ . ( . . ) , , . , , ]Ans x y MPa MPa MPa x x 55 6 8 23 10 130 18 5 6500 10 924 103 6 6


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5. Fig. Q5 shows part of a shouldered rod made from titanium, having a tensile yield stress of 900 MPa,

an ultimate strength of 1100 MPa and a Young's Modulus of 110 GPa. It is subjected either to (a) a

tensile force of 80kN, or (b) a bending moment of 300Nm.

In each case draw the radial profile of the longitudinal stress at a section in the smaller part of the rodand 20mm from the shoulder. Superimpose on this the corresponding approximate profile at the

section where the stress is largest.

State the maximum values of the longitudinal stresses and strains and the factor of safety based on

yielding.

[ .Ans (a) 255 MPa, 512 MPa, 76.1,10x4653 6 ; (b) 382 MPa, 730 MPa, 23.1,10x6636 6 ]

6. The plate shown in Fig. Q6 is made from the same material as that used for the rod of Question 5.

(a) Determine the tensile load that will just produce yielding.

(b) Sketch the stress profile at the critical section when the yield load is applied.

[ .Ans (a) 67kN]


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Topic 3 Buckling of struts

1. Construct a critical end-load intensity against slenderness ratio graph for a range of pinned columns

made from a material having a Young's Modulus of 200 GPa and a yield stress of 300MPa. Use

slenderness ratios from 0 to 300.

2. A steel bar is 1.75m long and has a rectangular cross-section 38mm x 50mm. It is carried in ball joints

at each end and is subjected to axial compression. The modulus elasticity is 206 GPa and the yield stress

in compression is 228 MPa.

Determine:

(a) the critical buckling load

(b) the critical end-load intensity

(c) the minimum length for which Euler's equation may be used.

(Ans 151.4kN, 79.6MPa, 1.03m)

3. A structural component having a rectangular tubular cross-section 20mm x 30mm and a wall thickness

of 2mm is made from steel having a yield stress of 400MPa and a Youngs modulus of 200GPa. In

service it is clamped rigidly at one end and pinned at the other, and subjected to a compression load of

15kN along it's centroidal axis.

Calculate the maximum length if buckling is to be avoided.

Redesign the cross-section so that the load can be raised. A tube is required and the weight must not be

increased.

Calculate the load capacity of the new component.

(Ans 1.71m)


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4. A length of rolled steel channel is fixed rigidly at one end and is free at the other, and is subjected to

an axial load. It has a depth of 60mm and a flange width of 40mm. Both the web and flange have a

thickness of 10mm. The modulus of elasticity is 200 GPa and the yield stress is 280MPa.

Determine the length and load at which, under perfect conditions, buckling and yielding occur

simultaneously.(Ans 500mm, 336kN)

5. A steel strut is built up of two T-sections riveted back-to-back to form a cruciform section of overall

dimensions 150mm x 220mm. The dimensions of each T-section are 150mm x 15mm x 110mm. The

ends of the strut are rigidly secured and it's effective length is 7m. Young's modulus for the steel is 210

GPa and the yield stress is 300MPa.

Calculate the maximum safe load to give a factor of safety of 5.

Rearrange the T-sections to increase the load. Calculate this load.

(Ans 287kN)

6. Show which of the equal area cross-sectional shapes in fig Q6 is the optimum to prevent buckling in acolumn.

Fig Q6

40mm

60mm

10mm

Box:

Length 1.414m

Width 1.414m

Triangle:

Equal sides

Length 2.1491m

Circle:

Radius 0.798m

Rectangle:

Length 2m

Width 1m


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Topic 4: Shear Stresses in Beams

1. The support bracket shown in Fig. Q1 is made from cast iron, for which the longitudinal stress is to be

limited to 60 MPa and the shear stress is not to exceed 40 MPa.

Calculate the maximum load F that can be carried. Ignore the stress concentrations.

Draw profiles of the longitudinal and shear stresses at the critical cross-section, ignoring the stress

concentrations.

[ .Ans F = 25kN, MPa5.12,MPa60 ]

2. The I section beam shown in Fig. Q2 is reinforced by plates bolted to the top and bottom flanges. The

bolts are spaced at intervals of 125mm along the beam.

Calculate the largest vertical shearing force that can be carried, for (a) the unreinforced beam and

a maximum shear stress of 50 MPa, and (b) the reinforced beam if the average shear stress in the bolts is

not to exceed 90 MPa. Ignore the friction between the plates and the flanges.

[ .Ans (a) 64 kN (b) 32 kN]

3. The beam shown in Fig. Q3 is made from steel for which the longitudinal stress is not to exceed 100

MPa and the shear stress is not to exceed 40 MPa.

Calculate the maximum load F that can be carried.

Draw the profiles of longitudinal and shearing stress at the critical cross-sections, and state the

maximum values.

[ .Ans N.A. = 54.2mm, I=670 x 10-9m4, MPa27,MPa100;kN5.18F

]

4. The beam shown in Fig. Q4 was manufactured by bonding together three pieces of wood of

rectangular cross-section.

Calculate the average shear stress in each of the two joints for the regions (1), (2) and (3) of the beam

respectively.

]689,81,731)(

,825,97,869;1063.8,3.68...[

321

321

46

kPakPab

kPakPaamxImmANAns x


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Topic 5: Stress Transformations

1. For each of the three states of stress given in the table calculate:

i) normal and shear components when measured from X is 30, -20ii) principal stress components and principal directions

iii) maximum shear stress components and the associated normal stress components and their

directions

For each of the values of show that (x+ y) = (x+ y)

Illustrate the original components and all answers using cube diagrams.

The variation of stress components as changes can be visualized using the "Stress" computer

program in the laboratory.

(a) (b) (c)

x(MPa) 100 200 50

y(MPa) 50 300 -50

xy(MPa) 20 -100 50

(ANS (a) See attached graph (b) (i) 138, 362, -6.7; 276, 224, -109 MPa. (ii) 138 MPa at 31.7, 362

MPa. (iii) -112 MPa at -13,3, 250 MPa. (c) (i) 68, -68, -18; 6, -6, 70 MPa (approx) (ii)

70.7 MPa at 22.5o, -70.7 MPa (iii) -70.7 MPa at 67.5o, 0)

2. The shaft shown on Fig Q 2 has a diameter of 17.5mm and is subjected to a twisting moment

of 100 Nm.

Calculate:

(a) the shear stress in the surface, relative to the Z,

axes(b) the corresponding principal stresses and their directions.

Illustate the answers using cube diagrams.

(Ans see Fig Q 2)


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3. A cylindrical bar 20 mm in diameter is subjected to a twisting moment of 120 Nm and a

bending moment of 80 Nm.

Calculate for the point where the bending stress is largest:

(a) the normal and shear stress relative to the longitudinal and circumferential axes.(b) the corresponding principal stresses and their directions.

(c) the corresponding maximum shear stresses and the associated normal stresses.

Illustrate the answers using cube diagrams.

(Ans see Fig Q 3)

4. For each of the two states of strain given in the table, calculate:

(i) the principal strain components and the principal directions

(ii) the maximum shear strain components and the associated normal strain components and

their directions.

For each value of show that (x + y) = (x + y)

Illustrate the original components and all answers using cube diagrams.

The variation of strain components as changes can be visualized using the

"Strain" computer program in the laboratory

(a) (b)

x(microstrain) -1500 400

y(microstrain) 1000 800

xy(microstrain) 800 -1000

(ANS (a) (i) -1562 at -8.9, 1062. (ii) 2625 at 36.1, -250. (b) (i) 1139 at 34.1, 61. (ii) 1078 at 79.1,

600.)

5. An element of a rectangular grid marked on the surface of an aluminium plate is shown in Fig Q 5

(a) in the unloaded and loaded conditions. The corresponding element of a finer grid on a plastic

plate is shown in Fig Q 5 (b). Young's modulus for the aluminium is 70 GPa, and Poisson's ratio

is 0.33. The values for the plastic are 1 GPa and 0.37 respectively.

Calculate x, y, z, xy, x, y, xyand illustrate these strain and stress states on cube

diagrams. Note that there is no stress on the surface of the plates, and that the strain znormal to

the surface cannot be calculated until the stresses have been determined.

(Ans (a) 3000, -1500, -740, 3490 microstrain; 197, -40, 0, 91 MPa.

(b) 3330, 15000, -10770, 5000 microstrain; 10.3, 18.8, 0, 1.8 MPa)


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6. For each of the two states of strain given in question 4, calculate the state of stress relative to the

x,y axes and the two sets of x, yaxes. The material for (a) is a filled epoxy, for which E = 20

GPa and = 0.37. The material for (b) is aluminium for which = 72 GPa and = 0.33

ANS in MPa

x y xy 2

(a) -26.2 10.3 5.8 11.2 -27.1 19.2 -7.9

(b) 53.7 75.3 -27.1 94 35.3 29.2 64.5

7. The two sets of measurements given in the table were taken from rectangular rosettes of strain

gauges bonded to an aluminium surface, for which Young's modulus is 71 GPa and Poisson's ratio

is 0.33.

For each set of values calculate:

(i) shear strain and stress components relative to the x, y axes

(ii) principal strains and stress components and their directions relative to x

(ii) maximum shear strain and stress components and their orientation relative to x

Illustrate these strain and stress components on cube diagrams

Values of strain can be checked using the "Rec.Ros" computer program in the laboratory.

(a) (b)

x(microstrain) -500 300

45(microstrain) 1000 -1500

y (microstrain) 500 900

ANS in microstrain, MPa and degrees.

xy xy 1 2 1 2

(b) -4200 -112 2721 -49.1 -1521 177 -50 -4243 -4.1 -113

(a) 2000 53 1118 58.3 -1118 60 -60 2237 13.3 60


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61.8


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Topic 6: Yield

1. A cylindrical pressure vessel having an outside diameter of 1m is made from 10mm

thick steel plate, for which the yield stress in uniaxial tension is 270MPa.

Determine expressions for the principal stresses in the wall of the vessel, and calculatethe value of the internal pressure at which yielding can be expected to occur.

(Ans 5.4MPa Tresca, 6.2MPa von Mises)

2. A torque of 3160Nm is transmitted by a cylindrical tube having an outside diameter of

104mm and a wall thickness of 2mm. The material has a yield stress in uniaxial

tension of 245MPa.

Calculate:

(i) the maximum shear stress at the outside radius

(ii) the corresponding principal stresses

(iii) the corresponding equivalent uniaxial stress based on the Tresca and von Mises

criteria

(iv) the factor of safety based on yielding.

(Ans. 98.5MPa; 98.5MPa; 197MPa; 121MPa; 1.2, 2.0)

3. A 12mm diameter drill is used in a chuck as shown in Fig. Q3; the material has a yield

stress of 900MPa. During the drilling operation an axial force of 6.78kN and a

twisting moment of 27.2Nm act on the drill. But at the instant illustrated a horizontal

force of 68N is accidentally applied to the plate being drilled.

Calculate:

(i) the principal stresses at the point where the stress magnitude is largest

(ii) the corresponding equivalent uniaxial stress using the Tresca and von Mises

criteria

(iii) the factor of safety based on yielding.

(Ans. (i) 40MPa, -160MPa, O

(ii) 200MPa Tresca, 183MPa von Mises

(iii) 4.5, 4.9)

4. A cylindrical pressure vessel has a length of 400mm, an outside diameter of 152mm

and a wall thickness of 5mm. The material has a yield stress in uniaxial tension of

220MPa. The tube is subjected to an internal pressure of 6MPa and a twisting moment

of 7kNm.

Calculate:

(i) the principal stresses at the outside surface

(ii) the corresponding equivalent uniaxial stress using the Tresca and von Mises

criteria

(iii) the factor of safety based on yielding

(Ans. (I) 111.5MPa, 16.3MPa, O

(ii) 111.5MPa Tresca, 104.3MPa von Mises

(iii) 1.97, 2.1)


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5. A closed cylindrical pressure vessel, shown in Fig. Q5, is made of an aluminium alloy

that has a Youngs modulus of 70 GPa, a Poissons ratio of 0.33 and a yield strength of

800 MPa. The internal diameter of the vessel is 96 mm and the outside diameter

100mm. It is held in a cradle which has rigid simple supports 300 mm apart at either

end of the cylinder and a rigid simple contact at the mid point of the cylinder acting on

the top surface.

When the cylinder is filled with pressure the supports and contact of the cradle cause

the vessel to bend but do not prevent its free expansion. Any effects on the radial and

circumferental stress due to the supports, contact or closed ends of the cylinder can be

ignored.

(a)Calculate the maximum increase in diameter of the pressure vessel giventhat the maximum deflection due to bending of a simply supported beam

with a centrally applied load is

EI48

PLv

3

and the maximum force the

cradle can withstand at the supports or contact is 70kN.

(b)What internal pressure would be necessary to give the increase of diameterfound in part a.

(c)Using Von mises and Tresca find the stress at which the cylindricalpressure vessel would fail and calculate the factors of safety.


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Fig Q5

150mm

300mm

100mmmm

Fig Q5


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Block 7: Beam Deflection and Strength

1. The two beams shown in Fig.Q1 are made from aluminium tube of rectangular cross- section,

having a vertical height of 50mm, a horizontal width of 30mm and a wall thickness of 3mm. The yield

stress in tension is 200MPa; Young's modulus is 71GPa.

Determine for each beam:

i. an expression for the bending moment at every point in the beam and draw the bending

moment diagram

ii. the maximum vertical movement

iii. the maximum bending moment

iv. the maximum longitudinal stress

v. the factor of safety based on the yield stress.

Show the necessary position and orientation of a strain gauge if it is to measure the maximum

strain in the beam. What strain will be indicated when the loading is applied

(Ans. (a) ( ) . , ,( ) , ( ) . ;ii mm iii Nm iv MPa v x5 5 1000 176 114 2480 10 6

)10992;84.2)(,4.70)(,400)(,25888.0)()( 6 xvMPaivNmiiimmxatmmiib

2. A 16mm diameter rod is supported and loaded as shown in Fig.Q2(a) and Fig.Q2(b). It is

made from steel having a Youngs modulus of 208GPa.

For each beam:

i. determine an expression for the bending moment at every point in the beam

ii. draw the bending moment diagram

iii. determine an expression for the deflexion curve

iv. draw the deflexion curve and state the maximum deflexion

v. calculate the maximum longitudinal stress

vi state where a strain gauge should be positioned to measure the largest

longitudinal tensile strain

MPavmmiv

mxxxviiiNmxxMiaAns

596)(0.6)(

)(10)8.47746597()(),(60002400)()(.( 3432

)382)(75.2)(

)(10)14.124.0995746199()()(24.040006000800)()(

3343

2

MPavmmiv

mxxxxviiiNmxxxMib


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3. Each of the three beams shown in Fig Q.3 has been provided with supports imposing more

constraints on movement than the minimum necessary to achieve static equilibrium. The built

in supports prevent all lateral movements and rotations, but do not resist longitudinal

movement. Beam (a) has a simple support at the right hand end which does not move vertically.

The right hand support for beam (b) prevents a change of slope but does not exert a vertical

force.

Each beam is made from titanium, for which Youngs modulus is 106GPa and the yield stress

in 780MPa. The cross-section is square and tubular, having outside dimensions of 12mm

and a wall thickness of 1.5mm. Loading is

parallel to the sides and acts through the centroid.

For each beam:

i. calculate the support forces and moments

ii. determine an expression for the bending moment at every point in the beam and draw thebending moment diagram

iii. determine an expression for the deflexion curve; draw the curve and state the maximum value

iv. calculate the maximum longitudinal stress and the factor of safety based on the yield stress

v. state where a strain gauge should be positioned to measure the largest longitudinal strain.

(Ans.)

54.1,508)(11639.1),(67.633.34.0)(

100),(102500100)(100,1500,2500)()(

432

24

MPaivmmzatmmvmxxxviii

NmMNmxxMiiNmNNia

02.1,763)(200x33.5

),(1.067.267.26.0)(150

),(1.020002000150)(50,150,2000)()(

332

MPaivmmatmmv

mxxxviiiNmM

NmxxMiiNmNmib

)32.1,593)(100x33.1

)(1.0667.2667.64467.0)(7.116

),(1.020001000030007.116)(7.116,3000)()(

3432

2

MPaivmmatmmv

mxxxxviiiNmM

NmxxxMiiNmNic

4. The diving board shown in Fig Q4 has been designed for people upto 20 stone in mass (Weight =1246 N). The board is made out of Glass Reinforced Plastic with a Youngs Modulus of 20 GPa, a

yield strength of 80 MPa and a weight of 744.2 N. For a 20 stone person standing stationary 150

mm from the right hand end of the board find:

a) the reactions and moments acting on the board

b) the maximum deflection of the board

c) the position of maximum moment

d) the maximum stress and the factor of safety for the board.


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Fig Q3


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Fig Q4

2440 mm

610 mm

150 mm

610 mm

50 mm

Cross Section


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Topic 8: Strain Energy

1. The bar shown in Fig.Q1 is made from aluminium having a Youngs modulus of 70 GPa and is

loaded in tension along its centroidal axis.

Calculate, ignoring stress concentrations:

(a) the strain energy stored when the load is applied

(b) the corresponding maximum longitudinal stress.

(Ans. (a) 54.6J (b) 191 MPa)

2. The simple pinned structure shown in Fig.Q2 is subjected to a vertically downward force at joint

C. It is made from aluminium having a Youngs modulus of 70 GPa. Except at the joints, the

cross-sectional areas of the members are:

AB 100 mm2, AC 100 mm2, BC 200 mm2

Calculate, ignoring the changes in section at the joints:


(b) the corresponding maximum longitudinal stress and say where it occurs.

Why has a larger area been used for member BC?

(Ans. (a) 7.86J (b) 120 MPa)

3. The simple pinned structure shown in Fig.Q3 is subjected to a horizontal force at joint C. It is

made from cast iron having a Youngs modulus of 90 GPa. Except at the joints, the cross-

sectional areas of the members are: AB 250mm2, AC 500mm2,

BC 1000 mm2.

Calculate, ignoring the changes in section at the joints:


(b) the corresponding maximum longitudinal stress and say where it occurs.

(Ans. (a) 0.87 J (b) 22.4 MPa)


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4. The beam shown in Fig.Q4 is supported as a cantilever and is subjected to a vertically downward

force near the right hand end. It is made from steel having a Youngs modulus of 210 GPa.

Draw the bending moment diagram and calculate, ignoring stress concentrations:

(a) the strain energy stored when the load is applied(b) the corresponding maximum longitudinal stress, stating precisely where it occurs.

(Ans. (a) 1.41 J (b) 354 MPa)

5. The beam shown in Fig.Q5 is simply supported near its ends, and is subjected to two equal

upward forces so that the loading of the beam is symmetrical. The material is 10 mm thick epoxy

having a Youngs modulus of 3 GPa.

Draw the bending moment diagram and calculate, ignoring stress concentrations:


(b) the corresponding maximum longitudinal stress, stating precisely where it occurs.

(Ans. (a) 0.164 J (b) 6 MPa)

6. The component shown in Fig.Q6 is supported rigidly at B and subjected to a horizontal force at A.

It is made from brass tubing having an outside diameter of

36 mm and an inside diameter of 30 mm; the Youngs modulus is 110 GPa.

Draw free-body diagrams for AC and CB, and calculate, ignoring stress concentrations:


(b) the corresponding maximum longitudinal stress, stating precisely where it occurs.

(Ans. (a) 1.64 J (b) 52.5 MPa)

7. The flat bar shown in Fig.Q7 is subjected to a tensile force applied through pins. It is made from

12 mm thick titanium having a Youngs modulus of 107 GPa.

Draw a free-body diagram for the critical region of the bar, and calculate, ignoring stressconcentrations:

(a) the strain energy stored in the 250 mm length when the load is applied

(b) the corresponding maximum longitudinal stress, stating where it occurs.

(Ans. (a) 6.42 J (b) 187 MPa)

8. For each of the components of questions 1 to 7 calculate the movement in the direction of

application of the force when it is applied without impact.

(Ans.(1) 1.82 mm, (2) 2.62 mm, (3) 0.17mm, (4) 1.41 mm, (5) 1.64 mm,(6) 5.47 mm, (7) 0.32 mm)


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9. The bar of question 1 is struck by a mass of 2 kg travelling at 5 mls from the left along a line

coincident with the centroidal axis.

Calculate ignoring stress concentrations:

(a) the maximum force exerted on the bar(b) the corresponding compression of the bar

(c) the maximum stress induced.

(Ans.(a) 40.6 kN, (b) 1.26 mm, (c) 129 MPa)

10. The bar of question 1 is attached to a rigid support at its larger end so that it hangs vertically

downwards. A mass of 2 kg, concentric with the bar, slides freely 200 mm down the 20 mm

diameter region to hit a large collar attached rigidly to its lower end.


(a) the maximum force exerted on the bar

(b) the corresponding extension of the bar

(c) the maximum stress induced

(d) the maximum stress when the bar is in its final steady-state condition, and compare this

with the value calculated in (c).

(Ans. (a) 16.1 kN, (b) 0.49 mm, (c) 51.2 MPa,

(d) 62.5 k Pa; (c) = 826 (d)

11. A weight of 100 N is dropped vertically 20 mm onto joint C of the structure of question 2. It

remains in contact.

Calculate ignoring the changes in section at the joints:

(a) the maximum force applied at joint C

(b) the corresponding vertical movement of joint C

(c) the maximum stress induced, stating where it occurs

(d) the maximum stress when the structure has reached the steady-state condition, and

compare this with the value calculated in (c).

(Ans. (a) 3.13 kN, (b) 1.37 mm, (c) 62.6 MPa,

(d) 2 MPa; (c) = 31.3 (d) )

12. A weight of 20 N is dropped vertically 50 mm onto the beam of question 4 to hit at the point

indicated.

Calculate, ignoring stress concentrations:

(a) the maximum force exerted on the beam, and compare this with the weight used

(b) the corresponding vertical movement at the point of contact(c) the maximum stress induced, stating precisely where this occurs

(d) the maximum stress induced if the weight is applied suddenly but does not fall before

contact, and compare this with the stress induced by a steady-state load of 20 N.


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(Ans. (a) 1.68 kN, 85, (b) 1.19 mm, (c) 297 MPa, (d) 7.1 MPa, 2 )

13. The component of question 6 is used to stop a body having a weight of 30 N which moves

horizontally at constant speed to make contact at point A. The maximum longitudinal stress in the

component is not to exceed 80 MPa.


(a) the maximum allowable speed to the body

(b) the maximum distance travelled by the body after hitting the component at the speed

calculated in (a).

(Ans. (a) 1.58 m/s, (b) 8.3 mm)

N. Fellows


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Tutorial Questions 4523