MINISTRY OF SCIENCE AND TECHNOLOGY
TECHNICAL AND VOCATIONAL EDUCATION
SAMPLE QUESTIONS AND WORKED OUT EXAMPLES
DESIGN OF MACHINE ELEMENTS
B.Tech (First Year)
Stresses in Simple Machine Members
** A steel member has a torque of 100 N m and an axial load of 9000N applied
as shown in figure (1). What is the magnitude of ( a ) the maximum shear stress,
( b ) the maximum normal stress , (c ) the minimum normal stress ?
Ans : (a) 12.2 MPa, (b) 23.6 MPa, (c) – 14.9 MPa (compression)
2. * A short circular bar 50 mm in diameter has a couple of 565 N m and a
compressive load of 65 kN applied as shown in figure 2. Determine (a) the
maximum shear stress in the bar , (b) the maximum tensile stress in the bar, (c)
the maximum compressive stress in the bar .
Ans . (a) 28.3 MN/m 2 ,( b) 11.8 MN/m2, (c) 44.9 MN /m 2(compression)
3. * Determine the maximum shear stress in the member loaded as shown in figure3.
Ans . 13.6 MPa (shear)
4. ** An overhung crank has a load of 10 kN applied as shown in figure 4.
Determine the maximum shear stress at section AA where the diameter is 50 mm.
Ans: sx = 224 MN/m2 , τ xy = 93.7 MN/m2 ,( τ (max) = 146 MN/m2 )
10kN ⊥ to page
φ100 spur gear
5. *** The three components of the total force acting on the bevel gear are mutually
perpendicular with the 5000N force being perpendicular to the paper and acting at
the mean radius of the gear as shown in figure 5. Determine the bending moment
and the maximum shear stress at section AA.
Ans . M = 1020 Nm, τ (max) = 28.2 MN/m 2
6. ** Determine the maximum normal and maximum shear stress at section AA for
the crank shown in figure 6, when a load of 10 kN, assumed concentrated, is
applied at the center of the crank pin .Neglect the effect of transverse shear in this
problem . Ans .sx= 21.2 MN/m2 ,τ xy = 13.3 MN/m2 ,τ (max) =17 MN/m2 (shear),
sn( max) = 27.7 MN/m2
7. ** The parallel side rod of a locomotive weighs 90kg/m. The crank length OP is
375mm and the radius of driver is 0.915m. If the speed of the engine is 96.6km/hr
and the tractive effort per wheel is 45kN. Find the maximum normal and the
maximum shear stresses in the side rod due to inertia and axial loading for the
piston shown in Fig. Take into account the weight of rod. The cross section of the
side rod is 75mm x 150mm.
8. *** A crank built up from cylindrical sections by welding required a loading of
1kN to overcome the resistance when in position shown.
(a) Compute the maximum normal stress and shear stress induced in section A-A.
(b) Determine the maximum shear stress induced in part I, II, III
9. * Determine the required thickness of the steel bracket at section A-A, when
loaded as shown in the Figure below, in order to limit the tensile stress to
10. * Calculate the maximum numerical normal stress and the maximum
at section A-A in the member loaded as shown in the Figure
1. **Interference of machine parts necessitated the use of a steel member as shown in
fig 1 below .If a load of 1 kN is applied, determine the maximum tensile stress and
the maximum shear stress and indicate the location.
Ans : 24.4MN/m2, 12.2 MN/m2 both occur at point A
2. **A ring is made from a 75 mm diameter bar. The inside diameter of the ring is 100
mm. For the load shown in figure 2, calculate the maximum shear stress in the bar
,and specify its location.
Ans :33.5 MPa at point A
P = 20kN
3. ** Determine the magnitude and location of the maximum tensile stress of the
machine part loaded as shown in figure 3 above. Ans :18.7 MPa at point P
4. *An offset bar is loaded as shown in the Figure. The weight of the bar can be
neglected. What is the maximum offset (dimension X) if the allowable stress in
tension is limited to 70Mpa? Where will the maximum tensile shear stress occur.
5. An open S link is made from a 25mm rod. Determine the maximum tensile stress
and maximum shear stress.
6. ***The offset bar has forces applied as shown. The bar is 25mm x 50mm. The
effect of the two applied forces is a pure couple which causes the same bending
moment at every section of the beam. Determine the maximum tension,
compression and shear stresses, and state where each occurs
R = 90
R = 115
7. ***The centerline of the supporting beam of the under carriage of a crane is as
shown in figure 5.The beam is supported in bearings at C and D. Consider the beam
as made from a 50 mm diameter bar. (a) What are the reactions at C and D (b) How
does the bending moment at sections perpendicular to the axis of the beam vary
between A and B ? (c) Determine the worst stressed section or sections .(d) What is
the maximum stress?
Ans : (a) Reaction at C = 4.5 kN , at D = 4.5 kN,( b) Bending moment is the same at
every section from A to B ,1130 Nm, (c) From A to E and F to B (d) 112MPa
Power transmission Shafting
1. * A 0.225m diameter solid shaft is used to drive the propeller of a marine vessel.
It is necessary to reduce the weight of the shaft by 70%. What would be the
dimensions of a hollow shaft made of the same material as the solid shaft ?
2. *A hollow shaft, 500mm outside diameter and 300mm inside diameter, is
supported by two bearings 6m apart. The shaft is driven by a flexible coupling at
one end and drives a ship's propeller at 100rev/min. The maximum thrust on the
propeller is 500kN when the shaft is transmitting 6000kW. The shaft weighs
60kN. Determine the maximum shear stress in the shaft considering the weight of
the shaft and the column effect.
3. *A machine shaft turning at 600rev/min is supported on bearings 750 mm apart as
shown in figure. 15kW is supplied to the shaft through a 450 mm pulley located
250mm to the right of the right bearing. The power is transmitted from the shaft
through a 200 mm spur gear located 250 mm to the right of the left bearing. The
belt drive is at an angle of 60º above the horizontal. The pulley weights 800N to
provide some flywheel effect. The ratio of the belt tensions is 3:1. The gear has a
20º tooth form and mates with another gear located directly above the shaft. If the
shaft material selected has an ultimate strength of 500 MN/m2 and a yield point of
310MN/m2, determine the necessary diameter using Kb = 1.5 and Kt = 1.0
W = 800N
4. *A shaft 1.2m long receives 1000Nm torque from a pulley located at the center of
the shaft, as shown in Fig. A gear at the left end of the shaft transmits 600Nm of
this torque from the shaft while the remainder is transmitted through a gear
located at the right end of the shaft. Calculate the angular deflection of the left end
of the shaft with respect to the right end of the shaft if the shaft is 50mm in
diameter and is made of steel. Neglect the effect of the keyways in the calculation.
5. *A 600 mm pulley driven by a horizontal belt transmits power through a solid
steel shaft to a 250 mm pinion which drives a mating gear .The pulley weighs
1000N to provide some flywheel effect. The arrangement of elements, the belt
tension, and the components of the gear reaction on the pinion are as shown in
(a) Sketch in order the following : vertical loading , vertical bending moment,
horizontal loading, horizontal bending moment , and combined bending
(b) Determine the necessary shaft diameter using ASME stress values for
commercial shafting and fatigue factors of Kb = 2.0 and Kt = 1.5.
Ans . Mt (max)= 1050 Nm ,Mb (max) =1784 Nm , d= 71.2 mm
6. **Power is transmitted to a shaft , supported on bearings 900 mm apart , by a belt
running on a 450 mm pulley which overhangs the right bearing by 250 mm .
Power is transmitted from the shaft by a belt running on a 250 pulley located
midway between the bearings . The belt drives are at right angles to each other
and the belt tension s are 3 to 1 with the total pull on the tight side of either belt
being limited to 2400 N.
a. Draw the moment diagrams .
b. Determine the necessary size of transmission shafting (ultimate tensile
strength 670 MN/ m2 , tensile elastic limit 120 MN/ m2 ). Assume Kb =
1.5 and Kt = 1.0.
c. Calculate the torsional deflection in degrees.
7. **A steel shaft 2 m long has applied to it a 1000Nm torque by a pulley located at
the center of the shaft .A gear at the left end of the shaft applies 800Nm of torque
to the shaft while a gear located 300 mm to the left of the right end of the shaft
applies 200 Nm of torque .Calculate the angular deflection of the shaft if the shaft
is 50 mm in diameter for a length of 1.2 m from the left end of the shaft and 40
mm in diameter in the remainder of the shaft . Neglect the effect of the keyways
in the calculations.
8. **A horizontal piece of commercial shafting is supported by two bearings 1.5 m
apart .A keyed gear , 20 involute and 175 mm in diameter ,is located 400 mm to
the left of the right bearing and is driven by a gear directly behind it .A 600mm
diameter pulley is keyed to the shaft 600 mm to the right of the left bearing and
drives a pulley with a horizontal belt directly behind it . The tension ratio of the
belt is 3 to 1 with the slack side on top . The drive transmits 45 kW at 330
a. Draw moment diagrams showing values at the change points.
b. Calculate the necessary shaft diameter.
c. Calculate the angular deflection in degrees.
9. **A solid shaft and a hollow shaft are to be of equal strength in torsion .The
hollow shaft is to be 10% larger in diameter than the solid shaft. What will be the
ratio of the weight of the hollow shaft to that of the solid shaft ? Both shafts are
made of the same material.
10. **A shaft is mounted between bearings located 9.5 m apart and transmits 10,000
kW at 90 rev/min .The shaft weighs 66,220 N, has an outside diameter of 450 mm
and inside diameter of 300mm. Determine the stress induced in shaft and the
angular deflection between bearings. Do not neglect the weight of the shaft
11. **A line shaft , 5.4m long and 40mm in diameter , is rotating at 500 rev/min and
has 10kW input at one end. Six kW is taken out at a point 2.4 m from the input
end and the remaining 4kW is taken out at the opposite end. Using G = 80 GN/m2
, find the angular deflection of one end relative to the other due to this loading.
12. ** A 250mm diameter solid shaft is used to drive the propeller of a marine vessel.
It is necessary to reduce the weight of the shaft by 70 %. What would be the
dimension of a hollow shaft made of the same material as the solid shaft ?
13. **Two bearings located 900 mm apart support a section of commercial shafting A
2000N ,750 mm diameter ,20 degree involute gears is keyed to the shaft 200 mm
to the right of the right bearing . The combined weight of the sprocket and that
part of the chain weight taken by the shaft is 800N downward. Assume no tension
on the slack side of the chain . The gear receives 7 kW at 210 rev/min from a
gear located above. Four kW is taken from the shaft at the sprocket and the
remainder is taken from the shaft through a flexible coupling located 150 mm to
the left of the left bearing .Figure shows an end view of the arrangement as
observed from the right.
(a) Draw the bending moment diagrams showing values at the change points.
(b) Calculate the diameter of commercial steel shafting based upon strength.
(c) Calculate the angular deflection in degrees of the right end of the shaft with
respect to the left end of the shaft when under load, neglecting the effect of the
keyways and stiffening effect of the pulley and sprocket hubs.
14. ***Figure shows an arrangement for a motor and exciter with a pinion on the
same shaft. The pinion drives a gear with the gear directly below the pinion .The
motor develops 55 kW at 200 rev/min. The exciter absorbs 5kW, the remainder
going to the pinion. The motor and exciter are assembled to the shaft by means of
the force fit while the pinion is keyed to the shaft.
For this unit, what is the required diameter of shaft ( a constant diameter
of shaft will be used.) ? The shaft is to be made of the steel which has an ultimate
strength of 520MN/m2 and a yield point of 330MN/m2 .The pressure angle of the gear
is 20 degrees,and the stub form of tooth is to be used .Neglect stress concentration
due to force fits .
Draw all moment diagrams ,showing values at change points.Kb=1.5 and Kt = 1.5
Motor Rotor Exciter Rotor
Critical Speeds of Shaft
1. **A shaft simply supported on two bearings 500 mm apart carries a 37 Kg
flywheel 175 mm to the right of the left bearing. The static deflection curve shows
left bearing, mm
Estimate the critical speed.
Ans. 2400 rev/ min approximately
2. **A steel shaft 1m long is simply supported at the ends and has diameter 76.2 mm
over the middle 500mm of length . The remainder
of the shaft is 63.5 mm in
diameter. Masses weighing 1.335 kN each are attached at the two locations where
the diameter changes Neglecting shaft mass and using the Rayleigh-Ritz equation
, estimate the first critical speed.
Ans. δ1 = δ2 = 1.07 x10-4 m ,ωc =303 rad/s
3. **Determine the critical speed for the steel shaft shown in figure below. Neglect
Ans. 1910 rev/min.
4. * The shaft shown in figure below is to be made of stainless steel (E = 175GPa).
Determine a safe diameter to insure that the first critical speed be no less than
Ans . d= 48.3 mm
5. *For the steel shaft shown in figure below estimate the first critical speed using
the Dunkerley equation.
Ans. 1750 rev/min
6. ***Determine the critical speed of the steel shaft shown in figure below .
7. *A shaft (bare) has a critical speed of 800 rev/min .If the shaft diameter were
doubled, what would be the critical speed?
Ans. 1600 rev/min
8. *A shaft carries two equal concentrated masses in locations 1 and 2 on the shaft.
With only mass 1 present , the static deflections at 1 and 2 are 0.2mm and 0.18
mm respectively. With only mass 2 present the static deflections at 1 and 2 are
0.18 mm and 0.25 mm respectively. Estimate the first critical speed for the twomass system. Ans. 1410 rev/min (Dunkerley), 1483 rev/minm ( Rayleigh- Ritz)
9. *For the shaft described in problem 8 determine the first and second critical
speeds by the frequency equation ( Note : m1 = m2 = m , a11 =0.2/mg , a21 =
0.18/mg = a12, a22= 0.25/mg )
Ans . 1483 rev/min, 4540 rev/min
10. **It has been determined for the shaft shown in figure that the static deflections
due to shaft bending are δ1 =0.02mm, δ2 =0.08 mm, δ3 = 0.03mm . The bearing
supports have a flexibility in the vertical direction equivalent to a spring constant
k= 315 MN/m . In the horizontal direction the supports are essentially rigid.
Investigate the first mode critical speed (or speeds)
11. *The steel shaft shown below has two gears weighing 225N and 450N
respectively. Neglecting the shaft mass, determine (i) over estimated value (b)
exact value and (c) under estimated value of the critical speed..