som unit - iii 2011-2012
DESCRIPTION
SOM Lecture notesTRANSCRIPT
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SBM COLLEGE OF ENGINEERING AND TECHNOLOGY, DINDIGUL
DEPARTMENT OF MECHANICAL ENGINEERING
Sub : Strength of materials Year : IISem : IV Acc.Year : 2011-2012Faculty Name : Nandagopal.K Subject Code : 10122ME405
QUESTION BANK
UNIT – IIITORSION AND SPRINGS
1. Write an expression for the angle of twist for a hollow circular shaft with external diameter D,
internal diameter d, length l and rigidity modulus G. (Apr 2003)
𝛉 =
G
( π16 )τ (DO4 −Di4 ) l
Do
2. Define torsion & twisting moment? (Nov 2009) (Apr 2010)When a pair of forces of equal magnitude but opposite directions acts on a body, it tends to twist the
body. It is known as twisting moment.
3. What is mean by section modulus? (Nov 2003)The ratio of the moment of inertia of the cross section of a beam undergoing flexure to
the greatest distance of an element of the beam from the neutral axis.
4. What is the power transmitted by a circular shaft subjected to a torque of 700 kN-m at 110 rpm?
(Nov 2003)
P=2πNT60
watts
P=2π x110 x70000060
=8059333.33Watts
5. Write torsional equation?Torsional equation
TJ= τR
=CθL
=qr
6. State the assumptions made in theory of pure torsion.In the theory of pure torsion, the following assumptions are made.The material of the shaft is uniform throughout.The shaft is of uniform circular section throughout.The twist along the shaft is uniformStresses do not exceed the limit of proportionalityAll diameters which are straight before twist remain straight after twist
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Normal cross section of the shaft which were plane and circular before twist, remain plane and circular after twist.
7. Define polar modulus. (June 2009)Polar modulus is the ratio between the polar moment of inertia of the shaft section to the maximum
radius. It is denoted by Zp.Polar modulus, Zp=
8. Define torsional rigidity. (Apr 2004) (Apr 2010)Torsional rigidity is the torque required to produce unit angle of twist on unit length of the shaft. The
term CJ is known as torsional rigidity and it is represented by K.Torsional rigidity, K = CJ. Where C-Modulus of rigidity, J-Polar moment of inertia
9. Define strength & stiffness of shafts. (Nov 2007)Strength: The maximum torque (or) maximum power that can be transmitted by the shaft is known as
strength of shafts.
Stiffness: The product of modulus of rigidity on the polar moment of inertia is known as stiffness of shafts.
10. Write down the formula for deflection of an open coiled helical spring subjected to an axial load ‘W’ (Apr 2004)
δ=64W R3nsec αd4 [ cos2α
C+ 2sin 2α
E]
11. State the advantages of a hollow shaft over a solid circular shaft.A hollow shaft has the following advantages over a solid circular shaft.A hollow shaft has greater strength & stiffness than solid shaft of equal weightThe removal of the core from the centre of large shafts increases their reliabilityHollow shaft is lighter in weight than a shaft of equal strength
12. What is stepped shaft?Some times a shaft, made up of different lengths having different cross sectional areas is required to
transmit some torque from one pulley to another. This shaft is called as stepped shaft.
13. What is compound shaft?A shaft made up of two (or) more different materials and behaving as a single shaft is known as
compound (or) composite shaft. Total torque transmitted by a composite shaft is the sum of the torque transmitted by each individual shaft.
SPRINGS14. What is spring? (June 2006)
Spring is a device which is used to absorb energy due to resilience, by very large change in its form without permanent deformation and then release the same when required.
15. Name two important types of spring. (Nov 2009)Bending spring (Leaf Spring)Torsional spring (Helical Spring)
16. Define helical spring. Name any two important types of helical spring. (Nov 2009)Helical spring is a torsional spring and made up of a wire coiled into a helix.
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Open coiled helical springClosely coiled helical spring
17. Difference between closed coiled helical spring & open coiled helical spring. (June 2006)Sl.No: Closely coiled spring Open coiled helical spring1
2
3
4
5.
The gap between the successive turns is small.
The helix angle is about 7o to 10o
Only tensile load is carried
Helix angle is negligible
If the slope of the helix of the coil is so small that the bending effect can be neglected, then the spring is called closed –coiled spring (only torsional shear stress)
The gap between the successive turns is more.
The helix angle is more than 10o
Both tensile & compressive loads are carried.
Helix angle is considerable.
If the slope of the helix of the coil is so quite appreciable then both bending and torsional shear stress are introduced, then the spring is called open –coiled spring.
18. Define stiffness of spring. (Apr 2003)The load required to produce a unit deflection of a spring is called stiffness of a spring
Stiffness (s) = Load / Deflection
19. What is mean by spring constant (or) spring index?Spring constant is the ratio of the mean diameter of the spring to the diameter of the wire.
20. What are the uses of close coiled helical spring? (June 2006)Close coiled helical spring is used in,BrakesCycle seatingCycle standSpring balance
21. What are the uses of open coiled helical spring? (June 2006)Open coiled helical spring is used in,Shock absorbers in automobilesRailway coaches
22. What kind of stress induced when an axial load acts on a closed soiled spring & open coiled spring?In close coiled spring, shear stress is induced.In open coiled spring, bending stress and shear stress are induced.
23. The stiffness of the spring is 20N/mm and the axial deflection is 5mm. What is the axial load on the spring?
Stiffness (s) = Load / Deflection, Load = Stiffness x Deflection = 20 x 5 = 100N.
24. What is the maximum value of shear stress in a close coiled helical spring subjected to axial force W? (June 2007)
In a close coiled helical spring, Maximum Shear stress (q) =
25. What kind of stress induced when an axial load acts on a open coiled spring?The stresses induced are,
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Bending stressShear stress
26. What kind of stress induced when an axial load acts on a close coiled spring?Shear stress is induced.
27. An open coiled helical spring of mean radius of coil of 20cm and helix angle of 12o is subjected to an axial load of 10N. What is the bending moment in coil?
Bending moment (m) = WRsinα = 10 x 200 x sin120= 415.82N-mm.
28. Shaft in series:If the shafts are connected in series means each shaft transmits the same torque.
The angle of twist is the sum of the angles of twist of the two shafts θ = θ1 ± θ2
When the shafts are made by same material modulus of rigidity is same C1 = C2
+ same direction - opposite direction
29. Shaft in Parallel:Shafts are said to be parallel when the driving torque is applied at the junction of the shaft & the
resisting torque is at the other ends of the shaft.The angle of twist is same for each shaft θ1 = θ2. But the applied torque is divided between the two
shafts.
When the shafts are made by same material modulus of rigidity is same C1 = C2
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SIXTEEN MARK QUESTIONS
1. Determine the diameter of a solid shaft transmitting 300 kW at 250 rpm. The maximum shear stress
should not exceed 30 N/mm2 and the twist should not be more than one degree in a shaft length of 2 m.
G= 100 kN/mm2. (Apr 2003)
2. A solid circular shaft is subjected to a torque of 150 Nm. Find the minimum diameter required if the
allowable shear stress is 100 N/mm2 and the allowable twist is 1° per 3 m length of the shaft. C= 100
kN/mm2. (Nov 2003)
3. A solid shaft is subjected to a torque of 100 Nm. Find the necessary shaft diameter if the allowable
shear atress is 100 N/mm2 and the allowable twist is 3° per 10 diameter length of the shaft. Take C = 1 x
105 N/mm2. (Apr 2005) (Apr 2010)
4. Derive the bending formula MI
= σy= ER (Apr 2005) (Apr 2010)
5. A hollow shaft with diameter ratio 3/8 is required to transmit 500 kW at 100 rpm, the maximum torque
being 20% greater than the mean. The maximum shear stress is not to exceed 60 N/mm2 and the twist in
a length of 3 m is not to exceed 1.4°. Calculate the minimum diameters required for the shaft. C = 84
kN/mm2. (Nov 2005) (Nov 2009)
6. Calculate the power that can be transmitted at a 300 r.p.m. by a hollow steel shaft of 75 mm external
diameter and 50 mm internal diameter when the permissible shear stress for the steel is 70 N/mm 2 and
the maximum torque is 1.3 times the mean. Compare the strength of this hollow shaft with that of an
solid shaft. The same material, weight and length of both the shafts are the same. (June 2006)
7. A helical spring of circular cross-section wire 18 mm in diameter is loaded by a force of 500 N. The
mean coil diameter of the spring is 125 mm. The modulus of rigidity is 80 kN/mm 2. Determine the
maximum shear stress in the material of the spring. What number of coils must the spring have for its
deflection to be 6 mm? (June 2006)
8. A hollow steel shaft of outside diameter 75 mm is transmitting a power of 300 kW at 2000 rpm. Find
the thickness of the shaft if the maximum shear stress is not to exceed 40 N/mm2. (Nov 2006)
9. A close coiled helical spring is to have a stiffness of 1.5 N/mm of compression under a maximum load
of 60 N. The maximum shearing stress produced in the wire of the spring is 125 N/mm2. The solid
length of the spring is 50 mm. find the diameter of coil, diameter of wire and number of coils C=4.5 x
104 N/mm2. (Nov 2006)
10. A solid circular shaft transmits 75 kW power at 200 rpm. Determine the shaft diameter if the twist in
the shaft is not to exceed 1° in 2 meters length of the shaft and shear stress is limited to 50 N/mm 2.
G=100 kN/mm2. (Nov 2006) (Nov 2007) (Apr 2010)
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11. Design a close coil helical spring of stiffness 20 N/mm. The maximum shear stress in the spring is not
to exceed 80 N/mm2 under a load of 500 N. The diameter of the coil is to be 10 times the diameter of
the wire. G=84 kN/mm2. (Nov 2006)
12. A solid cylindrical shaft is to transmit 300 kN power at 100 rpm. If the shear stress is not to exceed 60
N/mm2, find its diameter. What percent saving in weight would be obtained if this shaft is replaced by a
hollow one whose internal diameter equal to 0.6 of the external diameter, the length, the material and
maximum shear stress being the same. (June 2007)
13. A closely coiled helical spring of round steel wire 10 mm in diameter having 10 complete turns with a
mean diameter of 12 cm is subjected to an axial load of 250 N. Determine (i) the deflection of the
spring, (ii) maximum shear stress in the wire and (iii) stiffness of the spring and (iv) frequency of
vibration. Take C=0.8 x 105 N/mm2. (June 2007)
14. A solid shaft is subjected to a torque of 1.6 kN-m. find the necessary diameter of the shaft, if the
allowable shear stress is 50 MPa. The allowable twist is 1° for every 20 diameters length of the shaft.
Take C = 80GPa. (Nov 2007)
15. A closed coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50 mm
mean diameter is subjected to an axial load of 150 N. Find the deflection of the spring and the
maximum shearing stress in the material. Modulus of rigidity (C) = 80 GPa. Also, find the stiffness of
the spring. (Nov 2007)
16. A Solid shaft is subjected to a torque of 100 Nm. Find the necessary shaft diameter if the allowable
shear stress is 100 N/mm2 and allowable twist is 3° per 10 diameter length of the shaft. Take C = 1 x
105 N/mm2. (June 2008) (Nov 2009)
17. Stresses at a point are px = 80 N/mm2, py = -35 N/mm2, q = 11.5 N/mm2. Determine principal planes,
principal stresses and maximum shear stress. (June 2008) (June 2009)
18. Determine the dimensions of a hollow circular shaft with a diameter ratio of 3:4 which is to transmit 60
kW at 200 rpm. The maximum shear stress in the shaft is limited to 70 GPa and the angle of twist to
3.8° in a length of 4 m. For the shaft material the modulus of rigidity is 80 GPa. (Apr 2008)
19. A close coiled helical spring is required to absorb 2500 joules of energy. Determine the diameter of the
wire, the mean coil diameter of the spring and the number of coils necessary if (i) the maximum stress
is not to exceed 400 MPa, (ii) the mean diameter of the spring is eight times the wire diameter. For the
spring material, rigidity modulus is 70 GPa. (Apr 2008)
20. A solid steel shaft has to transmit 75 kW at 200 rpm. Taking allowable shear stress at 70 N/mm2, find
suitable diameter for the shaft, if the maximum torque transmitted at each revolution exceeds the mean
by 30% (June 2009)
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21. A closely coiled helical spring made out of a 10 mm diameter steel rod has 10 complete turns, mean
diameter of coil is of 80 mm. calculate stress induced in the section the rod, the deflection under the
pull and the amount of energy stored in the spring during extension, if it is subjected to an axial pull of
200 N. Take N = 0.84 x 105 N/mm2. (June 2009)
22. A solid shaft is subjected to a torque of 45 kNm. If angle of twist is 0.5 degree per metre length of the
shaft and shear stress is not to exceed 90 MN/m2 find (i) Suitable diameter of the shaft, (ii) Final
maximum shear stress and angle of twist per metre length. Modulus of rigidity = 80 GN/m 2. (June
2009)
23. A closely coiled helical spring having 12 coils of wire diameter 16 mm and made with coil diameter
250 mm is subjected to an axial load of 300 N. Find axial deflection, strain energy stored and torsional
shear stress. Modulus of rigidity = 80 GN/m2. (June 2009)
24. Derive a relation for deflection of a closely coiled helical spring subjected to an axial downward load
W. (June 2009)
25. A quarter elliptic leaf spring 60 cm long is made of steel plates of width 10 times the thickness. The
spring is to carry a load of 3 kN and the end deflection is limited to 5 cm. The bending stress of the
plates must not exceed 3000 N/mm2. Find suitable values of the size and number of plates to be used.
Take E = 2 x 105 N/mm2. (June 2009)
26. State any four assumptions made in the theory of simple bending. (i) Derive the bending formula (June
2009) (Nov 2009)
MI
= σy= ER
27. A closed coiled helical spring is to have a stiffness of 1200 N/m in compression with a maximum load
of 60 N and maximum shearing stress of 120 N/mm2. The solid length of the spring (i.e., coils are
touching) is 50 mm. Find the diameters and number of coils. G = 40 kN/mm2. (Nov 2009)
28. Calculate the size of the shaft which will transmit 50 kW at a speed of 100 r.p.m. The twist of the shaft
in 2 m length is not to exceed 1°. The modulus of rigidity (G) for the material of the shaft is 133.3
GN/m2. Assume the twisting moment to be uniform. Also determine the maximum shear stress
developed in the shaft, while the above power is being transmitted. (Apr 2010)
29. A closely coiled helical spring made of 10 mm diameter steel wire has 15 coils of 100 mm mean
diameter. The spring is subjected to an axial load of 100N. Calculate (i) the maximum shear stress, (ii)
the deflection and (iii) stiffness of the spring. Take modulus of rigidity, C = 8.16 x 10 4 N/mm2. (Apr
2010)
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SBM COLLEGE OF ENGINEERING AND TECHNOLOGY, DINDIGUL
DEPARTMENT OF MECHANICAL ENGINEERING
Sub : Strength of materials Year : II
Sem : IV Acc.Year : 2011-2012
Faculty Name : Nandagopal.K Subject Code : 10122ME405
QUESTION BANK
UNIT – IIITORSION AND SPRINGS
TWO MARK QUESTIONS
1. Write an expression for the angle of twist for a hollow circular shaft with external diameter D, internal
diameter d, length l and rigidity modulus G. (Apr 2003)
2. Define stiffness of a helical spring and write an expression for it. (Apr 2003)
3. What is mean by section modulus? (Nov 2003)
4. What is the power transmitted by a circular shaft subjected to a torque of 700 kN-m at 110 rpm? (Nov
2003)
5. What is torsional rigidity? Also give the expression for finding power transmitted by a shaft. (Apr
2004) (June 2006)
6. Write down the formula for deflection of an open coiled helical spring subjected to an axial load ‘W’
(Apr 2004)
7. A hollow shaft bar having external diameter twice the inner diameter is used as a beam. If the bar is
subjected to a bending moment of 40 kN-m and the allowable bending stress in the beam is limited to
100 MN/m2, find the inner diameter of the bar. (Nov 2004)
8. A laminated spring 0.9 m long is made up of plates each 5 cm wide and 1 cm thick. If the bending stress
in the plate is limited to 120 N/mm2, how many plates would be required to enable the spring to carry a
central point load of 2.65 kN? (Nov 2004)
9. Calculate the maximum torque that a shaft of 125 mm diameter can transmit, if the maximum angle of
twist is 1° in a length of 1.5 m. Take C = 70 x 103 N/mm2. (Apr 2005)
10. What are the two conditions to be satisfied in the design of a circular shaft. (Nov 2005)
11. Define principal plane and principal stress. (Nov 2005)
12. Find the torque which a shaft of 50 mm diameter can transmit safely, if the allowable shear stress is 75
N/mm2 (June 2006)
13. Differentiate open coiled helical spring from the close coiled helical spring and state the type of stresses
induced in each spring due to an axial load. (June 2006)
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14. What are the uses of springs? (June 2006)
15. Write the expression for stiffness of a close coiled helical spring. (Nov 2006) (Nov 2007)
16. Find the minimum diameter of a shaft required to transmit a torque of 29820 Nm if the maximum shear
stress is not to exceed 45 N/mm2. (Nov 2006)
17. Find the power that can be transmitted by a shaft rotating at 150 rpm under a torque 400 N-m. (Nov
2006)
18. Define the stiffness of a helical spring and write an expression for it, interms of the diameter of wire,
mean radius of coil and rigidity modulus. (Nov 2006)
19. Write the expressions for the polar moment of inertia of hollow circular section. (June 2007)
20. Define proof load of springs. (June 2007)
21. How will you find maximum shear stress induced in the wire of a close-coiled helical spring carrying
an axial load? (June 2007)
22. Express the strength of a solid shaft. (Nov 2007)
23. A close coiled helical spring is to carry an axial load of 500 N. Its mean coil diameter is to be 10 times
its wire diameter. Calculate these diameters if the maximum shear stress in the material is to be 80 MPa.
(Apr 2008)
24. Define polar modulus of a section. What is the polar modulus value for a hollow circular section of 100
mm external diameter and 40 mm internal diameter. (Apr 2008) (Apr 2010)
25. Define polar modulus. (June 2009)
26. Define slenderness ratio. (June 2009)
27. Compare closed and open coiled helical springs. (June 2009)
28. Give torsion formula. (June 2009)
29. What are helical springs? Name the two important types of helical springs. (Nov 2009)
30. Define: Torsion and Torsional rigidity. (Nov 2009) (Apr 2010)
31. Distinguish between closed coil helical spring and open coil helical spring. (Apr 2010)
32. Define the stiffness of a helical spring. (Apr 2010)