UNIT-3 PART-A 2. Write down the expression for the … 3.pdfC.K.GOPALAKRISHNAN, AP/MECH, MAHALAKSHMI...

C.K.GOPALAKRISHNAN, AP/MECH, MAHALAKSHMI ENGINEERING COLLEGE, TRICHY

UNIT-3

PART-A

1. List the loads normally acting on a shaft?

Bending load

Torsional load or tw isting load.

Axial thrust.

2. Write down the expression for the power transmitted by a shaft.

P=2πNT/60

Where

N-speed in rpm

T-Torque in N-m

P-pow er transmitted in Watts.

3. Write the polar modulus value of a rectangle.

It is the ratio betw een the polar moment of inertia and distance of extreme layer or the

shaft from neutral axis.

Zp=(bd2 + b3)/6

4. Give torsion formula.

T/J = Gθ/l = τ/R

5. Define torsional rigidity.

Product of rigidity modulus and polar moment of inertia is called torsional rigidity

Torsional rigidity = JG

Where,

J=Polar moment of inertia

G=modulus of rigidity.

6. State any four assumptions involved in simple theory of torsion.

The material of the shaft is homogeneous, perfectly elastic and obeys Hooke’s law .

Tw ist is uniform along the length of the shaft.

The stress does not exceed the limit of proportionality.

The shaft circular in section remains circular after loading

Strain and deformations are small.

7. What do you mean by the term shear flow?

It is defined as the gradient of shear stress through the body.

8. What do you mean by strength of a shaft?

The maximum torque that a shaft can transmit is called strength of the shaft.

9. Define polar modulus or torsional section modulus of a section.

It is the ratio betw een polar moment of inertia and radius of the shaft.

Zp = J/R

Where

Zp=polar modulus

J=polar moment of inertia

R=Radius of the shaft.

10. Express the strength of a solid shaft.

Strength of a solid shaft,


T = π x ζ x d3 / 16

11. Define section modulus and what is its value for a circular section of diameter d?

It is the ratio of moment of inertia of the section and the distance of extreme layer from

the neutral axis.

12. What do you mean by torsional stiffness?

Torsional rigidity or stif fness of the shaft is defined as the product of modulus of rigidity

G and polar moment of inertia of the shaft

Torsional rigidity = GJ = T x (L/θ).

13. What do you mean by equivalent twisting moment? Give the relation.

When a shaft is subjected to tw isting and bending moment, the resultant tw isting

moment is called equivalent tw isting moment. It is denoted by Te.

Equivalent tw isting moment, Te = (T2 + M2)1/2

14. What Is composite shaft.

Sometimes a shaft is made up of composite section i.e., one type of shaft is sleeved

over other types of shaft. At the time of sleeving, the tw o shafts are joined together, that

the composite shaft behaves like a single shaft.

15. Distinguish between closed coil helical spring and open coil helical spring.

Closed coil helical spring Open coil helical spring

The spring w ires are coiled very closely,

each turn is nearly at right angles to the axis of helix.

The w ires are coiled such that there is a

gap betw een the tw o consecutive turns.

Helix angle is less than 10o Helix angle is large (>10o)

16. What are the uses of leaf spring?

They are used in railw ay w agons, coaches and road vehicles.

They are used to absorb shocks w hich give unpleasant feeling to the passenger.

17. State any two functions of springs.

To measure forces in spring balance, meters and engine indicators.

To store energy.

18. What is a leaf spring?

The laminated carriage springs are called leaf springs.

They are tw o types, namely (i) semi-elliptical type and (ii) quarter-elliptical type.

19. What is meant by stiffness of spring or spring rate?

The spring stiffness or spring constant is defined as the load required per unit deflection

of the spring.

K= W/δ

Where

W – load

δ – deflection

20. What is spring index?

The ratio of mean or pitch diameter to the diameter of w ire for the spring is called the

spring index.


PART-B

1. A hollow shaft w ith diameter ratio 3/5 is required to transmit 450 kW at 120 rpm.

The shearing stress in the shaft must not exceed 60 N/mm 2 and the tw ist in a

length of 2.5 m is not to exceed 1o. Calculate the minimum external diameter of

the shaft. Take C = 80 kN/mm 2.


2. A solid aluminium shaft 1m long and 100 mm diameter is to be replaced by hollow

steel shaft of the same length and same external diameter. The angle of tw ist per

unit torsional moment over total length is same for both the shafts. If the modulus

of rigidity of steel is thrice that of aluminium, find the inner diameter of the steel

shaft.


3. A solid circular shaft transmits 75 kW power at 200 rpm. Calculate the shaft

diameter, if the tw ist in the shaft is not to exceed 1o in 2 meters length of the shaft,

and shear stress is limited to 50 N/mm 2. Take modulus of rigidity, G = 1x105

N/mm 2.


4. A solid steel shaft is subjected to a torque of 45 kN-m. If the angle of tw ist 0.5

degrees per meter length of the shaft and the shear stress is not to be allowed to

exceed 90 MN/m 2, find (i) suitable diameter for the shaft (ii) Find maximum shear

stress, and (iii) maximum shear strain in the shaft. Take G = 80 GN/m 2.


5. Derive the torsion equation for a solid circular shaft of diameter ‘d’ and length ‘l’

which is fixed at one end and subjected to a torque of intensity ‘T’ at the free end.


6. A hollow steel shaft of diameter ratio 3/8 has to transmit 500 kW of power at 1000

rpm. If the tw ist in a length of 2 m is not to exceed 1o and the maximum shearing

stress is not to exceed 60 Mpa, find the minimum external diameter required to

satisfy the above requirements. Take G = 80 GPa.


7. A hollow steel shaft of 100 mm internal diameter and 150 mm external diameter is

to be replaced by a solid alloy shaft. If the polar modulus has the same value for

both, calculate the diameter of the latter and ratio of their torsional rigidities.


8. A hollow shaft of 55 mm external diameter and 35 mm internal diameter is

subjected to a torque of 2.5 kN-m to produce and angular tw ist of 0.6o measured

over a length of 0.3 m of shaft. Calculate the value of modulus of rigidity.

Calculate also the maximum power which could be transmitted by the shaft at

2000 rpm, if the maximum allowable shearing stress is 70 Mn/mm 2.


9. A steel shaft of diameter 200 mm runs at 300 rpm. The steel shaft has a 30 mm

thick bronze bushing shrunk over its entire length of 8 m. If the maximum

shearing stress in the steel shaft is not to exceed 12 MPa. Take Gsteel = 84 GPa,

Gbronze = 42 GPa. Determine (i) Torsional rigidity of the shaft, (ii) Power of the

engine.


10. A bar of magnesium alloy 28 mm in diameter was tested on a guage length of 25

cm in tension and in torsion. A tensile load of 5 tonnes produced an extension of

0.4 mm and a torque of 1250 kg-cm produced as twist of 1.51 degrees. Determine

the (i) Young’s modulus, (ii) Modulus of rigidity, (iii) Bulk modulus, and (iv)

Poisson’s ratio for the material under test.


11. A hollow steel shaft 10 cm external diameter and 5 cm internal diameter transmits

800 kW at 5000 rpm and is subjected to an end thrust of 40000 N. Find the

bending moment hat be safely applied to the shaft if the greater principal stress is

not to exceed 100 N/mm 2.


12. Two shafts of the same material and of same lengths are subjected to a same

torque, if the first shaft is of a solid circular section and the second shaft is of

hollow circular section, whose internal diameter is 2/3 of the outside diameter and

the maximum shear stress developed in each shaft is the same, compare the

weights of the shafts.


13. Find the angle of tw ist per metre length of a hollow shaft of 100 mm external

diameter and 60 mm internal diameter, if the shear stress is not to exceed 35 MPa.

Take modulus of rigidity G = 85 GPa.


14. What do you mean by strength of the shaft? Compare the strength of solid and

hollow circular shaft.


15. Find the diameter of a solid shaft to transmit 90 kW at 160 rpm, such that the

shear stress is limited to 60 N/mm 2. The maximum torque is likely to exceed the

mean torque by 20 %. Also find the permissible length of the shaft, if the tw ist is

not to exceed 1o over the entire length. Take rigidity modulus as 0.8 x 105 N/mm 2.


16. Determine the dimensions of a hollow circular shaft w ith 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 MPa and the angle of tw ist to 3.8o in a length of 4 m. For the shaft

material, the modulus of rigidity is 80 GPa.


17. An open coiled helical spring of w ire diameter 12 mm, mean coil radius 84 mm,

helix angle 20 degrees carries an axial load of 480 N. Determine the shear stress

and direct stress developed at inner radius of the coil.


18. Derive a relation for deflection of a closely coiled helical spring subjected to an

axial downward load W.


19. Two coils made of the same material and 12 mm dia w ire w ith 10 coils each are

placed co-axially. If the mean diameter of the outer coil is tw ice that of the inner

coil, determine the coil sizes to support a load of 1 kN. Assume E 190 GPa, µ = 0.3

and ζ = 120 MPa. The inner and outer spring coil radius can be taken as 42.8 mm

and 85.6 mm, determine the resultant deflection.


20. Derive an expression for deflection, bending stress and shear stress induced an

open coiled helical spring subjected to an axial load ‘W’.


21. A close-coiled helical spring has a stiffness of 12 N/mm. Its length when fully

compressed, with adjacent coils touching each other is 400 mm. Taking modulus

of rigidity of the spring material as 80 GPa, determine the wire diameter and mean

coil diameter if their ratio is 0.1. Find the maximum load that can be applied

before the spring becomes solid i.e., adjacent coils touch, if the gap between any

two adjacent coils is 2 mm. What is the corresponding maximum shear stress in

the spring?


22. A close-coiled helical spring is made of a round steel w ire. It carries an axial load

of 150 N and is to just get over a rod of 36 mm. The deflection in the spring is not

to exceed 26 mm. The maximum allowable shearing stress developed in the

spring wire is 200 N/mm2 and G = 80,000 N/mm2. Find the mean coil diameter,

w ire diameter and number of turns.


23. A close coiled helical spring of 100 mm mean diameter is made of 10 mm diameter

ro0d and has 20 turns. The spring carries an axial load of 200 N. Determine the

shearing stress. Taking the value of modulus of rigidity as 84x109 N/m 2, determine

the deflection when carrying this load. Also calculate the stiffness of the spring

and frequency of free vibrations for a mass hanging from it.


24. A close-coiled helical spring is made of a round steel w ire. It carries an axial load

of 150 N and is to just get over a rod of 36 mm. The deflection in the spring is not

to exceed 25 mm. The maximum allowable shearing stress developed in the

spring wire is 200 N/mm 2 and G = 80,000 N/mm 2. Find the mean coil diameter, w ire

diameter and number of turns.


25. In a close-coiled helical spring, the diameter of each coil is to be 12 times the

diameter of the spring and the maximum shear stress is not to exceed 75 N/mm 2.

Maximum permissible deflection under a load of 500 N is 12 cm. Taking shear

modulus as 8 x 104 N/mm 2, determine the number of coils, diameter of the coil and

energy stored in the spring.


26. A close coiled helical spring is required to absorb 2250 joules of energy.

Determine the diameter of the w ire, 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 maximum compression of the spring is limited to 250 mm and (iii) the mean

diameter of the spring is 8 times the wire diameter. For the spring material,

rigidity modulus is 70 GPa.

UNIT-3 PART-A 2. Write down the expression for the … 3.pdfC.K.GOPALAKRISHNAN, AP/MECH, MAHALAKSHMI...

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