Holooly Plus Logo
Holooly Plus Logo

Question 16.2: A close coiled helical spring is made by 5 mm diameter steel...

A close coiled helical spring is made by 5 mm diameter steel wire having shear strength 500 MPa. The spring has mean diameter 50 mm. A prestress of 60 MPa causes the coils to be closed under no-load condition. Calculate the no load force in the spring and the maximum load that can be applied to the spring. Also calculate the maximum extension of spring having 30 number of coils of the modulus of rigidity is 80 GPa.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

Using Eq. (16.1)

\tau =\frac{16PR}{\pi d^3} \left\lgroup1+\frac{d}{4R} \right\rgroup

For no load condition force P is given by,

60=\frac{16P\times25}{\pi\times5^3} \left\lgroup1+\frac{5}{4\times25} \right\rgroup

or,              P=\frac{60\times\pi\times125}{16\times25\times1.05} =56.1  N

The maximum load is obtained when \tau= 500 MPa as follows:

P=\frac{500\pi\times125}{16\times25\times1.05} =467.5  N

Maximum deflection,

\delta =\frac{64nPR^3}{Gd^4}

 

=\frac{64\times30\times467.5\times25^3}{80000\times5^4} =109.57  mm

Related Answered Questions

Question: 16.3

A safety valve of diameter 50 mm is to blow off at a gange pressure of 0.5 MPa. It is held by a close coiled compression spring of average diameter 70 mm and the initial compression of the spring is 20 mm. Determine the diameter of the spring wire and the number of turns if the allowable shear ...

Verified Answer:

Force required to lift the valve =p\times\f...
Question: 16.11

A leaf spring carries a maximum central load of 10 kN. It is built-up with 1.5 m long, 100 mm wide and 12 mm thick plates. Determine the number of plates and the initial dip if the permissible bending stress is 275 MPa and the modulus of elasticity is 200 GPa. ...

Verified Answer:

Number of plates and initial dip is given by Eq. (...
Question: 16.10

Repeat Example 16.9 if the smaller coil is placed inside the larger coil. ...

Verified Answer:

Stiffness of smaller spring, \frac{P_1}{\de...
Question: 16.8

A 50 N weight is dropped on a close coiled helical spring from a height of 150 mm. The spring has 10 coils of mean diameter 30 mm. If the diameter of the spring wire is 5 mm, determine the deflection and stress in the spring. Take modulus of rigidity equal to 80 GPa. ...

Verified Answer:

Work done by impact load = 50(150+\delta )[...
Question: 16.6

A close coiled helical spring has a stiffness of 4 N/mm. Its solid length is 160 mm when the adjecent coils touch each other. Determine the mean diameter of the spring and the diameter of the wire if their ratio is 10:1. Take modulus of rigidity equal to 80 GPa. If the gap between the coils is 5 ...

Verified Answer:

Stiffness,      \frac{P}{\delta } =4  N/mm[...
Question: 16.12

A laminated spring is to carry a central load of 5 kN. It is made up of 16 plates 75 mm wide, 6 mm thick. If the central dip is 40 mm and the permissible bending stress is 190 MPa, determine the length and curvature for the leaf spring. ...

Verified Answer:

Using Eq. (16.12) W=\frac{8nEbt^3\delta _0}...
Question: 16.9

Two springs of mean diameters 15 mm and 25 mm are connected in series. Each spring has 10 coils and the diameter of spring wire is 3 mm. Determine the deflection of the spring under maximum load if the permissible shear stress is 160 MPa and the shear modulus is 80 GPa. ...

Verified Answer:

Using Eq. (16.1), maximum load is given by ...
Question: 16.7

A weight of 200 N drops axially on a close coiled helical spring. The spring has 15 coils of mean diameter 200 mm. The spring wire has diameter 25 mm. Determine the height of drop if the instantaneous compression is 120 mm and the modulus of rigidity is 80 GPa. ...

Verified Answer:

Equivalent static load P_e for 120 ...
Question: 16.5

A close coiled spring has a stiffness of 5 N/mm. The solid length of spring is 60 mm when the coils are touching each other. Determine (i) the mean diameter of the coil, and (ii) the diameter of the wire if the maximum load is 100 N corresponding to allowable shearing stress is 150 MPa. Take ...

Verified Answer:

Stiffness of the spring, \frac{P}{\delta } ...
Question: 16.4

A railway wagon weighing 200 kN is stopped by a buffer of 4 springs while moving at a speed of 10 km/hr. If the maximum compression of springs is 150 mm, find the diameter of the spring rod if the mean diameter of the spring coil is 200 mm and 8 number of turns are in a coil. Take modulus of ...

Verified Answer:

Kinetic energy = \frac{1}{2}mV^2 [...