Determine equivalent maximum shear stress in spring, Mechanical Engineering

Assignment Help:

Determine equivalent maximum shear stress in spring:

A close coiled helical spring contains a stiffness of 10 N/mm. Its length while fully compressed, with adjacent coils touching each other is 400 mm. G = 80 GPa.

(a) Find out the wire diameter and the mean coil radius, if their ratio is 0.02.

(b) If the gap among any two adjacent coils is 2 mm, what maximum load may be applied before the adjacent coils touch?

(c) What is the equivalent maximum shear stress in spring?

Solution

k = 10 N/mm, nd = 400 mm, G = 80 GPa = 80 × 103  N/mm2 , d = ?, R = ?,

d /R= 0.02  ∴R = 5d , Gap = 2 mm, W = ?, τmax  = ?

(a) k = W / Δ = G d 4/64 R3 n

            G d 4

∴ W/ Δ = G d 4/64 R3 n

or 10 =80 × 103 × d 4 / 64 (5d )3 . (400/d)

∴  d = 20 mm

R = 5d = 5 × 20 = 100 mm

n = 400/ d = 400 /20= 20

 (b) Gap between adjacent coils = 2 mm

Total gap = 2n = 2 × 20 = 40 mm, i.e. spring ought to deflect 40 mm if coils are to touch each other.

Δ= 64 W R3 n/ Gd 4

∴  40 = 64 × W × 1003 × 20 / 80 × 103 (20)4

or  W = 400 N

∴  τ max = 16 W R / π d 3 = 16 × 400 × 100 / π (20)3 = 25.5 N/mm


Related Discussions:- Determine equivalent maximum shear stress in spring

EM13939497, Do the answers come with the full calculations?

Do the answers come with the full calculations?

Slab hanging - mechanics, Slab hanging: Three similar uniform slabs ...

Slab hanging: Three similar uniform slabs each having length '2 a ' are resting on edge of table as shown in the figure given below. If each slab is overhung by the maximum

Describe shear force and bending moment, Describe the following terms:- ...

Describe the following terms:- a) Shear force and bending moment b) Concentrated load, Uniformly varying load and Uniformly distributed load c) Beam & Types of beam. d)

Evaluate the tension in the rope, Evaluate the tension in the rope: De...

Evaluate the tension in the rope: Determine the tension in the rope. Solution KE of the free-body of flywheel is developed due to (i) work-done by tension T in the rop

What is auto-ignition temperature, Q. What is Auto-Ignition Temperature? ...

Q. What is Auto-Ignition Temperature? Auto-Ignition Temperature (AIT) - The auto-ignition temperature is the temperature at which a product will burn without application of any

What do you mean by an inertial reference, (a) Comment on the require to id...

(a) Comment on the require to idealise a body as a particles, a rigid body or a continuum. (b) What do you mean by an inertial reference ? (c) Define quantitatively a force 1

Friction, Friction: you have learnt laws of friction and problems invo...

Friction: you have learnt laws of friction and problems involving dry friction. The relative sliding motion of one body on another body is resisted by forces called as frictio

Chemistry, Note on scale and sludge?

Note on scale and sludge?

Fourth gear position - shifting of gear, Fourth Gear Position: When g...

Fourth Gear Position: When gear M4 on the main shaft is in mesh with gear C4 on the countershaft then this is known as fourth gear position. The free gear M4 rotates with the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd