Determine the maximum permissible axial load, Mechanical Engineering

Determine the maximum permissible axial load:

In an open coiled spring of 10 coils the stresses because of bending and twisting are 120 N/mm2 and 150 N/mm2 respectively while the spring is loaded axially. Supposing the mean radius of the coil is 5 times the wire diameter, determine the maximum permissible axial load and the wire diameter for a maximum extension of 20 mm.

E = 200 GPa, G = 80 GPa.

Solution

n = 10, R = 5d, Δ = 20 mm, E = 200 GPa = 200 × 103 N/mm2 , τ = 120 N/mm2,

G = 80 GPa = 80 × 103 N/mm2 , W = ?,  d = ?

σ b = 32 W R sin α / π d 3= 120 N/mm2

τ= 16 W R cos α/ π d 3 =150 N/mm2

Taking ratio of τ/ σb

2 tan α=  120 / 150

tan α= 0.4

sin α= 0.37;  sin 2 α = 0.14

cos α= 0.93;  cos2 α= 0.86 , sec α = 1.075

Δ= 64 W R3 sec α/d4    (cos2 α/G+ 2 sin 2 α/E)

⇒         20 = (64 W (5d )3 (10)/ d 4 × 0.93)[ 0.86/ (80 × 103) +((2 × 0.14)/ (200 × 103)]

∴          W / d  = 19.99             ------------ (1)

              32 × W × (5d ) × 0.37/ π d 3  = 120

⇒         W  / d 2 = 6.37                           ---------- (2)

Eq. (1) divided by Eq. (2), we obtain

d = 3.0 m

W = 19.99 × 3 = 1145.43 N

Posted Date: 1/21/2013 1:27:41 AM | Location : United States







Related Discussions:- Determine the maximum permissible axial load, Assignment Help, Ask Question on Determine the maximum permissible axial load, Get Answer, Expert's Help, Determine the maximum permissible axial load Discussions

Write discussion on Determine the maximum permissible axial load
Your posts are moderated
Related Questions
Autocad screen- The autocad Screen basic chapter of Autocad course it will show the display of Autocad on computer screen

Projection Welding Projection welding is similar to spot welding but for the fact that the welding takes place at the projections on the surface of the metals and flat shaped e

What is Wire-frame Wire-frame models use the simplest data structures and they are ambiguous. Wire frame is a well-known example that consists of 16 vertices and 32 edges. We

A hollow mild steel tube 6 m long 4 cm internal diameter and 6 mm thick is used as a strut with both ends hinged. Determine the crippling load and safe load taking factor of safety

Illustrate the terms : (i) State (ii) Process and (iii) Cycle What is a quari static process ? Illustrate with an example. What are point function and path function.

(i) Use the GOAL SEEK tool in MS EXCEL to solve the following equation and determine the TWO roots of this equation between 0 X 4 -8x 3 -x 2 -14x+21=0 (ii). Use the SOLVER t


Obtain the equations of the elastic curve and use them to determine the deflection and rotation at point B  in terms of E, I, F and L. Determine the maximum bending stress in the

Difference between projectile motion and a rocket motion? Ans) A projectile has no motor or rocket on it, so all of its momentum is given to it as it is opened. An example of a