Calculate the axial deflection and angle of rotation, Mechanical Engineering

Calculate the axial deflection and angle of rotation:

Any open coiled helical spring along with 10 complete turns is built of 16 mm diameter steel rod, the mean radius of the coil being 50 mm. The angle of helix is 28o. Determine the deflection under an axial load of 300 N. Also determine the direct & shear stress induced in the section of the wire. If the axial load of 300 N is replaced by an axial moment of 9000 N-mm, calculate the axial deflection and angle of rotation.

Take E = 200 GPa, G = 80 GPa.

Also, determine the axial torque which shall cause a bending stress of 12 N/mm2.

Solution

n = 10, d = 16 mm, R = 50 mm, α = 28o, W = 300 N

Δ= 64 W R3 n / d 4 cos α [cos2 α/G + 2 sin 2 α /E]

 = 64 × 300 × 503 × 10 /164 × cos 20 [cos2 20/80 × 103 + 2 sin 2 20 /200 × 103 ]

∴          Δ = 4.74 mm

σb  = 32 W R sin α / π d 3= 32 × 300 × 50 × sin 20 / (π × 163) = 12.8 N/mm2

τ= 16 W R cos α/ π d 3 =16 × 300 × 50 × sin 20/ π × 16 =17.5 N/mm2

 Principal stresses,

993_Calculate the axial deflection and angle of rotation.png

= 6.4 ± 18.6 = 25 N/mm2 - 12.2 N/mm2

Maximum shear stress = (σ1 - σ2 ) /2= (25 - (- 1.22) )/ 2 = 18.6 N/mm2

M = 9000 N-m

φ= 64 M R n/ d 4 cos α [2 cos2 α/E    + sin 2 α / G]

=64 × 9000 × 50 × 10/(16)4 cos 20[(2 cos2 20)/ (200 × 103)) +( (sin 2 20/ (80 × 103))]

φ = 0.048 radians

φ= 64 M R2 n sin α/ d 4[(1/G) -(2/E)]

= ((64 × 9000 × 502 × 10 × sin 20)/ (16)4 )[1/80 × 103 - 2/200 × 103]

= 0.19 mm

σ b = 32 T cos α/ π d 3

⇒         12 = 32 T × cos 20 / π× 163

∴ T = 5135.2 N-mm

Posted Date: 1/21/2013 1:30:37 AM | Location : United States







Related Discussions:- Calculate the axial deflection and angle of rotation, Assignment Help, Ask Question on Calculate the axial deflection and angle of rotation, Get Answer, Expert's Help, Calculate the axial deflection and angle of rotation Discussions

Write discussion on Calculate the axial deflection and angle of rotation
Your posts are moderated
Related Questions
Q. How can you determine velocity by electromagnetic method? In electromagnetic method, a magnetic field is generated by the electric current flowing through a coil fixed below

Cylinder Head: It is fitted at top of the cylinder block. It provides space for the arrangement of spark plug, combustion chamber, camshaft, cam chain, valves and intake and exha

What is differential approach (differential formulation) in fluid mechanics? What are velocity and acceleration fields, give examples. Find, study and write down the differential f

What do you mean by Thermil-welding ? Describe the process with neat sketch.

The progressive liberalization of the norms for foreign investment and import of technology appear to have benefited the automobile sector with production of total vehicles increa

Calculate the amount of cement, sand, aggregate, and water needed to create a concrete mix with a 28-day compressive strength of 34 MPa for a 10 m x 10 m x 0.25 m structure given t

Find out the axial moment of inertia: Find out the axial moment of inertia of a rectangular area of base b and height d around centroidal axis GX and the base B 1 B 2 . So


to find a horizontal force acting on a body which is inclined to the plane with a particular angle

Principle of equilibrium: Sol.: Principle of equilibrium can be divided in to three main parts; (1) Two Force Principle: As the Resultant is zero when body is in equili