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
(a) Split up the harmonic x = 8 sin(ωt + 45°), into two harmonic motions, one of which has amplitude of 10 and phase difference zero. (a) A body is subjected to two harmonic mot

Determine the elongation of plate: Q: A steel bar AB which is having uniform thickness 2 cm, tapers from 1.5 cm to 7.5 cm uniformly in a length of 50 cm. From 1 st principle

Condenser ( Capacitor ) : A capacitor is used to store the electrical energy. The maximum value of stored energy depends on its capacity. It helps to achieve required high voltag

Find out the quality: ABC industries manufacture X-band radar scanners utilized to detect speed traps. The printed circuit boards in the scanners are bough from an outside ven

Applications of seam welding Lap seam welding is used for the manufacture of cans, buckets and water tanks and for welding thin walled large diameter pipes. Mash seam welding

Q. Flanged pressure vessel nozzles? The Designer is responsible for ensuring that the facings, bolt circle, number of bolts, and size of bolts of vessel nozzles, match the mati

For fan installation detail and indicate correct structural components, drip pan, acoustical and thermal insulation. Provide special acoustical curbs for critical areas. Chec

Explain about the eccentrically loaded footings. ECCENTRICALLY LOADED FOOTINGS When footings have overturning moments and axial loads, the base pressure under the footing wi

the spring k2 is attached to a base that is moving vertically with displacement y=yo sin(wt).assume x>y.derive the equation of motion .find the natural frequency and derive the ste

Manufacturing DATABASE system in FMS