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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page of calculations for the modulus of resilience and energy content of springs, including a worked example.

Identifier  ExFiles\Box 154\1\  scan0278
Date  7th April 1936 guessed
  
-9-

S² K
--
2G

G = 11,500,000
S = Stress in lbs/sq.in.

The modulus of resilience for springs with wire in torsion is:

S² K
--
2E

E = 30,000,000
S = Stress in lbs/sq.in.

Total energy in spring = load x deflection
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2

Approximate ratio of inch lbs. per pound of steel to inch lbs. per cubic inch of steel is 3.58 x inch lbs. per cubic inch of steel equals inch lbs. per pound of steel.

As an application of this method the following problems can be considered. Desired weight per thousand springs on extension springs with initial tension 10 lbs. and elongation of 2 inches giving 30 lbs. maximum load. Allowed stress 100,000 lbs/sq. in., material music wire.

Solution:

If the spring carries 30 lbs load and has a rate of 10 lbs/ per inch, we have an equivalent elongation of 3 inches.

Energy content = 30 x 3 = 45 lbs. per spring.
----
2

Modulus of Resilience = 100,000 x 100000 x 1/4
---------------------
2 x 11,500,000
or
  
  


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