The following formulae hold true only for cylindrical specimens:
γ = cφ/L
τ = cT/J
(for cylindrical bar)
J = π(c
(for tubular sections, general)
J = 2πc
(for thin wall, t = thickness of tube wall)
G = TL/Jφ = τ / γ
Percent of ductility = [(L' - L)/L]100
There is a theoretical relationship between the modulus of rigidity (G) and the tensile modulus of elasticity
(E) for homogeneous, isotropic materials, G = 0.4 E.
Experimental testing of steel shows this relationship
to hold true.
For a ductile steel the shearing proportional limit is approximately 60% of the tensile
Ductility in torsion is determined by comparing the final fiber length (L') at rupture to the original fiber
length or gage length (L).
The ductility is expressed as percentage of elongation.
The modulus of rupture in torsion is understood to be the nominal extreme fiber stress at rupture as
determined by the torsion formula.
This value is actually larger than the true maximum stress.
approximate correction to the value determined for the modulus of rupture in torsion for ductile materials
For a ductile material the ratio of shear strength to tensile strength is approximately 0.8.
The torsion test is not applicable to determining the shearing strength of brittle materials, such as cast iron,
since the specimen would fail in diagonal tension before the shearing strength was reached.
Mechanics of Materials
by R. C. Hibbeler or another strength of materials book.
With a micrometer caliper determine the mean diameter of the steel specimen near its mid-length.
Assume the shearing proportional limit is 0.6 of the tensile proportional limit and the shearing
modulus of rupture as equal to the tensile strength.
Check with instructor to ascertain tensile
strength of specimen.
Compute loading increments that will give at least 10 observations below the shearing proportional
limit, several close together near the proportional limit, and at least 10 beyond the proportional
Note the gage length and least reading of the troptometer.