Solid Mechanics | Assignment | Answers

Running Head: Solid Mechanics 1
Solid Mechanics
Student Name
Institutional Affiliation

SOLID MECHANICS 2
Part a)
The twist of a rectangular cross-sectional area shaft is complex due to warping of the cross-
section during twist. During the twist, the distortion is maximum at the middle of the cross-
section but varies along the sides and disappears at the corners. The rectangular section subjected
to torsion is analyzed for shear stress which is maximum at the middle of the cross-section area
and zero at the corners of the sides (Newchen, 2015).
The maximum shear stress, τ max occurs at the middle of the longer side and is given by
τ max= T
αD B2
And the angle of twist, θ is given by
θ= TL
βD B3 G
Where D is the longer side of the rectangular section
B is the shorter side,
α and β is the unit-less torsional parameter that depends on the D/B ratio (Chatopadhyaya, 2013).
L = length being considered, mm
G = shear modulus in MPa
T = resulting or applied torsion, in Nmm
For a rectangular section, the torsional parameters α and β, are given by the following formulas
can be used (Ugural & Fenster, 2013).
α = 1
3 [1−192
π5 ( D
B ) ∑
n=1,3,5...
∞
( 1
n5 tanh ( nπB
2 D ) ) ]
And
β=α
[1− 8
π2 ∑
n=1,3,5...
∞
( 1
n2 cosh ( nπB
2 D ) ) ]
Using the above formulas, α and β are calculated and tabulated as: