Define the angle of twist and angle of shear? Deduce the expression for the
couple required to twist a uniform cylinder.
Answers
Answer:
Follow the explanation part
Explanation:
The angle of shear is given by angle of the deformation that comes up on the sides when deformation force or shearing stress is exerted on an object.
The angle of twist is given as the angle along with which an element of a rotating machine rotates or twists w.r.t its free end.
Let us a cylindrical rod of length l and radius r also coefficient of rigidity -
nu.
As we make it's upper end
fixed and a couple is applied along a plane that will be perpendicular to its length at the lower end as shown
Consider the cylinder is consisting large number of co-axial hollow cylinder. Now to
consider a single hollow cylinder of radius x and radial thickness dx as shown in figure.
Let theta be twisting angle. The displacement is bound to be greatest at the rim and decreases as the center is
gradulally approached where it becomes zero.
As shown in the figure, Let AB be the line which is parallel to the axis OO’ before twist produced and
on twisting B shifts to B’ this makes the line AB become AB’.
Before twisting if the hollow cylinder had cut along AB and had got flatted out it will be forming the
rectangle ABCD as shown in figure. But if it is cut after twisting it gives the shape of a
parallelogram AB’C’D.
Follow the attachment for Derivation.
