Torsional Diagram

Presentation On

This Presentation Is An Accomplishment for The

Fulfillment of Course CE-416 : Pre-Stressed

Concrete Sessional

Presented By- Golam Shafi Mustafa 09.02.03.029 4th Year 2nd Semester Section-A

Definition of Torsion

• A moment acting about a longitudinal axis of the member is called a torque, twisting moment or torsional moment, T.

So, Torsion is the twisting of an object due to an applied

torque.• Twisting of a straight bar when loaded by

moments (or torques) or torques tend to produce rotation about the longitudinal axis of the bar.

Definition of Torsional Diagram

Torsional Diagram is a two-dimensional representation of torque. A typical representation of Torsional Diagram is as follows:

Assumptions of Torsion Theory

• Material is Homogeneous;• Material is elastic;• Circular section remains circular after loading;• Plane cross-section remains plane after

loading;• Each x-section rotates as if rigid.

Glossaries

• Sign Convention-------- Right Hand Rule;• Net Torque Due to Internal Stresses

Net of the internal shearing stresses is an internal torque, equal and opposite to the applied torque,Although the net torque due to the shearing stresses is known, the distribution of the stresses is not.

T = ∫ρdF = ∫ρ(τdA)

Torsion Loading

• Deformation of Circular Subject due to Torque T

• Deformation of Rectangular Subject due to torque T

Torsion Formula

Torsion for a circular shaft:

T/J = τr/r = Gθ/L

And Maximum Shear Stress, τmax = Tr/Ip

So, Generalized Torsion Formula,

τ = Tρ/Ipolar

Where, T = Torque; JT = Polar Moment of Inertia = Ip or Ipolar.

r = Radius of circular shaft, G = Shear Modulus, θ = Angle of Twist, τr = Shearing Stress at any point, L = Length of circular member.

Failure Mode

The shear stress in the shaft may be resolved into principal stresses via Mohr's circle. If the shaft is loaded only in torsion, then one of the principal stresses will be in tension and the other in compression. These stresses are oriented at a 45-degree helical angle around the shaft. If the shaft is made of brittle material, then the shaft will fail by a crack initiating at the surface and propagating through to the core of the shaft, fracturing in a 45-degree angle helicalshape. This is often demonstrated by twisting a piece of blackboard chalk between one's fingers.

SummaryThe shear stress at a point within a shaft is:

The highest shear stress occurs on the surface of the shaft, where the radius is maximum. High stresses at the surface may be compounded by stress concentrations such as rough spots. Thus, shafts for use in high torsion are polished to a fine surface finish to reduce the maximum stress in the shaft and increase their service life.The angle of twist can be found by using:

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