Name: Raktim BaruaID no.: 10.01.03.123Course no.: CE 416

Course title: Pre-stressed concrete lab.

Torsion Force

Objectives

1. Define torsion force and applications,2. Explain some formulas for torsion

force,3. Importance of torsion in pre-stressing.4. Analysis of torsion.

What is torsion force and it’s applications?????

Torsion force is a twisting force that is applied on an object by twisting one end

when the other is held in position or twisted in the opposite direction. Different materials

have a different way of responding to torsion. Some will deform, crack or even break depending on the type of material.

Chapter 5: Torsion

The Torsion Formula

• When material is linear-elastic, Hooke’s law applies.

• A linear variation in shear strain leads to a corresponding linear variation in shear stress along any radial line on the cross section.

Chapter 5: Torsion

The Torsion Formula

• If the shaft has a solid circular cross section,

• If a shaft has a tubular cross section,

Limitations

• The equations shown in this section are valid for bars of circular

cross-section (either solid or hollow) that behave in a linearly elastic manner

• These equations can not be used for bars of other shapes such as rectangular bars and non-circular bars

***Torsion theory originated from the work of C.A. de Coulomb and further developments were due to Thomas Young

YoungCoulomb

Why do we need to understand torsion in pre stressed concrete lab course?????

• One of the primary reasons for this recent desire for an understanding of the effects of torsion is that modern structures tend to be of higher degrees of statical indeterminacy and continuity, thereby incurring combined stress states which regularly include torsion.

• The second reason is found in those instances in which torsion cannot be eliminated, not even on paper.

In the past this was either ignored or taken care of by reducing the permissible stresses.

Analysis of torsion

The analysis of reinforced concrete and pre-stressed concrete members for torsion is more difficult compared to the analysis for axial loads or flexure.

The conventional analysis for reinforced concrete and pre-stressed concrete members for torsion is based on the equilibrium of forces by simple equations. The compatibility of strains in concrete and steel reinforcement is not considered.

Torsion generated in a member can be classified into two types based on the necessity of the analysis and design for torsion.

1.Equilibrium torsion: This is generated due to loading eccentric to the centroidal axis. For example:

(a) in a beam supporting cantilever slab or

precast slab or floor joists on one side, (b) in a (curved) bridge deck subjected to

eccentric live load, (c) in an electric pole subjected to loads from

wires on one side.

2.Compatibility torsion : This is generated by twisting to maintain compatibility in deformation with connected member. This type of torsion generates in a primary beam supporting secondary beam. For example: grid beam system.

The primary beam need not be analyzed and

designed for torsion if secondary beams are designed as simply supported.

The code allows us to neglect torsion if it is in the case of compatibility torsion.

Here the emphasis is laid on equilibrium torsion. The behavior of a beam under torsion can be understood by these following sequences.

(1)stresses in an uncracked (homogeneous) rectangular beam without pre-stressing due to pure torsion (in absence of flexure),with constant torque along the span.

(2)Crack pattern under pure torsion; (3)components of resistance for pure torsion; (4)Modes of failure under combined torsion and

flexure; (5)Effect of pre-stressing force.

What is pure torsion?????

The theory of pure torsion is used to find out the value of shear stresses at various distances from the centre of the shaft. Under pure torsion the cross section of the shaft is only under pure shear stress.

Although pure torsion is absent in structures, understanding the behavior under pure torsion helps to analyze under combined torsion, flexure and shear.

Certain assumptions are made to work out this theory.

No more to discuss.

Sorry to make anyone bored or for wrong information…..

Thank you