Torsion

Design for

Torsion

PresentersSyed Ubaid UllahSyed Mohammad NomanImad Mohsin

PresenterSyed Ubaid Ullah

Design for Torsion

Definitions Usual Practice and Requirements Effects

◦ Rotation◦ Warping◦ Cracking

Torsion Moments in Circular Beams◦ Cases for Design Moments

Elastic Torsional Stresses Torsional Moment in Rectangular Sections

Introduction

Design for Torsion

1. In solid mechanics, torsion is the twisting of an object due to an applied torque.

2. Torsion refers to the twisting of a structural member loaded by torque, or twisting couples.

Definition # 01 & 02

Design for Torsion

A twisting action applied to a generally shaft-like, cylindrical, or tubular member. The twisting may be either reversed (back and forth) or unidirectional (one way).

Definition # 03

Design for Torsion

The act of turning or twisting, or the state of being twisted; the twisting or wrenching of a body by the exertion of a lateral force tending to turn one end or part of it about a longitudinal axis, while the other is held fast or turned in the opposite direction

Definition # 04

Design for Torsion

The structural engineer typically designs steel members to be loaded such that torsion is not a concern.

Eccentric loads are typically avoided.

Any engineer that is evaluating beam stresses and deflections must also consider the impact of any torsional loads imposed upon their designs.

Usual Practice and Requirements

Design for TorsionSyed Ubaid Ullah

1. Rotation:A member undergoing torsion will rotate about its shear center through an angle as measured from each end of the member

Effects

Rotation of I-Beam

Design for Torsion

2. Warping:Torsional warping is defined as the differential axial displacement of the points in a section perpendicular to the axis, due to torque.

Effects

Design for Torsion

3. Cracks generated due to pure torsion

follow the principal stress trajectories

The first cracks are observed at the middle of the longer side.

Next, cracks are observed at the middle of the shorter side.

Effects

Design for Torsion

Assumptions

1. This analysis can only be applied to solid or hollow circular sections.

2. The material must be homogeneous.

Torsion Moments in Circular Beams

Design for Torsion

Cases for Design MomentsCantilever beam: point torque.

Mt=T

Cantilever beam: uniform torque.Mt=mtL

Beam fixed at both ends: point torque at center.

Mt=T/2


Design for Torsion

Cases for Design Moments (continued)

Beam fixed at both ends: point torque at any distance.

Mt= (Tb/L)Mt= (Ta/L)

Beam fixed at both ends: two point torque.

Mt= [ T1 (b+c) + T2 c ] / LMt= [ T2 c - T1 a] / LMt= [ T1 a + T2 (a+b) ] / L


Design for Torsion

Shear stress developed in a material subjected to a specified torque in torsion test. It is calculated by the equation

Where;T is torque,R is the distance from the axis of twist to the outermost fiber of the specimen,J is the polar moment of inertia.

Elastic Torsional Stresses

Design for Torsion

The maximum shearing stress for rectangular sections can be calculated as follows

Where; T = the applied torquex = the shorter side of the rectangle sectiony = the long side of the rectangular sectionα = coefficient that depends on the ratio of y/x

Torsional Moment in Rectangular Sections

Design for Torsion

α = coefficient that depends on the ratio of y/x, the value is taken as per the ratio from the following chart


Design for Torsion

For members composed of rectangles Members like T-, L-, I-, or H sections the value of α can be

assumed to be equal to , and the section may be divided into several rectangular components having a long side yi, and a short side xi. The maximum shearing stress can then be calculated from

OR


Design for Torsion

PresenterS. M. Noman

Design for Torsion

ACI code analysisIntroductionFinding of x & y

a. For Rectangular Section b. For T, L or I section c. For Hollow Section

Torsion Theories for Concrete Member Skew bending theory Space truss analogy

Discussed Area

Design for Torsion

Introduction: The analysis of concrete beam in torsion, we assumed the

concrete will be cracked. According to ACI code 1983, an approximate

expression use to calculate the nominal torsional moment: Tn = 1/3 And, Φ Tn ≥ Tu

ACI CODE ANALYSIS

Design for Torsion

Ultimate torsional stress can be calculated as follow, Where; Φ = 0.85 & x and y are the shorter and longer side of

each of the rectangular concrete section. Finding of x & y: There are several cases for deriving x and y .

ACI CODE ANALYSIS (cont’d)

Design for Torsion

For Rectangular Section: For rectangular section , x and y can be directly calculated

by using the short dimension as x and longer as y For T, L or I section: First the component section divided into

numbers of rectangle. According to ACI code, limits the effect

over hang width of the flange thickness,or y ≤ 3x T-section. (2Fig) The same principle is applied for other

section.


Design for Torsion

For Hollow Section: According to one and only ACI code,

torsional moment resist by the hollow section on the bases of the following three limitations;

When the wall thickness h ≥ x/4: (fig) (In this case, the same procedure as for solid sections may

be used for the rectangular components of the hollow section).


Design for Torsion

When the wall thickness x/10 < h >x/4: (In this case, the section may be treated as solid rectangles except that

must be multiplied by 4h/x, Also ( x/4h ) When the wall thickness h / x/10: (In this case, the wall stiffness must be considered because of the flexibility

of the wall and the possibility of buckling. such section should be avoided. So when this type of hollow section is used, a fillet is required at the corner

of the box).


Design for Torsion

There are various theories available for the analysis of reinforced concrete member subject to torsion. The two basic theories are

1. Skew bending theory 2. Space truss analogy

Torsion Theories For Concrete Member

Design for Torsion

Introduction:First this concept was given by Lessing in 1959.then this theory were improved by many researchers in which Goode & Helmy in 1968,Hsu in 1968 & Rangan in 1975.

The concept of this theory applied to reinforced concrete beam subjected to torsion &bending. This theory was adopted by ACI code of 1971.

Explanation:The basic approach this theory is that failure of a rectangular section in torsion occurs by bending about an axis parallel to the wider face of the section. (Fig), and inclined at about 45◦ to the longitudinal axis of the beam.

Skew Bending Theory:

Design for Torsion

Tn = Where, Is the modulus of rupture of concrete, and assumed

to be 5 in this case, as compared to 7. 5, adopted by the ACI code for the computation of deflection of beams

Skew Bending Theory: (cont’d)

Design for Torsion

,

Introduction: This theory was first presented by Rauch in 1929, and

also called as ‘Rausch Theory’.

Further developed by Lampert cover it theoretical approach,

Mitchell & Collins cover it modeling and also by McMullen and Rangan discussed the design concept.

Space Truss Analogy

Design for Torsion

Explanation:

T his concept of the space truss analogy is based on the assumption that the torsional capacity of a reinforced concrete rectangular section is derived from the reinforcement and the concrete surrounding the steel only.

Space Truss Analogy (cont’d)

Design for Torsion

In this case a thin walled section is assumed to be act as a space truss. The inclined spiral strips between cracks resist the compressive forces produce by the torsional moment

Space Truss Analogy (cont’d)

Explanation: (cont’d)

Design for Torsion

PresenterImad Mohsin

Design for Torsion

Concrete structural members subjected to torsion will normally be reinforced with special torsional reinforced.

In case that the torsional stresses are relatively low and need to be calculated for plane concrete members.

The shear stresses can be estimated using equation:

Torsional Strength Of plain Concrete members

Design for Torsion

Equation

Where, T = Applied torqueø = Angle of twistG = Shear modulus

NOTE:

We did not usually design plain concrete section for torsion case

Torsional Strength Of plain Concrete members

Design for Torsion

The design procedure for torsion to that for flexural shear. When the ultimate torsional moment applied on a section exceeds that which the concrete can resist torsional cracks develop and consequently torsional reinforcement in the form of close stirrups and hoop reinforcement must be provided.

The stirrups must be closed because torsional stresses occur on all faces of the section

Torsion In Reinforced Concrete Members

Design for Torsion

The nominal ultimate torsional moment

WhereTc= ultimate torsional moment resisted by concrete.Ts= ultimate torsion moment resisted by hoop reinforcement.

Introducing the factor

Torsion In Reinforced Concrete Members

Design for Torsion

Check the torsional stress in the section using equation

Calculate the torsional moment resisted by the concrete. If the torsional moment to be contributed by the concrete in the compression zone is taken as 40 percent of the plain concrete torque capacity of equation.

Design Procedure

Design for Torsion

Calculate the nominal torsional moment strength provided by torsion reinforcement:

Calculate the longitudinal reinforcement. The required area of the longitudinal bars

Or

Design Procedure

Design for Torsion

The longitudinal bars must be distributed around the perimeter of the stirrups and their spacing shall not exceed 12 in.

At least one longitudinal bar shall be placed in each corner of the stirrups

Torsional reinforcement must be provided for a distance ( d+b) beyond the point theoretically required , where d is the effective depth and b is a width of the section

Limitation Of The Torsional Reinforcement

Design for Torsion

The critical section is at a distance d from the face of the support , with the same reinforcement continuing the face of the support.

To avoid brittle failure of the concrete, the amount of reinforcement must be provided according to the following limitations.

Ts≤4Tc

For members subjected to significant axial tension , the shear or torsion moment carried by the concrete is neglected

Limitation Of The Torsional Reinforcement

Design for Torsion

http://instruct1.cit.cornell.edu/ http://en.wiktionary.org/ http://www.ndt-ed.org/GeneralResources/ http://www.archoneng.com/ http://www.proz.com/kudoz/ Chapter 15: design for torsion by Nadim

Hasoon http://www.instron.us/ http://research.ttlchiltern.co.uk/

Design for Torsion

References

Thank you

Torsion

Education

space truss

reinforced

aci code analysis

skew bending

aci code

torsional

torsional

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