Torsion

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An intorduction to Torsion.

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Torsion

  1. 1. Design for Torsion<br />Presenters<br />Syed Ubaid Ullah<br />Syed Mohammad Noman<br />Imad Mohsin <br />
  2. 2. Presenter<br />SyedUbaidUllah<br />Design for Torsion<br />
  3. 3. Definitions<br />Usual Practice and Requirements<br />Effects<br />Rotation<br />Warping<br />Cracking<br />Torsion Moments in Circular Beams<br />Cases for Design Moments<br />Elastic Torsional Stresses<br />Torsional Moment in Rectangular Sections<br />Introduction<br />Design for Torsion<br />
  4. 4. In solid mechanics, torsion is the twisting of an object due to an applied torque.<br />Torsion refers to the twisting of a structural member loaded by torque, or twisting couples.<br />Definition # 01 & 02<br />Design for Torsion<br />
  5. 5. Definition # 03<br />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).<br />Design for Torsion<br />
  6. 6. 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<br />Definition # 04<br />Design for Torsion<br />
  7. 7. Usual Practice and Requirements<br />Any engineer that is evaluating beam stresses and deflections must also consider the impact of any torsional loads imposed upon their designs.<br />The structural engineer typically designs steel members to be loaded such that torsion is not a concern.<br />Eccentric loads are typically avoided.<br />Design for Torsion<br />Syed Ubaid Ullah<br />
  8. 8. 1. Rotation:<br /> A member undergoing torsion will rotate about its shear center through an angle as measured from each end of the member<br />Effects<br />Rotation of I-Beam<br />Design for Torsion<br />
  9. 9. 2. Warping:<br /> Torsional warping is defined as the differential axial displacement of the points in a section perpendicular to the axis, due to torque.<br />Effects<br />Design for Torsion<br />
  10. 10. 3. Cracks<br />generated due to pure torsion follow the principal stress trajectories<br />The first cracks are observed at the middle of the longer side.<br />Next, cracks are observed at the middle of the shorter side. <br />Effects<br />Design for Torsion<br />
  11. 11. Torsion Moments in Circular Beams<br />Assumptions<br />1. This analysis can only be applied to solid or hollow circular sections.<br />2. The material must be homogeneous.<br />Design for Torsion<br />
  12. 12. Torsion Moments in Circular Beams<br />Cases for Design Moments<br />Cantilever beam: point torque.<br /> Mt=T<br />Cantilever beam: uniform torque.<br />Mt=mtL<br />Beam fixed at both ends: point torque at center.<br /> Mt=T/2<br />Design for Torsion<br />
  13. 13. Cases for Design Moments (continued)<br />Beam fixed at both ends: point torque at any distance.<br /> Mt= (Tb/L)<br /> Mt= (Ta/L)<br />Beam fixed at both ends: two point torque.<br /> Mt= [ T1 (b+c) + T2 c ] / L<br /> Mt= [ T2 c - T1 a] / L<br /> Mt= [ T1 a + T2 (a+b) ] / L<br />Torsion Moments in Circular Beams<br />Design for Torsion<br />
  14. 14. Shear stress developed in a material subjected to a specified torque in torsion test. It is calculated by the equation<br />Where;<br /> T is torque,<br /> R is the distance from the axis of twist to the outermost fiber of the specimen,<br /> J is the polar moment of inertia.<br />Elastic Torsional Stresses<br />Design for Torsion<br />
  15. 15. Torsional Moment in Rectangular Sections<br />The maximum shearing stress for rectangular sections can be calculated as follows<br />Where; T = the applied torque<br /> x = the shorter side of the rectangle section<br /> y = the long side of the rectangular section<br /> α = coefficient that depends on the ratio of y/x<br />Design for Torsion<br />
  16. 16. Torsional Moment in Rectangular Sections<br />α = coefficient that depends on the ratio of y/x, the value is taken as per the ratio from the following chart<br />Design for Torsion<br />
  17. 17. Torsional Moment in Rectangular Sections<br />For members composed of rectangles<br />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 <br />OR<br />Design for Torsion<br />
  18. 18. Presenter<br />S. M. Noman<br />Design for Torsion<br />
  19. 19. ACI code analysis<br /><ul><li>Introduction
  20. 20. Finding of x & y</li></ul>For Rectangular Section <br />For T, L or I section <br />For Hollow Section<br />Torsion Theories for Concrete Member<br /><ul><li>Skew bending theory
  21. 21. Space truss analogy </li></ul>Discussed Area<br />Design for Torsion<br />
  22. 22. ACI CODE ANALYSIS<br />Introduction:<br /> The analysis of concrete beam in torsion, we assumed the concrete will be cracked.<br /> According to ACI code 1983, an approximate expression use to calculate the nominal torsional moment:<br />Tn = 1/3 <br /> And, <br />Φ Tn ≥ Tu<br />Design for Torsion<br />
  23. 23. ACI CODE ANALYSIS (cont’d)<br />Ultimate torsional stress can be calculated as follow,<br /> Where;<br /> Φ = 0.85 &<br />x and y are the shorter and longer side of each of the rectangular concrete section.<br /> Finding of x & y:<br />There are several cases for deriving x and y .<br />Design for Torsion<br />
  24. 24. For Rectangular Section:<br /> For rectangular section , x and y can be directly calculated by using the short dimension as x and longer as y<br />For T, L or I section: <br /> First the component section divided into numbers of rectangle.<br /> According to ACI code, limits the effect over hang width of the flange thickness,<br />or y ≤ 3xT-section. (2Fig)<br /> The same principle is applied for other section.<br />ACI CODE ANALYSIS (cont’d)<br />Design for Torsion<br />
  25. 25. ACI CODE ANALYSIS (cont’d)<br />For Hollow Section:<br /> According to one and only ACI code, torsional moment resist by the hollow section on the bases of the following three limitations;<br /> When the wall thickness h ≥ x/4: (fig)<br /> (In this case, the same procedure as for solid sections may be used for the rectangular components of the hollow section).<br />Design for Torsion<br />
  26. 26. ACI CODE ANALYSIS (cont’d)<br />When the wall thickness x/10 < h >x/4:<br /> (In this case, the section may be treated as solid rectangles except that must be multiplied by 4h/x,<br /> Also <br /> ( x/4h )<br />When the wall thickness h / x/10:<br /> (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.<br /> So when this type of hollow section is used, a fillet is required at the corner of the box).<br />Design for Torsion<br />
  27. 27. Torsion Theories For Concrete Member<br />There are various theories available for the analysis of reinforced concrete member subject to torsion. The two basic theories are<br />Skew bending theory <br />Space truss analogy <br />Design for Torsion<br />
  28. 28. Introduction:<br /> First this concept was given by Lessing in 1959.then this theory were improved by many researchers in which Goode & Helmyin 1968,Hsu in 1968 & Rangan in 1975. <br /> The concept of this theory applied to reinforced concrete beam subjected to torsion &bending. This theory was adopted by ACI code of 1971.<br />Explanation:<br /> 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.<br />Skew Bending Theory:<br />Design for Torsion<br />
  29. 29. ,<br />Skew Bending Theory: (cont’d)<br />Tn = <br /> Where,<br />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<br />Design for Torsion<br />
  30. 30. Space Truss Analogy<br />Introduction: <br />This theory was first presented by Rauch in 1929, and also called as ‘Rausch Theory’.<br />Further developed by Lampert cover it theoretical approach,<br />Mitchell & Collins cover it modeling and also by McMullen and Rangan discussed the design concept.<br />Design for Torsion<br />
  31. 31. Space Truss Analogy (cont’d)<br />Explanation: <br />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. <br />Design for Torsion<br />
  32. 32. Space Truss Analogy (cont’d)<br />Explanation: (cont’d)<br />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<br />Design for Torsion<br />
  33. 33. Presenter<br />Imad Mohsin<br />Design for Torsion<br />
  34. 34. Torsional Strength Of plain Concrete members<br />Concrete structural members subjected to torsion will normally be reinforced with special torsional reinforced.<br />In case that the torsional stresses are relatively low and need to be calculated for plane concrete members.<br />The shear stresses can be estimated using equation:<br />Design for Torsion<br />
  35. 35. Torsional Strength Of plain Concrete members<br />Equation<br />Where, T = Applied torque<br /> ø = Angle of twist<br /> G = Shear modulus<br /> <br />NOTE:<br /> We did not usually design plain concrete section for torsion case<br />Design for Torsion<br />
  36. 36. Torsion In Reinforced Concrete Members<br />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.<br />The stirrups must be closed because torsional stresses occur on all faces of the section<br />Design for Torsion<br />
  37. 37. Torsion In Reinforced Concrete Members<br />The nominal ultimate torsional moment<br /> <br />Where<br />Tc= ultimate torsional moment resisted by concrete.<br />Ts= ultimate torsion moment resisted by hoop reinforcement.<br />Introducing the factor<br />Design for Torsion<br />
  38. 38. Design Procedure<br />Check the torsional stress in the section using equation<br />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.<br />Design for Torsion<br />
  39. 39. Calculate the nominal torsional moment strength provided by torsion reinforcement:<br />Calculate the longitudinal reinforcement. The required area of the longitudinal bars<br /> Or<br />Design Procedure<br />Design for Torsion<br />
  40. 40. Limitation Of The Torsional Reinforcement<br />The longitudinal bars must be distributed around the perimeter of the stirrups and their spacing shall not exceed 12 in.<br />At least one longitudinal bar shall be placed in each corner of the stirrups<br />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<br />Design for Torsion<br />
  41. 41. Limitation Of The Torsional Reinforcement<br />The critical section is at a distance d from the face of the support , with the same reinforcement continuing the face of the support.<br />To avoid brittle failure of the concrete, the amount of reinforcement must be provided according to the following limitations.<br /> Ts≤4Tc<br />For members subjected to significant axial tension , the shear or torsion moment carried by the concrete is neglected<br />Design for Torsion<br />
  42. 42. http://instruct1.cit.cornell.edu/<br />http://en.wiktionary.org/<br />http://www.ndt-ed.org/GeneralResources/<br />http://www.archoneng.com/<br />http://www.proz.com/kudoz/<br />Chapter 15: design for torsion by Nadim Hasoon<br />http://www.instron.us/<br />http://research.ttlchiltern.co.uk/<br />Design for Torsion<br />References<br />
  43. 43. Thank you<br />

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