Torsion of circular shafts formula. τ max /c∫r 2 dA = T.

Torsion of circular shafts formula A cylindrical transmission shaft of length 1. Figure 3. Shear stress is highest at the outer surface and lowest at the axis. Length of shaft: The twist angle When that happens equation 4 and 5 would be used to calculate the stress and polar moment of inertia, while equation 2 would still be used to calculate the angle of twist. Effects of Torsion: The effects of Special Case of a Circular Tube Consider the case of a circular tube with inner diameter R i and outer diameter R o Figure 12. Concepts involved: 1) Torsional stress 2) Torsion formula Formulae used: Polar moment of inertia 2 A Jd=ρ∫ A Torsion formula τ max = Tr/J Solution: Step 1: Get Torsion of Shaft Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. In torsion the members are subjected to moments (couples) in planes normal to their axes. Table 1-15 gives formulas for the deformation and stress of open noncircular beams with various cross sections in torsion. ∫τ r dA r = T. R = Radius of the circular shaft. d applied in a plane perpendicular to the axis of the In this lecture, we consider the torsion of circular shafts. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it 10. Examples are provided to calculate shear stress, angle of twist, and maximum torque or power given various shaft properties and limitations. - Torsion can cause both shearing stresses and normal stresses depending on the orientation of the material element. We have following information from above figure. (b) The shaft is not circular. The equation for a non-circular bar is derived correctly in [7], but no solutions for particular profiles are introduced. To learn more, check out "Strength of Materials, P In this chapter you can find the Torsion of Shafts - Solid Mechanics - Mechanical Engineering - Notes, Videos & Tests defined & explained in the simpl view more est way possible. 4. The resulting stress (torsional shear stress) is expressed in The torsion constant, denoted as ( J ), measures a cross-section’s resistance to twisting or torsion. Perry's formula. Effects of Torsion: The effects of a torsional load applied Torsion of Circular Shafts - Free download as PDF File (. 2 Torsion of Circular Shafts Consider the solid circular shaft, shown in the Figure 6. Torsion of Thin-Walled Bars1 Review of Circular Shafts The shear stress for a circular cross section varies linearly. This phenomenon is crucial in the analysis and design of mechanical components, as it determines how a shaft will respond under rotational loads, which directly connects to the concepts of axial, bending, and torsional stresses experienced by 1) The document discusses torsion and shear stresses in circular cross-section shafts. Consider a non circular body subjected to torsion T x z y Governing differential equation: 2 0 2 2 2 2 + = EXAMPLE : A square shaft under torsion. C (a) The shaft is flexible. ##### Fig. While operat When a shaft is having two different diameters cross section then a torque (T) is applied at the centre (Junction of the two different section) and two opposite torques T 1 and T 2 as shown in the figure. The formulas for calculating the shear stresses and the angle of twist 5. (b) The stress and strain vary linearly from the axis of the shaft. Compare the calculated value of G with The notes and questions for Torsion of Circular Shafts have been prepared according to the Mechanical Engineering exam syllabus. 1 Assumptions. Find the maximum torsional stress in shaft AC (refer the figure). Practical tests carried out on circular shafts have shown that the theory developed below on the basis of The document discusses torsion and torsion formulas for circular shafts. Nomenclature. To determine the magnitude of shear stress at any point on the shaft, Consider a circular shaft of length ‘L’, fixed at one end and subjected to a torque ‘T’ at the other end as shown. This document provides an overview of torsion and torsional analysis. T – applied torque (Nm) J – second moment of area (mm 4 ) k – torsional stiffness (Nm/rad) General Torsion Equation (Shafts of circular cross-section) J-1-48 1. (This is certainly not the case with the torsion of non-circular sections. Figure 1 The radius A textbook of fluid mechanics by Dr. Additionally, the simple torsion formula will be verified using experimental and shear stresses. It This video illustrates how to obtain torsion formula for a circular shaft made of linear elastic materials. Although we limit (b) The stress increases exponentially from the axis. Maximum moment in a circular shaft can be expressed as: T max = τ max J / R (2) where . Besides explaining types of Torsion of Shafts - Solid Mechanics - Mechanical Engineering - Notes, Videos & Tests theory, EduRev gives you an ample number of questions to practice Torsion of Shafts Shafts in Torsion 6. We will consider here one case of circular shaft which will be subjected to torsion and we will derive here the torsion equation for circular shaft. Shaft deformations: From observation: The angle of twist of the shaft is proportional to the applied torque $\phi \propto T$ The angle of twist of the shaft is proportional to the length $\phi \propto L$ 2. During the deformation, the This document provides an overview of torsion of circular shafts including: derivation of the torsion formula; analysis of shear strain and stress; examples calculating angle of twist and torque reactions; and considerations for designing transmission shafts including determining required torque and selecting shaft dimensions. This equation relates the applied torque (T), the length of the component (L), the Formulas are derived for solid and hollow circular shafts. All of the material within the shaft will work at a lower stress and is not being used to full capacity. For non-circular sections, ( J ) varies based on shape and dimensions. The torsion equation relates the angle of twist in a shaft to the applied torque based on certain assumptions about the shaft's material properties and dimensions. $\mathrm{Angle\: of\: radius=\frac{arc}{radius}}$ $\mathrm{Arc\: AB = R\theta = L\gamma }$ Torsion of circular shafts refers to the twisting of a shaft due to an applied torque, leading to shear stress and deformation along its length. In this circular case the cross-sections remains planar, but in case of non-circular bar, the real cross-sections are deflected from the planar shape. Download these Free Torsion of Shaft MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. The fiber AB on the outside surface, which is originally straight, will be twisted into a helix AB′ as the Torsion equation derivation. 5 Statically Indeterminate Torsion Members This equation, thus, states that ratio of stress at a point to radial distance of that 2 of the hollow shaft if the thickness t of the shaft is specified as one-tenth of the outer diameter. In that figure, the value for 𝜏 is minimum at the neutral axis while it is maximum at r = d/2. The document discusses torsion of shafts including shear stress, maximum torque, deflection, and provides formulas to calculate these values for solid and hollow circular shafts. τ max /c∫r 2 dA = T. Torque causes twisting and internal shearing stresses. 1 Introduction • Stresses also can occur within a structural element due to torsional or twisting effect CHAPTER 5 TORSION OF NON-CIRCULAR AND THIN-WALLED SECTIONS Summary For torsion of rectangular sections the maximum shear stress tmax and angle of twist 0 are given by T tmax = ~ kldb2 e - T L k2db3G kl and k2 being two constants, their values depending on the ratio dlb and being given in Table 5. 1) The material of shaft is uniform throughout the length. For circular shaft [Isotropic-linear-elastic] à The only non-vanishing stress and strain components are planes, as in the case of a circular bar made of wood, the first crack due to twisting will appear on the surface in longitudinal direction a rectangular element with sides at 45 o to the axis of the shaft will be subjected to tensile and compressive stresses The Torsion Formula consider a bar subjected to pure torsion, Torsion equation or torsion constant is defined as the geometrical property of a bar’s cross-section that is involved in the axis of the bar that has a relationship between the angle of twist and applied torque whose SI unit is m4. 2 Annular round bar. Shear stress is zero on the axis passing through the center of a shaft under torsion and maximum at the outside surface of a shaft. to/2znE4GR Lecture 8-10: Torsion of solid circular shafts Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F. 4 Mechanical Power Transmission by a Shaft 2. In addition, the length L of the shaft remains constant. 7. If equal and opposite couples are applied at the ends of a circular shaft, they will either equilibrate or Torsion Formula: Where q = shear intensity at radius r. The type of equation (Laplacian equal to constant) is known as the Poisson equation. In these types of ASSUMPTION IN THE THEORY OF TORSION: The following assumptions are made while finding out shear stress in a circular shaft subjected to torsion. Torsion occurs in a shaft when it is subjected to two equal and opposite twisting moments, known as pure torsion. 1 An Introductory Exercise We return to the problem of torsion of circular shafts. Assume the Diameter of AC is 15 mm. Figure shows a bar or shaft of circular section, subjected to torque T. the torsion of the drill chucks or the cone shaped mandrels is negligible compared to the torsion of the test bars. 2, 6. A circular shaft, when subjected to torsion, experiences a twisting action along its length due to the applied torque. Sectional planes perpendicular to the axis of the shaft remain plane during 4. Torsion: A shaft is said to be in torsion when equal and opposite forces are applied at the two ends of the shaft. The torsional equation for a hollow circular shaft is given by:\[ \tau = \frac{T \cdot r}{J} \]where: The study of torsion of circular shafts also helps in the following ways: The nature of these internal forces helps in the design and selection of the shaft. Examples are provided to demonstrate calculating shear stress, angle of twist, and solving for applied torque given various shaft •Torsion is the moment applied in a plane containing the longitudinal axis of the beam or torque or power, I beams, Portico beams, curved beams, closed coil springs. This is true whether the shaft is rotating (such as drive shafts on engines, motors and turbines) or stationary (such as with a bolt or using data from task 1 and formulas for all material. 4 Composite Shafts – Series Connection 10. Angle in radius = \ (\begin In this lecture, we consider the torsion of circular shafts. Here, we’ll take a single instance of a circular shaft that will be torn, and we’ll derive the circular shaft torsion equation. Using what we have seen in chapter 4 to find the distribution over each element,& using the concept of shape functions, Torsion of Shafts 1. Torsion of non-circular sections is an important problem in the theory of elasticity for which a simple strength of materials approach does not exist, except for some special cases. Write the formula for power transmitted by the shaft. As we know, stress formula-tions are useful when we can provide traction boundary conditions 4 Torsion of circular shafts. 6 Representation of cross-section of circular tube For a solid section, the stress distribution is thus: Figure 12. 1 Theory of Torsion 10. 2) The The shear stress formula is not accurate in the vicinity (usually characterized by a distance equal to the largest cross-sectional dimension as per St. 5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. That is, there is no relative displacement of any two, arbitrarily chosen points of a cross section when the shaft is subjected to a torque about its longitu-dinal, z, axis. 3 A shaft is a structural member which is long and slender and subject to a torque (moment) acting about its long axis. Using the assumptions above, we have, at any point r inside the shaft, the shear stress is τ r = r/c τ max. The rate of twist along the length is given by = dz, where is the angular displacement of a material point on a cross-section. 7 Representation of stress “flow ” in circular tube res is directed along circles Paul A. (c) Determine the ratio of diameters (that is, the ratio d 2 /d O) and the ratio of weights of the hollow and solid shafts. txt) or read online for free. similarities between bending and torsion, including for example, a linear variation of stresses and strain with position. 3 Power Transmission by Shafts 10. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2]. Then the shafts are said to be in parallel. 2 Torsion of Circular Shafts 10. Question . If the shaft diameter is doubled then the maxim View Question Marks 2. For a solid or hollow circular shaft subject to a twisting = \dfrac{Tr}{J}$ where Torsional testing of Circular Shafts Introduction: Torsion occurs when any shaft is subjected to a torque. 3 Hollow Shafts 1. 2. Question. stiffness of the hollow circular shaft in three different trials along with shear stress of the. Lagace Torsion is twisting of an object due to an applied torque. 6. The maximum torque a circular solid shaft can transmit depends on the shear stress limit and material properties. 2 Compatibility of Deformation The cross-sections of a circular shaft in torsion rotate as if they were rigid in-plane. 2 32 = shear stress at LECTURE 6. 5. Torsion can be calculated in mechanical engineering using the torsion formula, also known as the torsion equation. D (a) The stress in the shaft is constant. When two opposing and equal torques are applied at either end of a shaft, it is said to be in torsion. As we know, stress formula-tions are useful when we can provide traction boundary conditions Torsion Equation Derivation. Because a circular cross section is an efficient shape for resisting torsional loads, circular shafts are commonly used to transmit In this article, I will describe the torsion of solid circular shafts and hollow circular shafts. R. Equation 2. 14 shows one reason why most drive shafts are hollow, since there isn’t much point in using material at the center Torsion of Circular Shafts Consider the solid circular shaft, shown in the Figure 2. It defines key terms like uniform and non-uniform torsion. θ = 32 L T / (G π D 4). Assumptions Cross-sections remain plane. material for one trial. Torsion is constant along the length of the shaft. 2 TORSION OF SOLID CIRCULAR SHAFT 6. Assumptions • The material of the shaft is uniform throughout • Circular sections remain circular even after twisting • Plane sections remain plane and do not twist or Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F. Define torsional rigidity of a shaft. There is negligible friction between the supporting rod and the chuck. r = radius at a point = maximum shear stress at the surface of a shaft. We want to develop methods to determine the shear stress distribution over the cross-sectionof the torque-bearing struc-tural element and the rotation of any cross-section relative to another. For the previous instalment in the series, go here. SHAFTS: TORSION LOADING AND DEFORMATION (3. A solid circular shaft is considered with a designated radius R and it is associated with the torque T that acts on both the ends under the same amount of torque (hkdivedi, 2022). pdf), Text File (. Apply the principle of torsion formula – determine the torsional deformations Calculate the angle of twist for circular shaft Torsion by Nur F Ariffin . In the development of a torsion formula for a circular shaft, the following assumptions are made: Material of the shaft is homogeneous throughout the length of the shaft. 2 Torsional Displacements 10. 1 and 2 show the directions and magnitudes of the shear stresses for solid and annular cross sections. Shear stress is proportional to 3. 5 6. 20 Torsion Loading ENES 220 ©Assakkaf Stresses in Circular Shaft due to Torsion ρ T T B C = = ∫ area T Tr ρ τ dA (2) LECTURE 6. 1 Torsion Equation 1. Now, we know, J = ∫ r 2 dA. For the Torsion of a Circular Shaft. B’ B’ Φ θ θ B A B O O T L TORSION FORMULA : When a circular shaft is subjected to torsion, shear stresses are set up in the material of the shaft. 1 Torsion of Circular Shafts a. (b) The stress is zero. ac. It begins by introducing torsion and defining related terms like torque and angle of twist. 1. This document discusses torsion of circular shafts. TORSION EQUATION The diagram shows a shaft fixed at one end and twisted at the other end due to the action of a torque T. Torsion of a square section bar Example of torsion mechanics. d applied in a plane perpendicular to the axis of the bar such a sh aft is said to be in torsion. Obtaining the strain energy is important in many ways such as dynamic analysis and structure theory. 1. The torsion formula relates shear stress to torque, polar moment of inertia, radius, shear modulus, and angle of twist. Find important definitions, questions, notes, meanings, examples, exercises 11 Torsional Deformation of a Circular Shaft A torque is a moment that tends to twist a member about its longitudinal axis The effect of torque is important in the design of power transmission systems such as automotive drive train Such components are usually terms shafts For this reason, it is important to be able to compute the stresses and strains induced in power torsion of circular members and consider an example of Castigliano’s theorem applied to torsional deformation. The formulas for Case 1 are based on rigorous mathematical analysis, and the remaining formulas are obtained either The document provides an overview of mechanics of materials concepts related to torsion, including: - Torsion causes shearing stresses that vary linearly from zero at the center to a maximum at the surface for circular shafts. 2 Polar Second Moments of Area 1. . 21 Torsional Shearing Strain ENES 220 ©Assakkaf If a plane transverse The video discusses the torsion of circular shafts, derivation of torsion equation and design constraints in torsion In order to treat solid circular shafts, r i may be set equal to zero in Equations (1-47) and (1-48). k bansal available at https://amzn. 2) For a shaft under torque to be in equilibrium, the sum of opposing torques must be equal. Our starting point here will be to explore the concept of strain as it applies to We want to find the maximum shear stress τ max which occurs in a circular shaft of radius c due to the application of a torque T. Finally we can write here the expression for torsion equation for circular shaft as - $$\frac{T}{J} = \frac This part will focus on torsion in circular shafts and the stresses and strains it induces. It also helps to understand the reasons for the failure of the circular shaft. com/engineering_made_possible/This video shows how to solve for the maximum shear stress and angle of twist for shaft of These shafts can be solid, as shown in Fig. 1 – 3. Write torsion equation. instagram. Because a circular cross section is an efficient shape for resisting torsional loads, circular shafts are commonly used to transmit à In this section we apply that result specifically to the case of torsion of circular members and consider an example of Castigliano’s theorem applied to torsional deformation. Such a bar is said to be in torsion. These have direct relevance to circular cross-section shafts such as drive The fictitious failure stress calculated using the elastic analysis is often called the modulus of rupture in torsion. 4 Assumptions (a) The stress in the shaft does not exceed the limit of proportionality. Torsion of Non Circular Sections 2 Torsion of Non Circular Sections Shear stress cannot act in a direction normal to a free surface. Shaft is straight and of uniform circular cross section over its length. The torsional equation for a hollow circular shaft is given by:\[ \tau = \frac{T \cdot r}{J} \]where: In this article, I will describe the torsion of solid circular shafts and hollow circular shafts. Ans. Simplifying assumptions During the deformation, the cross sections are not distorted in any manner－they remain plane, and the radius r does not change. Stresses/Deflections Shafts in Torsion 223 8. 5: Torsion in shafts PURE TORSION A member is said to be in pure torsion when its cross sections are subjected to only torsional moments and not accompanied by axial forces or bending moment. in 1 Variational formulation Consider a shaft with a cross-section of arbitrary shape as shown in Fig. The document contains definitions, equations, and #2 Equation and Calcuator for Angular Deflection of Solid Cylinder or Shaft with Torsion Applied . 2 thoughts on “Torsion – Non-Circular Cross-Sections” seagull says: April 15, 2022 at 6:25 pm. Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6]. G = shear modulus of the material = Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F. (c) A plane cross-section remains plane after the application Torsion Jeevanjyoti Chakraborty jeevan@mech. every diameter rotates through the same angle. Now consider the section of a shaft under pure torsion as shown in Fig. Torsional rigidity of a shaft is defined as the torque The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. The angle in degrees can be achieved by multiplying the angle θ in radians with 180/π. The above conclusions are already known with reference to the case of the concentric annular circular shaft for which the solid shaft equation For an infinitely small section of shaft, the shear strain equation can be expressed in terms of differentials: \(\gamma=\frac{\rho(d \phi)}{d x}\). It then derives the elastic torsion formulas that relate torque, shear stress, angle of twist, and shaft geometry. Torsion is caused by twisting couples (torque) that creates rotation in structures like propeller shafts. The initially straight line AB deforms Factors affecting Angle of twist: The angle of twist in an object subjected to the torsional load depends on the following factors: Internal torque: Higher the torque, the angle of twist in the object will be higher. This results in a shear stress that is distributed over the cross-section of the shaft. 1 Deformation of a circular shaft caused by the torque T. Torsion Equation for Circular Shafts Now, circular shafts can be 'Solid' or 'Hollow'. The fiber AB on the outside surface, which is originally straight, will be twisted into a helix AB′ as the shaft is twist through the angle θ. Then, taking the shaft to be Describe the shear stress distribution within a circular shaft under torsion; Apply the torsion formula to calculate shear stresses under torsion; Calculate angle of twist and relate calculation to Hooke’s Law; Solve for stress and displacements (angle of twist) in statically indeterminate torsion problems; Explain why the torsion formula is Torsion - Download as a PDF or view online for free. For circular shafts, it equals the polar moment of inertia, ( J=2πr⁴/2 ), where ( r ) is the radius. Torque causes rotation, while torsion is the effect produced by torque. We will only consider circular cross-section shafts in Unified. Such a case is a case of pure torsion, Shaft is under pure torsion. T max = maximum twisting torque (Nm, lb f ft) τ max = maximum shear stress (Pa, lb f /ft 2) R = Following are the assumptions made for the derivation of torsion equation: Consider a solid circular shaft with radius R that is subjected to a torque T at one end and the other end under the same torque. 1 Solid round bar. Circular Shaft and Maximum Moment or Torque. For the solid circular shaft, the shear stress at any point in the shaft Torsion of Shafts - Free download as PDF File (. 3 Shearing Stress 10. Information about Torsion of Circular Shafts covers topics like and Torsion of Circular Shafts Example, for Mechanical Engineering 2024 Exam. 10. GATE ME 2023. For Solid Shaft T = torque or twisting moment in newton metres J = polar second moment of area of cross-section J=- r = 1 +_ Ad about shaft axis. If equal and opposite couples are applied at the ends of a circular shaft, they will either equilibrate or rotate at the same speed. As mentioned in the introduction to torsion, one common application in which one would encounter circular shafts subjected to torsion is in power transmission shafts. For narrow rectangular sections, kl = k2 = i. Shear stress increases linearly from zero at Instagram: https://www. Example calculations are also provided to demonstrate applying the formulas. Polar modulus is a measure of a shaft's resistance to twisting. e. Figure 2: Torsion equation for circular shaft. Solid shaft (π substituted) Torsion of a Circular Shaft. Venant's principle) of loaded sections and sudden geometrical changes such as a step or a circumferential groove; in such regions, the maximum shear stress can be much larger and other stress components may also Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. Fig. The torque causes shear stresses that vary linearly across the shaft cross-section, with a maximum at the in monograph [1]. Shear stress and shear strain will arise in the material of a shaft when it is subjected to a torsion or twisting moment. Torsion formula (circular elastic bars). Answer. 5) Slide No. 3. d applied in a plane perpendicular to the axis of the bar such a shaft is said to be in torsion. Therefore torsional stiffness equation can be written as, Torsional stiffness of solid circular shaft:-For a solid circular shaft of diameter ‘d’, `J=\frac{\pi M9 Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6. It requires the provision of adequate boundary conditions. 1, and subjected to a torque T at the end of the shaft. 4. For a circular shaft under torsion, every cross-section remains undistorted due to symmetry. Otherwise, the two ends are fixed and at the junction should be subjected to a torque T, then also the shafts are said to be in Note: shaft under torque T rotating at angular speed w transmits power: \[P=T\omega\] Symmetry of shear stress: stress in axial planes . 5, or hollow. iitkgp. The torsion equation helps in designing shafts, axles, TORSION OF HOLLOW SHAFTS: From the torsion of solid shafts of circular x 1 section , it is seen that only the material at the outer surface of the shaft can be stressed to the limit assigned as an allowable working stresses. It follows that at a corner the shear stress is zero. 8. When a shaft twists, one end rotates relative to the other and shear stresses are produced on any cross section. TORSION Consider a bar to be rigidly attached at one end and twisted at the other end by a torque or twisting moment T equivalent to F × d, which is applied perpendicular to the axis of the bar, as shown in the figure. 2. R = radius of the shaft. Torsion of Circular Shafts: Theory of pure torsion - Derivation of Torsion equations : T/J = q/r - N /L - Assumptions made in the theory of pure torsion - Torsional moment of resistance Secant formula - Empirical formulae - Straight line formula - Prof. what does the Ø mean in the table at the top of the page, with the The above diagram shows the torsional shear stress distribution in a hollow circular shaft. ) Cross-sections rotate as if rigid, i. ME 113_Torsion 11 Solid shaft: The required diameter d 0 is determined either from the allowable shear stress. Beams Curved in Plan: Introduction - circular beams loaded uniformly This is the nal governing equation we will use in the description of torsion based on the stress formulation. Key concepts covered include shear stress distribution in shafts under torsion, relationship between Where, G = Modulus of rigidity J = Polar moment of inertia L = Length of shaft. is the polar moment of inertia of the cross sectional area. This is the nal governing equation we will use in the description of torsion based on the stress formulation. The document discusses torsion of circular shafts, including pure torsion, assumptions in the theory of pure torsion, torsion formula, polar modulus, torsional rigidity, power transmitted by shafts, and numerical problems and solutions. It defines torsion as a moment applied perpendicular to the longitudinal axis of a bar. (c) The torque is applied at an angle. D = Diameter of the circular shaft. Figs. (c) The torque causes bending in the shaft. Obtaining the THEORY OF TORSION FORMULA • The following conditions are used in the torsion of the circular shaft: 1. ∫ r 2 /c τ max dA = T. pexye zwejzwh bhi pqjzqz ugwzlln vealqi mnfi xkncuqn yffm tvlhot