polar moment of inertia equations circle

In structural design the use of sections i.e I sections, channel section, angle sections etc. Torsion constant for circular and non circular sections. Important Note : In the notes and tables below J is used throughout for the Table value 2,97 η = 1,10 Torsion in Sections. Table value 63 η = 1Ģ) Channel section 100x50x10 calculated J' = 2,39 cm 4. Testing the values of J' obtained using the above equations (with η = 1) with the values obtained from the tableġ)Channel section 430x100圆4 calculated J' = 63,118 cm 4. The general formula of torsional stiffness of bars of non-circular section are as shown below the factor J' is dependent of theĭimensions of the section and some typical values are shown below. Stress in a section is not necessarily linear.

G Modulus of rigidity (N/m 2) θ angle of twist (radians) Formulasįormulas for bars of non - circular section.īars of non -circular section tend to behave non-symmetrically when under torque and plane sections to not remain plane. R o = radius of section OD (m) τ = shear stress (N/m 2) R = radial distance of point from center of section (m) K = Factor replacing J for non-circular sections.( m 4 ) J' = Polar moment of inertia.(Non circluar sections) ( m 4 ) J = Polar moment of inertia.(Circular Sections) ( m 4 ) The equations are based on the following assumptionsġ) The bar is straight and of uniform sectionĢ) The material of the bar is has uniform properties.ģ) The only loading is the applied torque which is applied normal to the axis of the bar.Ĥ) The bar is stressed within its elastic limit. This page includes various formulas which allowĬalculation of the angles of twist and the resulting maximums stresses. To a level greater than its elastic limit. This assumes that the bar is not stressed To its axis will twist to some angle which is proportional to the applied torque. Therefore equation and equation give the radius of gyration of the body.A bar of uniform section fixed at one end and subject to a torque at the extreme end which is applied normal

Thus the total mass of the body can be given by,

Polar moment of inertia equations circle