At a particular point in a structural member a direct tensile stress of 60 N/mm² exists on a plane perpendicular to the longitudinal axis of the member while a direct compressive stress of 40 N/mm? occurs on a plane parallel to this axis; in addition shear and complementary shear stresses of 50 N/mm? act on these planes. If Young's modulus E is 200000 N/mm² and Poisson's ratio v is 0.3 calculate the direct and shear strains on these planes and hence, using a graphical method, determine the principal strains at the point, the maximum shear strain and the angle the plane of maximum principal strain makes with the longitudinal axis of the member. Finally, calculate the principal stresses at the point. Ans. E= 3.6x104, ɛ, = -2.9x104, Yy=6.5x10-4 ɛ1 = 4.95x10, 01 = 80.8 N/mm², o1=-60.8 N/mm2. Ɛ11 =-4.25x10 Ymax=9.2x10-, 67.5°

At a particular point in a structural member a direct tensile stress of 60 N/mm² exists on a plane perpendicular to the longitudinal axis of the member while a direct compressive stress of 40 N/mm? occurs on a plane parallel to this axis; in addition shear and complementary shear stresses of 50 N/mm? act on these planes. If Young's modulus E is 200000 N/mm² and Poisson's ratio v is 0.3 calculate the direct and shear strains on these planes and hence, using a graphical method, determine the principal strains at the point, the maximum shear strain and the angle the plane of maximum principal strain makes with the longitudinal axis of the member. Finally, calculate the principal stresses at the point. Ans. E= 3.6x104, ɛ, = -2.9x104, Yy=6.5x10-4 ɛ1 = 4.95x10, 01 = 80.8 N/mm², o1=-60.8 N/mm2. Ɛ11 =-4.25x10 Ymax=9.2x10-, 67.5°

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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