NED UNIVERSITY OF ENGINEERING & TECHNOLOGY Department of Civil Engineering CE 502 –Advanced Mechanics of Solids HW # 3 (Fall 2021) Name:__________________________________ Roll No.: Due on: Monday, 24th January 2022 1. Problem 1-1 (Martin Sadd) 2. Problem 1-3 (Martin Sadd) 3. Problem 1-4 (Martin Sadd) 4. Problem 1-5 (Martin Sadd) 5. Problem 1-9 (Martin Sadd) 6. (a) Consider a square plate of unit size defined as shown. Find all the Lagrangian and Eulerian strain components. (b) Repeat the problem in (a) but with the angle of distortion reduced from 30o to 1o. Comment on the influence of reduced deformations on the Lagrangian and the Eulerian strain components. 7. A circular cylinder in its undeformed configuration has radius ‘a’ and its axis lies along X3 axis. It undergoes the deformation: x1 = X1 cos (βX3) + X2 sin (βX3), x2 = -X1 sin (βX3) + X2 cos (βX3), x3 = X3 where β is a constant. A line drawn on the surface of the cylinder has unit length and is parallel to the axis of the cylinder (X3-axis). Determine the length of the line after deformation in terms of radius ‘a’ and the constant β. 1 3 2 8. The strain tensor at a point is given by ij 3 1 2 2 2 4 i. Find the principal stresses ε1, ε2 and ε3 ii. Find the maximum shearing strain at the point. iii. Obtain the transformation tensor relating the principal axes xi* to the coordinate axes xi. ^ ^ ^ e e e iv. Find the normal strain in the direction of 1 2 3 2 2 2 ^ ^ ^ ^ e e e v. Find the shear strain between and 1 2 3 2 2 2 ^ ^