problem1 - 22.314/1.56/2.084/13.14 Fall 2006 Problem Set I...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 22.314/1.56/2.084/13.14 Fall 2006 Problem Set I Due 09/19/06 1. A tensile test on 1020 steel gives the following results: Load (kN) Diameter (mm) 0 12.8 22.2 – 28.5 – 50.2 12.2 51.2 (Max.) 10.4 43.6 – Length (mm) 50.800 50.848 –(yielding begins) 56.1 67.3 69.8 (fracture) (a) Calculate the elastic modulus. (b) Calculate the maximum nominal strain. (c) Calculate the tensile strength of this steel. 2. Calculate the maximum normal stress and the maximum shear stress in the cube shown below. 1 3. This problem illustrates some important stress tensor concepts and some calculation methods for treating a stress tensor. Consider three stress tensors σa , σb , and σc defined as follows: ⎡ ⎤ 55 −5 30 ⎢ ⎥ σa = ⎣ −5 55 30 ⎦ ; 30 30 20 ⎡ ⎤ −10 0 0 ⎢ ⎥ σb = ⎣ 0 −10 0 ⎦ ; 0 −10 0 σc = σa + σb where the stresses are given in MPa units. (a) What are the three principal stresses that characterize each of these stress tensors ? (b) Draw a 3-D Mohr’s circle to represent the three stress states. (c) Also place points on your Mohr’s circles that give the stresses on planes normal to each of the original coordinate axes (x, y, z). (d) What are the unit vectors (direction cosines) that define principal directions for the three stress tensors? (e) What is the Tresca Stress for each stress tensor? What is the von Mises Stress for each stress tensor? 2 ...
View Full Document

This note was uploaded on 02/24/2012 for the course MECHANICAL 2.084J taught by Professor Mujids.kazimi during the Fall '06 term at MIT.

Ask a homework question - tutors are online