# STEP-BY-STEP SOLUTIONS: PROBLEMS IN SOLID MECHANIC. 2

Al Emran Ismail

## Synopsis

This tutorial book is designed to help students in understanding the contents of solid mechanics 2 teaches in the Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia. In order to comprehensively understand the contents, students are required to sit for solid mechanics 1 successfully.  There are six sub-contents of this syllabus such as Strain transformations, Beam deflections, Column buckling, Strain energy method, Thick cylinders, and Theories of elastic failure.

The first content focused on the strain transformation when the element is rotated at a certain degree of orientation. The concepts of principal strains are introduced and they are solved using the equation of principal strains and Mohr’s circle. The applications of strain gauges are emphasized in measuring surface strains on engineering materials and structures. The stress-strain relationship is discussed and utilized.

The second content is on the determination of deflection and slope of the beam under loading. Two methods of solving such problems are introduced. First method is on the use of integration method. The second one is on the implementation of Macaulay’s method to determine the deflections and slopes. Third content is on the buckling of column under axial and eccentric compressive loading. The derivation of critical force is emphasized for both axial and offset loading conditions. Then, it is used to solve the varieties of buckling problems.

The determinations of strain energy of simple shape mechanical components are concentrated. Then, Castigliano’s theorem is introduced and used to calculate the displacements and slopes on engineering structures. This theorem is basically based on the strain energy concept. In solid mechanics 1, students are introduced with the thin cylinder and now in solid mechanics 2, students are exposed with the thick cylinder. First, students are introduced on the Lame’s equation which can be used the problems of thick cylinders. Graphical method is also emphasized in order to solve similar problems. Last content of this book is on the theories of elastic failure. Five basic theories of failures are discussed and applicable for ductile and brittle materials only. On the same time, students are exposed how to predict whether the structures are safe or not under certain type of loading.

1 January 2019

## Details about the available publication format: PDF

PDF

### ISBN-13 (15)

978-967-2216-99-5

## How to Cite

Al Emran Ismail. (2019). STEP-BY-STEP SOLUTIONS: PROBLEMS IN SOLID MECHANIC. 2. Penerbit UTHM. https://publisher.uthm.edu.my/omp/index.php/penerbituthm/catalog/book/248