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2868 results in Solid mechanics and materials

Page 2 of 144

  • Chapter 3 - Stress Analysis

  • S. K. Roy Chowdhury, Indian Institute of Technology, Kharagpur, Prasanta Sahoo, Jadavpur University, Kolkata
  • Book:
    An Introduction to Solid Mechanics
    Published online:
    28 February 2025
    Print publication:
    31 December 2025, pp 35-59

  • Summary

    Learning Objectives

    After careful study of this chapter, students should be able to do the following:

    • LO1: Define stress at a point.

    • LO2: Describe stresses on an oblique plane.

    • LO3: Define principal stresses, hydrostatic, and deviatorial stress tensor.

    • LO4: Calculate shear stresses.

    • LO5: Construct Mohr's circle.

    • LO6: Analyze equations of equilibrium.

    3.1 STATE OF STRESS AT A POINT [LO1]

    When a body is subjected to external forces, its behavior depends on the magnitude and distribution of forces and properties of the body material. Depending on these factors, the body may deform elastically or plastically, or it may fracture. The body may also fail by fatigue when subjected to repetitive loading. Here we are primarily interested in elastic deformation of materials.

    In order to establish the concept of stress and stress at a point, let us consider a straight bar of uniform cross-section of area A and subjected to uniaxial force F as shown in Figure 3.1. Stress at a typical section A - A′ is normally given as σ = F/A. This is true only if the force is uniformly distributed over the area A, but this is rarely true. Therefore, definition of stress must be considered by progressively reducing the area until it is small enough such that the force may be considered to be uniformly distributed.

    To understand this, consider a body subjected to external forces P1, P2, P3, and P4 as shown in Figure 3.2. If we now cut the body in two pieces,

    Internal forces f1, f2, f3, etc. are developed to keep the pieces in equilibrium. Now consider an infinitesimal element of area ΔA Dat the cut section and let the resultant force on the element be Δf.

Mechanical Behavior of Materials
  • 3rd edition
  • Marc A. Meyers, Krishan K. Chawla
  • Published online:
    31 October 2025
    Print publication:
    22 May 2025
  • Fully revised and updated, the new edition of this classic textbook places a stronger emphasis on real-world test data and trains students in practical materials applications; introduces new testing techniques such as micropillar compression and electron back scatted diffraction; and presents new coverage of biomaterials, electronic materials, and cellular materials alongside established coverage of metals, polymers, ceramics and composites. Retaining its distinctive emphasis on a balanced mechanics-materials approach, it presents fundamental mechanisms operating at micro- and nanometer scales across a wide range of materials, in a way that is mathematically simple and requires no extensive knowledge of materials, and demonstrates how these microstructures determine the mechanical properties of materials. Accompanied by online resources for instructors, and including over 40 new figures, over 100 worked examples, and over 740 exercises, including over 280 new exercises, this remains the ideal introduction for senior undergraduate and graduate students in materials science and engineering.

Foundations and Applications of Engineering Mechanics
  • H. D. Ram, A. K. Chauhan
  • Published online:
    26 June 2025
    Print publication:
    16 March 2015
  • Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.

Strength of Materials
  • Fundamentals and Applications
  • T. D. Gunneswara Rao, Mudimby Andal
  • Published online:
    03 June 2025
    Print publication:
    13 August 2018
  • Designed for a single-semester course on strength of materials, this textbook offers detailed discussion of fundamental and advanced concepts. The textbook is written with a distinct approach of explaining concepts with the help of solved problems. The study of flexural shear stress, conjugate beam method, method of sections and joints, statically determinate trusses and thin cylinders is presented in detail. The text discusses advanced concepts of strength of materials such as torsion of non-circular sections, shear center, rotating discs, unsymmetrical bending and deflection of trusses. The textbook is primarily written for undergraduate mechanical and civil engineering students in India. Numerous review questions, unsolved numerical problems and solved problems are included throughout the text to develop clear understanding of fundamental concepts.

Page 2 of 144