Basic Definitions in Structural Analysis and Design

Stress: The force of resistance offered by a member per unit area is called stress The external force acting on it is called load. The load is applied on the body and the stress is induced in the material of the body.

Stress = Force(P)/ Area(A) N/mm²

Strain: Due to the application of load, the length of a member will change. The ratio of change in length to the original length of the member is called Strain.

Strain (e) = change in length (dl)/original length (l)

Tensile Stress: The force of resistance offered by a section of a member, against an increase in length, is called tensile stress. The corresponding strain is called tensile strain.

Compressive Stress: The force of resistance offered by a section of a member due to pushing against a decrease in length allied Compressive stress. The corresponding strain is called Compressive strain.

Temperature Stresses (α): A member will offer stresses if natural change in dimensions is restricted due to rise and fall in temperatures.

Temperature stress = α TE

Where, α = Coefficient Of thermal expansion,

T= temperature rise

E= Elastic Modulus.

Temperature Strain = Expansion or Contraction prevented /Original length.

Young's Modulus: The Young Modulus, E is a material property that describes its stiffness and is therefore one of the most important properties in engineering design Within the limits of elasticity, the ratio of the linear stress to the linear strain is termed the modulus of elasticity or Young'sModulus

Young's Modulus (E) = Stress/Strain

This property determines how much a bar will sag under its own weight or under a loading when used as a beam within its limit of proportionality.

Poisson Ratio: Poisson's ratio deals with the way stretching or compressing an object in one direction causes it to compressor stretch in the other direction. The ratio measures the extent of this effect in a particular substance.

The technical definition of Poisson's ratio is "the ratio of transverse contraction strain to longitudinal expansion strain.”

In most cases, Poisson's ratio is positive, meaning a material stretches in one direction by a greater degree than it contractsin other directions. In most cases, a material's Poisson ratio will range between 0 and 0.5. Among common materialrubber has a Poisson ratio very close to 0.5, whereas steel has one of 0.3 and cork is much closer to 0.

Density: Density is a physical property of matter, as each element and compound has a unique density associated with it Density defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume.

Density is defined as the mass per unit volume of a substance. It can be expressed as follows:

Density = mass/volume

Shear Modulus: The shear modulus is one of several quantities for measuring the stiffness of materials. In materials science, shear modulus or modulus of rigidity, denoted by G, is defined as the ratio of shear stress to the shear strain. 

Coefficient of thermal expansion: All materials change their size when subjected to a temperature change as long as the pressure is held constant. The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in volume per degree change in temperature at a constant pressure. 

Shear Force: The sum of vertical forces at a given section of a member is defined as shear Force. 

Bending Moment: The algebraic Sum of all the moments at a given section of a member is defined as the Bending moment. 

Structural Analysis: Structural analysis is defined as the calculation of the response of structures to actions. 

Design: Design of a structure is to assess the loads and to provide members of sufficient proportions to resist the assessed loads with a sufficient margin of safety. 

Design Basics: All the component members are to be arranged so that they transmit their self-weight and other superimposed loads to foundation or supporting structure by cheapest means to satisfy the requirements of architecture and structural stability Design should be made in accordance with the principles of mechanics, recognized methods of design and sound engineering practice. Consideration should be given to the effects of continuity on the distribution of bending moment and shear force due to monolithic construction. Structural members should be designed to have strengths at least equal to the structural effects of design load at all sections. 

Idealization of Structures: To carry out practical analysis, it is necessary to idealize a structure. Their censorial axes normally represent the members. There may be difference between clear spans and center-to-center spans ordinarily used in analysis. These differences can be ignored unless the cross-sectional dimensions of members are sufficiently large to influence the results. The idealized form of a structure is shown in the following image. 

Idealized Structure: Usually, a single line represents the centroidal axes or the edges of the members. Sometimes towlines are drawn to indicate the depth of the members and unless the depth of the member is specified, it is disregarded in analysis.