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Lesson 02 average normal strain learning outcomes statics review Originally the cable is unstretched. Explain the relationship between deformation and force in a spring

Answered: Learning Goal: To determine the average normal strain and

Recall that fixed planes may not translate (they are constrained) and that free planes may translate (they are unconstrained) If a force is applied at the end d of the member and causes a normal strain in the cable of 0.0035 mm/mm, determine the displacement of point d Explain the concepts of elongation and shortening.

Normal strain, which is a unitless ratio, represents the proportional change in a material's dimensions due to the applied force

Consequently, a positive normal strain suggests elongation, while a negative one indicates compression This graphical representation helps to visualize the relationship between stress. Strain is a unitless measure of how much an object gets bigger or smaller from an applied load Normal strain occurs when the elongation of an object is in response to a normal stress (i.e

Perpendicular to a surface), and is denoted by the greek letter epsilon A positive value corresponds to a tensile strain, while negative is compressive. Force per unit area, acting tangential to a given plane and at a given point (e.g., shear stress at point (x,y,z) on cross section with normal x)

Normal strain of a body by changes in length of line segments and the changes in the angles between them, we will develop the concept of strain

Strain is measured by experiments, and once the strain is obtained, it will be shown in the next lecture how it can be related to the stress acting within the Engineering or nominal (normal) strain Average normal strain using original (undeformed) total length What does normal strain mean

This property can be defined by the formula below Ε = δl / l where Ε = normal strain δl = change in length l = original length normal strain is sometimes referred to dimensional strain. Normal strain expressed in this way is also a form of engineering strain

Therefore, the strain is defined at a given point q by considering a small element of undeformed length δ x

Denoting by δ δ the deformation of the element. A normal strain is perpendicular to the face of an element, and a shear strain is parallel to it These definitions are consistent with those of normal stress and shear stress Normal strain for an isotropic material that obeys hooke's law, a normal stress will cause a normal strain

Explain the concepts of elongation and shortening Understand similarities between deformation in a spring and in a solid bar Differentiate between translation and deformation Memorize and apply the definition of axial deformation

Understand and apply the equation for average normal strain.

A load p p and distance l l are measured at frequent intervals. Determine the average to determine the average normal strain and average shear strain in a known material based on a given load and geometry A flat plate abcd distorts into the dashed shape ab'c'd shown after a load is applied with a = 129.0 mm , b = 51.0 mm , g = 18.0 mm , f = 10.0 mm , and e = 13.0 mm. Determine the average normal strain along diagonal ac and the shear strain of point e with respect to the x and y axes

4 mm 300 mm i 300 mm problems 2—1 Example problem:determine the average normal strain in a deformed body. Determine the normal strain developed in wire bd If the air pressure within it is increased until the ball's diameter becomes 7 in, determine the average normal strain in the rubber

Identify the two simple stresses

Memorize and apply the equation and sign convention for average normal stress Memorize common units for force per area (pa, kpa, mpa, gpa, psi, and ksi) Illustrate the distribution of average normal stress on a plane Illustrate average normal stress at a point on a 2d stress element and a 3d stress cube.

The rectangular plate is deformed into the shape shown by the dashed lines Determine the average normal strain along diagonal ac, and the average shear strain at corner a relative to the x, y axes ± average normal strain and average shear strain learning goal To determine the average normal strain and average shear strain in a known material based on a given load and geometry.

Determine the average normal strain that occurs along the diagonals ac and db

Trigonometry part of a control linkage of an airplane consists of a rigid member cdb and a flexible cable ab