Strengths Chapter 10 Strains

1-1 Intro Structural materials deform under the action of forces Three kinds of deformation Increase in length called an elongation A decrease in length called a contraction Change in shape called an angular distortion Deformation per unit length is called linear strain

10-2 Linear Strain Axial forces applied to a member tend to elongate or compress the member Original length L of the member is elongated to a length after the tensile load P is applied. The total deformation Greek lowercase letter delta Linear strain defined as deformation per unit of original length of the unstressed member Formula 10-1 page 357 and page 358

10-3 Hooke’s Law Linear relationship exists between stress and strain – to a point – stress is proportional to the strain – beyond this limit stress will no longer be proportional to strain – limiting value is called the proportional limit of the material – this relationship is called hooke’s law formula 10-2a page 358 Modulus of elasticity expressed usually as psi or ksi or GPa or Mpa Modulus of elasticity indicates its stiffness or ability of material to resist deformation 210gpa for steel and 70gpa for aluminum – aluminum will stretch three times more than steel of the same length when subjected to the same stress.

10-4 Axial Deformation Axial loaded member elongates under a tensile load and contracts under compressive load – can be computed as long as it does not exceed proportional limit Figure 10-2 and formulas page 359 For structural materials the moduli of elasticity for tension and for compression are the same, so they will work for compression or tension – tension forces are positive – compression forces negative. Example 10-1 page 360 Example 10-2 page 360 Example 10-3 page 362

10-5 Statically Indeterminate problems When unknown forces in structural members cannot be determined by the equilibrium equations alone – structure is said to be statically indeterminate – statically indeterminate problems – involve axially loaded members to be analyzed by introducing the conditions of axial deformations Example 10-4 page 363 Example 10-5 page 364 Example 10-6 page 365

10-6 Thermal Stresses Homogeneous materials deformation due to temperature change can be calculated using formula page Stresses produced by a temperature rise or drop are called thermal stresses Example 10-7 page 368 Example 10-8 page 368 Example 10-9 page 369

10-7 Poisson’s ratio When a bar is subjected to an axial tensile load, it is elongated in the direction of the applied load at the same time its transverse dimension decreases Axial compressive load is applied to the bar the bar contracts along the axial direction while its transverse dimension increases Formula 10-7 page 371 Examples page 371

10-8 shear strain A shear force causes shape distortion of a body Total deformation occurs over a length Shear strain is thus the change in radians in a right angle between tow perpendicular lines. Use of hookes law Formula page 373 G is a constant of proportionality called the shear modulus of elasticity or the modulus of rigidity. Example page 373