StrengthsChapter 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 l+ @

after the tensile load P is applied. The total deformation is @ 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 10-4 10-5 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 367 10-6• 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 10-10 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 10-10 page 373• G is a constant of proportionality called the shear modulus of

elasticity or the modulus of rigidity.• Example 10-11 page 373