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 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
• 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
• 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
• 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