ENGR 107 – Introduction to Engineering Static Equilibrium, and Stress and Strain (Lecture #8)

ENGR Introduction to Engineering2 Static Equilibrium

ENGR Introduction to Engineering3 Static Equilibrium Example: Fig. 7.38

ENGR Introduction to Engineering4 Static Equilibrium Example: Fig. 7.40

ENGR Introduction to Engineering5 Static Equilibrium Example: Fig. 7.44

ENGR Introduction to Engineering6 Stress

ENGR Introduction to Engineering7 Deformation Forces will tend to deform or change the shape of any body. An extremely large force may cause observable deformation. In most applications, slight deformations are experienced, but the body returns to its original form after the force is removed.

ENGR Introduction to Engineering8 Deformation The engineer must design a structure within limits that allow it to resist permanent change in size and shape so that it can carry or withstand the force (load) and still recover.

ENGR Introduction to Engineering9 Stress The force applied on a body is assumed to be equally shared over the entire cross-sectional area. The stress on a body is the force per unit area resulting from the applied load.  = F / A  = stress (Pa) F = force (N) A = cross-sectional area (m 2 )

ENGR Introduction to Engineering10 Stress Figure 7.22 (p. 232)

ENGR Introduction to Engineering11 Types of Stress Tensile  Tends to pull the atoms apart  Acts perpendicularly to the plane of the cross-sectional area. Compressive  Tends to push the atoms together  Acts perpendicularly to the plane of the cross-sectional area.

ENGR Introduction to Engineering12 Types of Stress Shear  Tends to slide the layers of atoms in the body across each other  Acts in a direction that is parallel to the plane of the cross-sectional area.  = F / A  = shear stress (Pa) F = force (N) A = cross-sectional area (m 2 )

ENGR Introduction to Engineering13 Shear Stress Figure 7.23 (p. 233)

ENGR Introduction to Engineering14 Stress Example: Problem 7.39(a)

ENGR Introduction to Engineering15 Stress Example: Problem 7.41(a)

ENGR Introduction to Engineering16 Stress Example: Problem 7.42(a)

ENGR Introduction to Engineering17 Strain

ENGR Introduction to Engineering18 Strain The design engineer must consider not only the external forces applied to a system, but also the strength of each individual part or member that comprise the system. Each component must be strong enough, yet not contain an excessive amount of material. Thus, knowledge of material properties is essential in Engineering Design.

ENGR Introduction to Engineering19 Strain Strain (  ) is defined as a dimensionless ratio of the change in length (elongation) to the original length.  =  L / L =  / L  = strain (mm / mm)  = deformation (mm) L = length (mm)

ENGR Introduction to Engineering20 Strain Example:

ENGR Introduction to Engineering21 Strain Example:

ENGR Introduction to Engineering22 Stress and Strain Linear relationship between stress and strain. For stresses below the proportional limit,    = strain (mm / mm)  = stress (Pa)  = proportionality constant  = Modulus of Elasticity Hooke's Law

ENGR Introduction to Engineering23 Stress and Strain Example: