Introducing and Classifying Materials

6. Define stress and explain how it is different from pressure although both use the same units.

• Stress = (force) / (unit of area) at any given point inside an object
• Pressure = (force) / (unit of area) applied to the outside surface of an object
• Pressure is an external load. Stress is an internal condition resulting from external loads of forces and pressures.

7. Define strain: the ratio of a change in dimension to the original value of that dimension.

8. Calculate a tensile or compressive stress given a force and area.

9. Calculate a tensile or compressive strain given an original dimension and the change in the dimension.

10. Mechanical Properties

• tensile strength - the amount of tensile stress a material can withstand before failure

  • yield stress - max stress before permanent deformation

  • ultimate tensile stress - max stress before catastrophic failure

  • rupture stress - max stress at catastrophic failure

• stiffness - modulus of elasticity or Young's modulus

• toughness - resistance to abrasion and cutting. Work required to make a material fail catastrophically. Tough materials are generally not brittle.

• ductility - ability to extrude

• malleability - ability to shape plastically. Note: the IB syllabus makes a special point to make a distinction between ductility and malleability. For all practical purposes. ductile materials are also malleable.

9. Explain a design context where each of the above properties is an important consideration.

Draw and describe a stress/strain graph (see at right) elastic region yield stress plastic flow region ultimate stress (UTS).

11. Explain the relationship of the 2 most common structural members (beams and columns).

• Beams : horizontal
• Columns: vertical

12. Explain how both modulus of elasticity and moment of inertia are related to stiffness.

• Modulus of elasticity or Young’s modulus (a material property) - directly proportional to stiffness
• Area Moment of inertia (a design property) - directly proportional to stiffness

13. Calculate the Young’s modulus of a material.

    (Young’s modulus) = stress / strain

14. Calculate area moment of inertia for a beam with a rectangular cross section.

I ₀ = (bh³) / 12

 

where:

I ₀ = Area Moment of Inertial for a rectangular cross section of a beam

b = width

h = height in the direction of the load

15. Define elastic stability (the tendency of a structure to resist buckling) and state why it is an important consideration in design.
16. Give examples of elastic instability.

• External pressure applied to a plastic soft drink bottle's exterior
• Long thin columns