Topic 9 Structures
Unit Plan 
Practice Test 
Study Guide 

Objectives 
Introducing and Classifying Materials
 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.

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

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

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

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.

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).





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

Beams : horizontal

Columns: vertical

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

Calculate the Young’s modulus of a material.
(Young’s modulus)
=
stress / strain

Calculate area moment of inertia for a beam with
a rectangular cross section.
 I _{0} = (bh^{3}) /
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

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

Give examples of elastic instability.

External pressure applied to a plastic soft
drink bottle's exterior

Long thin columns

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