Statics and Strength of Materials
A piece of a framework or structure is called a "member". The members are pinned or hinged together and when a load is applied to it this is transferred to the structure via the joints.
A truss is a two-force member.
Each member is then either being squashed, or pulled apart. We say it is in a state of compression or tension.
Any frame structure, no matter how simple or complicated, must provide an equal and opposite reaction to the forces acting on it so that equilibrium is possible.
Test it out
Tap the diagram for more information and click on the buttons to change a component and see what happens!
Example calculations
In order to work with Statics and Strength of Materials, mechanical engineers need to understand and work with a variety of calculations. Here are just a few:
Static Equilibrium:
$\Sigma F = 0$
Hooke's Law:
$F = k \Delta L$
Young's Modulus (E):
$E = \frac{FL}{A \Delta L}$
Simple Bending Equation:
$\frac{M}{I} = \frac{\sigma}{Y} = \frac{E}{R}$
Moment of Inertia for Standard section:
$I_{xx} = \frac{BD^3}{12}$
$I_{yy} = \frac{BD^3}{12}$
 Force $F$ Inertia $I$ Maximum Moment of Resistance $M$ Stress $\sigma$ Elongation $\Delta L$ Elasticity $E$
In order to build strong objects and structures that can perform a particular purpose, we need to understand the forces acting on that object, and how it's framework and materials handle stress and strain when it's being used. This strength comes down to different factors, such as its physical resistance to cracking, twisting or deformation, as well as the shape of the object or frame being created. In vehicles, areas that might be affected include the car body, the suspension, chassis, axel or even seatbelts.
When we study mechanics, we analyse how an object, framework, material or body behaves when forces are applied to it. In Statics, we look at how internal and external forces act on a stationery object, and in Dynamics, we analyse bodies that are moving, such as machine parts.
Strength of materials is a related field that often depends on a static body being balanced, or in equilibrium. For example, how do we create a car jack that is made from the right material, and has the right shape, so that it is strong enough to lift a car, and keep the car in position without bending, or breaking? Yes, they might change shape a little, but they'll be able to tolerate stress and strain up to a point, and still fulfil their purpose.
Sometimes, we also need to think about areas or materials that need to fail on purpose, so we can control how force move through a body. Think about a crumple zone of a car. In a crash, this area helps shift some of the car’s kinetic energy and impact of the crash into a controlled buffer zone. The material crumples, which creates more damage to the car, but helps protect the person inside.
Practice Questions
Test your new knowledge on statics and strengths by answering these questions.
1. When is a body in a state of static equilibrium?
2. What happens when the stress on an object is too great?
3. A steel bar of 10mm is resting on the ground, and heated from 30˚C to 45˚C. What type of stress is it experiencing?