This is a complete summary for the mechanics of materials/strength of materials part of the biomechanics course. It entails the content of the lectures given within this part of the course as well as additional information from the corresponding book sections.
Mechanics of materials
- This is a branch of mechanics that develops relationships between the external loads
applied to a body and the intensity of internal forces and stresses acting within the
body.
- Studies the stability of the body under applied loads and also computes the
deformation of the body.
Mass: the property of a body that causes it to have weight in a gravitational field
Units: g, kg, lb, tonne, stone …
Force: equals mass multiplied by acceleration
F=ma Units: N
Weight: the vertical force exerted by a mass as a result of gravity
F = mass * g
Load: all the forces and moments acting on a surface or body
What is a “tangent” to a surface?
Line parallel to the surface at a particular point
What is a “normal” to a surface?
Line perpendicular to the surface at a particular point
Internal loading – Chapter 7
Relationship between applied external loads to the body and the intensity of internal forces
You can see a very non-geometric object with 4
different forces acting on it. All of these forces
are randomly oriented and have randomly hit
random magnitude. From statics we know that
we can make a cut as shown by the red plane.
When we make this cut we can see that there will be an
infinite number of internal forces illustrating the complexity of
the situation. The forces with the arrow upwards are tensile
forces whereas the arrow pointing towards the cut surface is
compressive. Ultimately all of them together balance F1 and
F2. That is why this object remains in place and does not
rotate.
,If we take a center point or a center of gravity on
this surface we can determine the causing forces.
We have taken one force of the many previously
shown. It can be resolved into the parallel surface
and the perpendicular surface. We now have 2 new
forces that are located at a distance r from the
center point. If we look at the perpendicular force
the resulting force it is able to do 2 things:
1. It will pull the object upwards in reference
to the center point.
2. It will try to rotate the object in reference to
the center point. Fx is able to cause a normal force at the center point and a bending
moment which tries to rotate the object
If we look at the force parallel to the surface, it will give rise to two resultant forces
1. Will try to shift the object above this object to the left by a shear force.
2. It is also going to give rise to a torsional moment T
So, you can see there are 2 moments and 2 forces. So, the forces on the object will be a
sum total of N M T V at the center point.
When we sum all of the effects of the forces at
the center point O, we get that there will be a
resultant force in a certain direction as well as a
resultant internal moment in a certain direction.
This Fr and Mr are able to balance F1 and F2 so
this object can remain stationary and it does not
rotate in any axis.
If we look at this force in a certain direction it can be
resolved into two directions based on the cartesian system
(XYZ axis). We see that one of the components of Fr would
be along Z which is the total normal force acting at the
center point due to all of the different kind of forces as act
acting on the surface of the other components.
The other component of Fr would be shear force. Fr will
cause a lot of shear force and normal force at the center
point.
,The normal tries to pull the two parts of the object apart.
We have made a section in the blue plane and the
resulting force Nz will have a tendency to pull the two
parts apart.
Normal force acts perpendicular to the area on which it
acts
Force which was acting parallel to the area – shear force.
Shear force tries to shift the top part of the object relative
to the bottom part of the object
This can be observed in the image on the right. There are
two sheets of metal with a hole that are connect by a bolt,
which holds the two sheets in place. The two sheets are
being pulled in opposite directions.
Note: the nut and the bold are not extremely tight so there
is no friction at the interface and all of the load is help by
the presence of the nut and bolt.
, If we cut open the bolt, we are only looking at the
bottom plate and part of the bolt. You can see that
there must be forces on this cross section, which are
going to balance the force P acting on this sheet of
metal.
These forces are shear forces which balance the force
pulling the sheet towards the right-hand side
direction. Shear forces give rise to shear stresses
Shear force is tangential so it lies in the plane of the
area and normal forces acted perpendicular to the
plane of the area.
This resultant internal moment can also be solved in 2
directions. One is perpendicular to the area on which it is
acting called torsional moment. The force which is in the
plane is called the bending moment.
The torsional moment tries to rotate the top part of the
object relative to the bottom part/ it tries to twist the
object
If torsional moment was experienced on the closer end,
we see that the circular sections have remained circular
and the lines have remained as lines which are pretty
much parallel to each other. The only change is that the
lines have become twisted but were parallel originally.
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