Finding Force on a Surface: Mechanics Basics

[chandran]

I was just working on a mechanics problem of finding the stress at a cross
section of a member. The example problems on mechanics give the solution as
follows.

1.cut a freebody diagram at the cross section of interest

2.The solution then says that a force acts normal to the surface(normal force),one more force parallel to the surface(shear force) and force that
turns the section(bending moment and hence a force).

3.Put an arrow representing all the forces.


My worrying and confusing point is point no.3. Inside the cross section where should i put the force. For example for a normal i can put an arrow on the normal to the surface but at any point.


usually all the example problems show the force at the centre of the section
(centroid).


I will now come from the basics. A force is a push or pull. When i put a force
at the centroid the centroid(small area around the centroid) will be pushed to some depth compared to their surrounding. but when i apply a force(push/pull) that point(a small area) only will be pushed
or pulled.

So which is the correct place in the cross section to be considered for a force to act?

 

[FredGarvin]

Take a look at the attached. This is the usual approach to looking at combined forces on a surface.

http://www.mech.uwa.edu.au/DANotes/SSS/loads/blocks.gif

 

[chandran]

fred,
the first one in the image, the tensile force on the surface is of confusion to
me. How can we say that the force acts at the centre of the surface.

 

[pack_rat2]

Do you have a picture of the member the problem refers to, which shows the external force(s) acting on it?

 

[chandran]

PAT. i HAVE ATTACHED THE FILE.
my question is as follows. To analyse force components on a surface
we usually put the force symbol at the centroid.

Imagine that we push(i.e give a force) at the centroid of a surface then
the small area at the centroid only will be pushed and not the entire surface

 

[FredGarvin]

It is an assumption that is made in most cases that is very much justifyable. Most times when dealing with basic stress analysis, the loading is in the elastic range of the material so no permanent deformations occur and the loading is gradually applied. It is a simplifying assumption that the load is placed in the centroid and the material to facilitate an equal stress distribution across the section you are looking at. This is not always possible or wise, but when learning the basics, it is perfectly acceptable to assume that the stress will be evenly distributed across the face.