# Finding Force on a Surface: Mechanics Basics

• chandran
In summary, the conversation discusses finding the stress at a cross section of a member in a mechanics problem. The solution involves creating a freebody diagram and placing forces on the surface, including a normal force, a shear force, and a bending moment. The question arises about where to place the force on the cross section, with the example problems typically showing the force at the centroid. There is also a discussion about the justification for this assumption and its applicability in basic stress analysis.
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?

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

Last edited:
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.

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

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

#### Attachments

• FORCE.gif
20.8 KB · Views: 500
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.

## 1. What is force on a surface?

Force on a surface refers to the amount of pressure or push that is exerted on an object by another object or surface. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is force on a surface calculated?

Force on a surface can be calculated by multiplying the mass of an object by its acceleration, using the equation F = ma. It can also be calculated by measuring the pressure on a surface and multiplying it by the surface area.

## 3. What are some examples of forces on a surface?

Examples of forces on a surface include gravity, friction, and normal force. Gravity is the downward force exerted on an object by the Earth, while friction is the force that opposes motion between two surfaces in contact. Normal force is the force exerted by a surface to support an object placed on it.

## 4. How does the angle of a surface affect force?

The angle of a surface can affect the amount and direction of force. For example, if an object is on an inclined plane, the force of gravity pulling it down will be split into two components: a force parallel to the surface and a force perpendicular to the surface. The steeper the angle of the surface, the greater the perpendicular force and the smaller the parallel force.

## 5. How can the force on a surface be changed?

The force on a surface can be changed by altering the magnitude or direction of the force acting on the object, or by changing the properties of the surface itself. For example, increasing the mass of an object will increase the force it exerts on a surface, while increasing the roughness of a surface will increase the friction force.

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