# Statics: Force on a member of a frame

In summary, the homework statement is to determine the forces acting on a member ABCD. The 100 lb force acts horizontally at point D, the large, bold circle is a wheel, and the smaller, less bold circles indicate pins connecting the members. Member BE is solid. The Attempt at a Solution is to find the moment about A when taking the moments around A, and noting that if the magnitude of Cx = Ex then the magnitude of Bx is also the same.

## Homework Statement

Determine the forces acting on member ABCD

The 100 lb force acts horizontally at point D, the large, bold circle is a wheel, and the smaller, less bold circles indicate pins connecting the members. Member BE is solid.

I forgot to label point F in the picture. Whenever I refer to point F, it will be the point at the wheel. Also, lengths AB = 12, CE = 6, EF = 6, BC = 6 and CD = 6

## The Attempt at a Solution

When taking the moment around A, the x components of the B and C forces will create a moment that "cancels out" the moment from the 100 lb force (right?). However, this is probably one of the later steps. I'm pretty sure I should start by analyzing member CEF.

There are x and y components at points C and E and just a y component at F. I'm not sure where to go from here.. I think that because BE is a two force member, the force vector at E is directly towards B and B's vector directly at E.

FBD of member CEF

It just dawned on me that if the magnitude of Cx = Ex then the magnitude of Bx is also the same, right? So from there I could find the moment about A:

(assuming clockwise is positive)

MA = 0 = (100lbs)(24in) + (Bx)(12in) - (Cx)(18in) would then turn into

2400 + 12x - 18x = 0, x = 400 so the magnitudes of Cx, Ex and Bx all = 400Andddd then: since BE is basically a 45-45-90 triangle, Ey and By would also = 400?

Last edited:
Although you are right in your answers, this is possibly more by luck of this particular geometry. You could obtain Fy by taking moments about A for the whole thing. Then deduce Ax and Ay. Graphically, the applied load and Fy meet at a point, through which the reaction at A must pass. Hence the force triangle for external forces gives you all the reactions and their components. The lesson to learn is that when taking moments, you must be careful to identify clearly the object about which you are making an equilibrium statement, and include all the forces action on it.

## 1. What is the definition of statics?

Statics is a branch of mechanics that deals with the study of objects at rest or in a state of constant motion.

## 2. What is a member of a frame in statics?

A member of a frame in statics refers to any structural element, such as a beam or column, that is part of a larger framework or structure.

## 3. How is force calculated on a member of a frame?

Force on a member of a frame is calculated by considering the external forces acting on the frame and using equations of equilibrium to determine the internal forces within the member.

## 4. What are the different types of forces that can act on a member of a frame?

The different types of forces that can act on a member of a frame include external forces such as applied loads, reactions at supports, and self-weight of the member, as well as internal forces such as axial, shear, and bending forces.

## 5. How is the stability of a frame determined in statics?

The stability of a frame in statics is determined by analyzing the forces and moments acting on the frame and ensuring that the sum of all forces and moments equal zero, indicating a state of equilibrium.

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