# Statics - Pin & Slider Structure - Equilibrium

• raniero
In summary, the problem involves finding the moment on member 4 given a force of 5000N. The person has drawn a diagram and added letters and angles to certain points. They have also calculated the forces and moments on other members and pins using equilibrium equations. They have found that member 2 is a zero force member and have a result of -3000Nm for the moment on member 4. They are unsure if their equations and diagram are correct.
raniero

## Homework Statement

Given force F (=5000N), find Moment on member 4.

I have attempted to start solving this problem by drawing the following diagram:

I added the letter 'A' to the support of member 2, and also put an angle of 7 degrees to the vertical at the support 1.

I have drawn force and moment reactions on bodies 3, 5 and 8 which are all sliders and reaction forces on pins D, F, E, G and A.

I worked out the geometry so as to be able to work out moments and components.

## Homework Equations

To solve the problem I tried to use the Equilibrium equations which state that forces in all directions should equal to zero and also that all moments should equal to zero.

## The Attempt at a Solution

Member 4:$$\sum{F_x} = 0: B\cos(15)+G_x-C\cos(7)=0 \\ \sum{F_y}=0: B\sin(15)-C\sin(7)-G_y=0 \\ \sum{M_G}=0: B(1.54) - C\cos(7)(6.4) -C\sin(7)(1.71) + M_3 = 0$$

Member 2:$$\sum{F_x}=0: A\sin(30) - B\cos(15) = 0 \\ \sum{F_y}=0: A\cos(30) + B\sin(15) = 0 \\ \sum{M_A}=0: B(0.8)=0$$

Problems:

Equations of member 2 get me to a conclusion that member 2 is a zero force member. Am I right?
Are my equations and diagram correct ?

For the moment on member 4, I am getting a result of M4= -3000Nm. Is this correct or am I missing something?

## 1. What is the definition of equilibrium in the context of statics?

Equilibrium in statics refers to the state in which an object or system has a balanced distribution of forces and moments, resulting in no net change in its motion or position. This means that the sum of all external forces acting on the object is zero and the sum of all external moments is also zero.

## 2. How do you determine if a pin and slider structure is in equilibrium?

To determine if a pin and slider structure is in equilibrium, we must first draw a free body diagram of the structure, including all external forces acting on it. Then, we use the equations of equilibrium (sum of forces in the x and y directions, and sum of moments) to solve for the unknown forces and determine if they balance out to zero. If they do, the structure is in equilibrium.

## 3. What are the three types of equilibrium in statics?

The three types of equilibrium in statics are stable, unstable, and neutral. In stable equilibrium, the object will return to its original position after a small displacement. In unstable equilibrium, the object will continue to move away from its original position after a small displacement. In neutral equilibrium, the object will remain in its displaced position after a small displacement.

## 4. How does the number of unknowns and equations of equilibrium relate to solving a statics problem?

The number of unknowns and equations of equilibrium must be equal for a statics problem to be solved. This means that for a 2D problem, there must be two equations (sum of forces in x and y directions) and two unknowns (usually the reaction forces at the pin and slider). For a 3D problem, there must be three equations (sum of forces in x, y, and z directions) and three unknowns.

## 5. What is the difference between a pin and slider structure and a cantilever structure in terms of equilibrium?

A pin and slider structure is a type of statically indeterminate structure, meaning that it has more unknowns than equations of equilibrium and requires additional information to solve. A cantilever structure, on the other hand, is a statically determinate structure with an equal number of equations and unknowns. This means that a cantilever structure can be solved using only the equations of equilibrium, while a pin and slider structure may require additional information such as compatibility equations.

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