2.76 The couple acts on the handles of a steering mechanism. In the position shown, the moment applied by the couple about the z-axis is zero. Determine the distance b. Use F = 200i - 110j - 80k kN.
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
![### Section 2.76
The problem involves a couple acting on the handles of a steering mechanism. The task is to determine the distance \( b \) such that the moment applied by the couple about the \( z \)-axis is zero. The force vector is given as \(\mathbf{F} = 200\mathbf{i} - 110\mathbf{j} - 80\mathbf{k}\) kN.
#### Figure P2.76 Description:
- The diagram shows a steering mechanism in a 3D coordinate system (x, y, z).
- Two handles are labeled \( A \) and \( B \), connected by a bar.
- The bar is 180 mm long along the \( x \)-axis, with the distance \( b \) along the \( y \)-axis from point \( A \) to \( B \).
- A force \( \mathbf{F} \) is applied at handle \( A \) in the direction opposite to the force \( -\mathbf{F} \) applied at handle \( B \).
The problem seeks to find the distance \( b \) where the moment about the \( z \)-axis is zero, implying rotational equilibrium with regards to that axis.
#### Figure P2.77 Description:
- This is a separate diagram likely intended for another question or part of the same problem.
- It shows a flat plate oriented in a 3D coordinate system (x, y, z).
- The dimensions of the plate are indicated: 16 inches along the z-axis and 24 inches along the y-axis.
- Three forces are acting on the plate: 50 lb along the x-axis, 30 lb along the z-axis at point \( A \), and 80 lb along the x-axis at point \( C \).
- A rotational moment of 500 lb-in is also shown clockwise around an axis extending from point \( B \).
The detailed diagrams provide essential visual support for analyzing mechanical equilibrium using principles of statics, including force vectors and moment calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffddfa066-ae14-4710-b68e-f1412b1153a3%2F8eb99a97-7d5e-4260-b000-13c353534afc%2Fx0bbmfb_processed.jpeg&w=3840&q=75)
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