determine the reaction of horizontal and vertical components in
the axis A and the reaction of the rocker arm B on the beam, the image is
a little fuzzy but there is a force of 4kN pushing down, it’s an 8m
beam, there are 6 m from point A on the left to where the force is
applied, so there are 2 meters from where the force is applied
the rocker arm, or point B. Point B is at a 30 degree angle.
Answer 1
general orientation
Concepts and reason
Equilibrium of a rigid body:
An object is said to be in equilibrium when the sum of all external forces and torques is zero.
The equilibrium conditions of a three-dimensional rigid body are that the sum of the external forces acting in the x, y, and z directions must be zero, and the sum of the external torques around any point must be zero.
The magnitude of the moment of the force acting around a point or axis is directly proportional to the distance of the force from the point or axis. It can be determined by the product of the force and the perpendicular distance between the point at which the force is applied and the point around which the moment is to be calculated.
Support reactions:
If there is a force acting on a support due to which, the translational motion of the object is limited or impeded. The force developed is therefore called the support reaction.
Main types of media:
Fixed bracket:
Prevents rotation, horizontal and vertical translation. It is shown in figure (1a).
Fixed bracket:
This bracket prevents horizontal and vertical translation. It is shown in figure (1b).
Roll holder:
This support cannot prevent rotation or horizontal movement, but can only provide vertical support reaction to the surface as shown in figure (1c).
Rocker bracket:
This support is almost similar to the roller and will only have a vertical force acting as shown in figure (1d).
free body diagram:
It is a graphic and symbolic illustration which is used to visualize the forces which are applied, the movements and the reactions of a body to a particular condition.
Sign convention:
Represent upward forces and forces acting on the right side with a positive sign and downward forces and forces acting on the left side with a negative sign. Represent clockwise moments with a positive sign and counter-clockwise moments with a negative sign.
Fundamentals
Write the equilibrium condition for the forces along the x axis.
Here, the sum of the forces along the x axis is .
Write the equilibrium force equation on the y-axis.
Here, the total force acting on the y axis is .
Write the equilibrium moment condition around any point.
Here, the sum of the moments is .
Write the formula for the moment due to the force.
Here the force is and the perpendicular distance is .
Step by step
Step 1 of 3
Draw the free body diagram of the given bundle.
Calculate the external support reactions:
Use the balance equations:
Consider the sum of the forces in the x direction:
…… (1)
Consider the sum of the forces in the y direction:
…… (of them)
Evaluate so that the moments around are zero
The reaction force on rocker arm B is .
Consider the equilibrium moment at A to find the reaction at rocker arm B.
Given the balance of moments at A, represent clockwise moments with a positive sign and counter-clockwise moments with a negative sign, but do not represent clockwise and counterclockwise moments with the same sign.
Use the vertical and horizontal equilibrium conditions to find the vertical and horizontal components of the reaction at A.
Step 2 of 3
Calculate the horizontal component of the reaction at A:
Substitute into equation (1).
The horizontal component of the reaction at A is
Consider the horizontal equilibrium condition to find the horizontal component of the reaction at A.
Use the vertical equilibrium conditions to find the vertical component of the reaction at A.
Step 3 of 3
Calculate the vertical component of the reaction at A.
Substitute the value in equation (2),
The vertical component of the reaction at A is
Consider the vertical equilibrium condition to find the vertical component of the reaction at A.
Answer
The reaction force on rocker arm B is .
The horizontal component of the reaction at A is
The vertical component of the reaction at A is
answer only
The reaction force on rocker arm B is .
The horizontal component of the reaction at A is
The vertical component of the reaction at A is
Types of support Reaction forces Fixed support TI Spindle support Roller support Probe support Tilt support (d) Figure 1
ΣF = 0
ΣΕ, = 0
ΣΜ = 0
M = Fd
4 kN – B—– R. cos 60° 4 6 m | 2m 60° Rp R, sin 60°
ΣΕ = 0 Α, – R, cos 60° = 0
ΣΕ, = 0
4, +R, sin 60º = 4 kN
0=’W3
R, sin 60°x8-4×6=0 R, sin 60° x 8 = 24 24 R, = sin 60° 8 Rx = 3.46 kN
3.46 kN at RB
4x-RB Cos 60º = 0 4x -3.46cos 60º = 0 4x = 1.732 kN
3.46 kN at RB
A, – Rp sin 60º = 4 A, -3.46 sin 60º = 4 Ay = 4 – 3.46 sin 60° A, = 1.00 KN
3.46kN
3.46kN
4.46kN
5.46kN
6.62kN
1,732 KN
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