# How Are Reaction Forces Calculated in a Hinged Beam and Strut System?

• M_Abubakr
In summary, the beam "A-B" and strut "C-D" have an applied force of 8 kN at point B. The reaction force at hinge "A" is 22.627kN, with horizontal and vertical components of -16kN and 8kN respectively. The reaction force on the beam at "C" is 16kN in both the horizontal and vertical directions.
M_Abubakr

## Homework Statement

Consider beam “A-B” and strut “C-D” from Figure QA1. The beam “A-B” is hinged at point “A” and hinged with strut “C-D” at point “C”. It has an applied force of 8 kN applied at point B as shown in Figure QA1. Strut “C-D” is hinged at point “D” and it is also hinged with beam “A-B” at point “C”

## Homework Equations

(a) Calculate the horizontal and vertical components of the reaction force at hinge “A”.
(b) Calculate the horizontal and vertical components of the reaction force on the beam at “C”.

## The Attempt at a Solution

(a)
Summation of moments about point A.
-8x3+DCxCos(45)x1.5=0
DC=22.627kN

Summation of moments about C
1.5xAy-8x1.5=0
Ay=8kN

Summation of forces in x direction
Ax+DCSin45=0
Ax=-22.627Sin45
Ax=-16kN

(b)
DCx=22.627sin(45)
DCx=15.99kN = 16kN

DCy=22.627cos(45)
DCx=15.99kN=16kN

Is this correct?

#### Attachments

• Strut_1.png
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M_Abubakr said:

## Homework Statement

Consider beam “A-B” and strut “C-D” from Figure QA1. The beam “A-B” is hinged at point “A” and hinged with strut “C-D” at point “C”. It has an applied force of 8 kN applied at point B as shown in Figure QA1. Strut “C-D” is hinged at point “D” and it is also hinged with beam “A-B” at point “C”
View attachment 223673

## Homework Equations

(a) Calculate the horizontal and vertical components of the reaction force at hinge “A”.
(b) Calculate the horizontal and vertical components of the reaction force on the beam at “C”.

## The Attempt at a Solution

(a)
Summation of moments about point A.
-8x3+DCxCos(45)x1.5=0
DC=22.627kN

Summation of moments about C
1.5xAy-8x1.5=0
Ay=8kN

Summation of forces in x direction
Ax+DCSin45=0
Ax=-22.627Sin45
Ax=-16kN

(b)
DCx=22.627sin(45)
DCx=15.99kN = 16kN

DCy=22.627cos(45)
DCx=15.99kN=16kN

Is this correct?
Looks good.

## 1. What is a reaction force in a strut?

A reaction force in a strut is the force that is exerted on the strut due to an external load or force acting on the structure it is supporting. This force is equal in magnitude and opposite in direction to the force applied on the strut, according to Newton's third law of motion.

## 2. How is the reaction force calculated in a strut?

The reaction force in a strut can be calculated by using the principle of equilibrium, which states that the sum of all forces acting on a structure must be equal to zero. By applying this principle to the forces acting on a strut, the reaction force can be determined.

## 3. What factors affect the magnitude of the reaction force in a strut?

The magnitude of the reaction force in a strut is affected by several factors, including the external load or force applied on the strut, the angle at which the force is applied, and the material properties of the strut such as its cross-sectional area and Young's modulus.

## 4. Can the reaction force in a strut be greater than the applied force?

No, according to Newton's third law of motion, the reaction force in a strut will always be equal in magnitude and opposite in direction to the applied force. Therefore, the reaction force cannot be greater than the applied force.

## 5. How does the reaction force in a strut affect the stability of a structure?

The reaction force in a strut plays a crucial role in maintaining the stability of a structure. It helps to counteract external forces and prevent the structure from collapsing or buckling. The magnitude and direction of the reaction force must be carefully considered in the design of a structure to ensure its stability.

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