All about civil construction knowledge- PARAM VISIONS

How to find the resultant of coplanar concurrent forces?/ Finding magnitude & direction of coplanar concurrent forces./Resolution of forces.

 Let us determine the magnitude & direction of the resultant of coplanar concurrent forces as shown below.



As you can observe in the above drawing, there are 5 forces acting at a given angle. Let us split those inclined forces into horizontal & vertical components as shown below.




Points to remember:

The component of a force opposite to the angleθ is taken as sinθ & remaining components are taken as cosθ, where θ is the angle of a particular force.

Let us now resolve the forces into ΣFx & ΣFy, 

Where, 

ΣFx 👉 whatever the forces acting in the X-direction.

ΣFy 👉  whatever the forces acting in the Y-direction.


Note:

One more thing you should know before proceeding further 👇

The direction of the horizontal component (along the X-axis)

  Moving towards the right direction 👉  +ve.

  Moving towards the left direction  👉  -ve. 


The direction of the vertical component (along the Y-axis)

  Moving towards the upward direction 👉  +ve.

  Moving towards the downward direction 👉  -ve. 


Now,

ΣFx = [150cos55° - 200sin35° - 60sin60° - 130cos40°]

        = [86.036 - 114.71 - 51.96 - 99.585]

ΣFx  = - 180.219 N ( ← )

As ΣFx is -ve, it is moving in the left-hand side direction.


ΣFy = [150sin55° + 200cos35° - 60cos60° +130sin40° + 50]

         =[ 122.87 + 163.83 - 30 + 83.562 +50]

 ΣFy = + 390.262 N ( ↑ )

As ΣFy is +ve, it is moving in the upward direction.


1. Resultant of coplanar forces:

R = √ (ΣFx)² + (ΣFy)² 

    =  √ (- 180.219)² + (390.262)² 

    =  √ 119,825.54

  R = 346.158 N

Resultant of coplanar concurrent forces = R = 346.158N.


2. Direction of forces ( θ):

tanθ = [ΣFy  ÷ ΣFx]

        = [390.262  ÷ 180.219]

        = 2.165

    θ = tan⁻¹(2.165)

    θ = 65.21°

The direction of resultant force = θ = 65.21°



As you can observe in the above drawing, the resultant is lying in the 4th quadrant at a direction of 65.21° from the X-axis.


Thank you for going through these calculation steps. Have a good day 😄.

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