Mr. Waleed Ali Tameemi M.Sc. Kansas University/USA

College of Engineering Environmental Engineering Department

1st Stage

Resultant of a Non-concurrent, Coplanar Force System I

Outline

Introduction

Parallelogram Law

Forces Resolution

Resultant of a Cunccurent, Coplanar Force System

Moment (Moment of a Force)

Couples

Resultant of a Non-concurrent, Coplanar Force System

Resultant of a Concurrent Non-coplanar Force System

Equilibrium

Fraction

Truss

Resultant of a Non-concurrent, Coplanar Force System

• The resultant of this system can be a single force or a couple.

φ

f p

α

• In order to calculate the resultant magnitude, location, and direction, the following procedure is required.

Methodology

Step 1

𝑝𝑦

𝑓𝑦

𝑓𝑥 𝑝𝑥

1. Resolve each single force to its perpendicular components.

𝑓𝑥 = 𝑓 × cos 𝜑

𝑓𝑦 = 𝑓 × sin𝜑

𝑝𝑥 = 𝑝 × cos 𝛼

𝑝𝑦 = 𝑝 × sin 𝛼

φ

f p

α

Step 2 & 3

2. Calculate the resultant’s components in x direction and y

direction.

𝑅𝑥 = 𝐹𝑥 = 𝑓𝑥 + 𝑝𝑥

𝑅𝑦 = 𝐹𝑦 = 𝑓𝑦 + 𝑝𝑦

3. Calculate the magnitude of the resultant.

𝑅 = 𝑅𝑥 + 𝑅𝑦

Step 4 & 5

4. Find the location of the resultant using the moment law. 𝑅

𝑝𝑦 𝑓𝑦

𝑓𝑥 𝑝𝑥

𝑑𝑝𝑦 𝑑𝑅 𝑑𝑓𝑦

𝐴

𝑀 𝑎𝑏𝑜𝑢𝑡 𝐴 =𝑅 × 𝑑𝑅 = (𝐹𝑦 × 𝑑𝑓) = 𝑝𝑦 × 𝑑𝑝𝑦 + 𝑓𝑦 × 𝑑𝑓𝑦

5. Calculate the resultant’s slope Slope = tan−1(𝑅𝑦

𝑅𝑥)