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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)