mechanical engineering moment
TRANSCRIPT
Mechanical Engineering
Moment
Mr. Waleed Ali Tameemi M.Sc. Kansas University/USA
College of Engineering Environmental Engineering Department
1st Stage
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
Moment
The measurement of the force tendency to rotate or twist a subject around a known axes (axes of rotation).
The moment (𝑀) of a force with respect to a known axis
is equal to the production of multiplying the magnitude of the force by the perpendicular distance between the force and the axis of rotation.
The moment of a force with respect to an axis is equal to the moments of the force’s components around the same axes.
Moment
30o
F
Axis of
Rotation
a
a
𝐹𝑦
30o
F
𝐹𝑥
Axis of
Rotation
a
a
dF
dFy
𝑀𝐹 = 𝐹 × 𝑑𝐹
𝑀𝐹 = 𝐹𝑦 × 𝑑𝐹𝑦 + 𝐹𝑥 × 𝑑𝐹𝑥
= 𝐹𝑦 × 𝑑𝐹𝑦 + 𝐹𝑥 × 0
= 𝐹𝑦 × 𝑑𝐹𝑦
Steps of Solution
Law of Moment
The moment of the resultant force of a force system with
respect to an axis is equal to the algebraic summation of
the forces’ moments around the same axis.
𝐹
P a
a
d1 d2 A B
Law of Moment
𝐹 P a
a d1 d2 A B
𝑅 a
a
dR
A B
𝑅 = 𝐹𝑦 = 𝐹 + 𝑃
𝑀𝑅 = 𝑅 × 𝑑𝑅
𝑹 × 𝒅 ≡ 𝑭 × 𝒅𝟏 + 𝑷 × (𝒅𝟏 + 𝒅𝟐)
Moment Sign Convention
1. Positive sign (+ve), if the couple is rotating counter clockwise.
Axis of Rotation
M
2. Negative sign (-ve), if the couple is rotating clockwise.
Axis of Rotation
M