STRUCTURES 1 - LECTURE 04 MOMENT IN EQUILIBRIUM

moment of a force

the tendency to make an object or a point rotate.
- a force will only produce it about its point when applied at a distance.
- calculated as the product of a force's magnitude and the perpendicular distance from the force's line of action to the rotation point (called the moment arm).
- has magnitude and direction.
- expressed in terms of the product of length and force units (ex: lb x ft = lbft)

equation for moment of a force:

M₀ = fd (force x distance)
- also written as force x arm

what type of effect will a force have on a point that doesn't have any perpendicular distance from the line of action?

translational effect (it moves through a space wthout rotating).

what type of effect will a force have on a point that does have perpendicular distance from the line of action?

rotational effect (it moves by rotating on an axis).
- happens when nonconcurrent forces act on an object (must be balanced by an equal moment in the opposite direction; summation of moment has to equal 0 to prevent rotation).

when does a force not have any moment about a point?

when it passes through or acts on said point.

clockwise = ?
counter-clockwise = ?

clockwise = negative moment
counter-clockwise = positive moment

couple

two forces seperated by distance that have the same magnitude, parallel lines of action, and opposite senses.
- the moment of the two forces about a point ≠ 0 even though the sum of couple forces in any direction is = 0.
- the action of a couple will rotate the object at that point.
- to find magnitude of a couple, multiply one of the couple forces by the perpendicular distance.

external force/moment

an applied force that causes an object to translate, rotate, or stay at rest.

internal force/moment

an internal force within an object that develops in response to an eternal force/moment.

when is an object stationary/at rest?

when the internal and external forces are in balance.

the two types of external forces that act on a rigid body

applied forces and reactive forces

applied forces

forces directly applied on a structure (ex: snow load)

reactive forces

forces created by the action of one body on another body.
- usually occurs at the supports.
- realized by newton's 3rd law.

equations for the equilibrium conditions of nonconcurrent forces:

ΣFₓ = 0 (summation of forces in the horizontal direction = 0)

ΣFᵧ = 0 (summation of forces in the vertical direction = 0)

ΣM = 0 (summation of moments in any direction should = 0, meaning no external net rotation)