文档介绍：Statics
静力学
力对点的矩
PART2 Moment of a force about a point
Bilingual Edition
Moment of a force about a point
Definition
PART TWO
Magnitude
Force times Arm of force
Symbol
Rotate around the center of Moment: Counterclockwise “+” Clockwise “-”
Moment of a force about a point
Theorem of Moment of Resultant force
合力矩定理
PART TWO
The moment of resultant force of coplanar concurrent force system to optional point in a plane equals the algebraic sum of every moment ponent force to the same point. That is :
平面汇交力系的合力对于平面内任一点的矩等于各个分力对于同一点的矩的代数和。
Moment of a force about a point
Prove:
PART TWO
According to
Use vector r times each end of the equation, we obtain:
1. Point O and every forces are coplanar
2. The vectors of each result r×Fi are parallel.
Moment of a force about a point
Deduction:
PART TWO
From the theorem above, we can get the analytic expression:
Sample problem 1
Compute the moment of F about point O and A
PART TWO
Solution:
Sample problem 2
A triangle distributed load is applied to a horizontal beam, the maximum density of load is represented by symbol “q”, determine the resultant force of this force system.
PART TWO
Solution of Sample problem 2
pute the magnitude of resultant force FR
PART TWO
Solution of Sample problem 2
PART TWO
the position of the resultant force
The force applies on the tiny section of dx
The moment of this force about point A : -(qxdx)x, so
Solution of Sample problem 2
PART TWO
:
1) The magnitude of resultant force is equal to the area of the triangle distributed load: (1/2)ql
2) The acting line of the resultant force is located at the 2/3 distance from point A to point B