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Notes 4

This document discusses the concepts of resultants and force systems. It defines the resultant of a force system as the simplest system that can replace the original system without changing its external effects. It provides examples of calculating the resultant force and couple for coplanar and concurrent force systems. The document also introduces the concept of normal loads on beams and how to calculate the resultant force from a load diagram.

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74 views17 pages

Notes 4

This document discusses the concepts of resultants and force systems. It defines the resultant of a force system as the simplest system that can replace the original system without changing its external effects. It provides examples of calculating the resultant force and couple for coplanar and concurrent force systems. The document also introduces the concept of normal loads on beams and how to calculate the resultant force from a load diagram.

Uploaded by

g.albarracin.535488
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CHAPTER 3:

RESULTANTS OF
FORCE SYSTEMS
Reduction of Force Systems

CHAPTER 3 Resultants of Force Systems


𝑹 = 𝜮𝑭 = 𝑭𝟏 + 𝑭𝟐 + 𝑭𝟑

𝑅𝑥 = Σ 𝐹𝑥 𝑅𝑦 = Σ 𝐹𝑦 𝑅𝑧 = Σ 𝐹𝑧

𝑪𝑹 = 𝜮𝑴𝒐 = 𝒓𝟏 × 𝑭𝟏 + 𝒓𝟐 × 𝑭𝟐 + ⋯
𝑅
𝐶𝑥 = Σ 𝑀𝑥 𝐶𝑦𝑅 = Σ 𝑀𝑦 𝐶𝑧𝑅 = Σ 𝑀𝑧

CHAPTER 3 Resultants of Force Systems


For a system that lies on a
plane (say xy-plane)
𝑅𝑥 = Σ 𝐹𝑥 𝑅𝑦 = Σ 𝐹𝑦

𝐶𝑅 = Σ 𝑀𝑜

CHAPTER 3 Resultants of Force Systems


EXAMPLE

The coplanar force


system consists of three
forces and one couple.
Determine the equivalent
force-couple system with
the force acting at point
O.

CHAPTER 3 Resultants of Force Systems


EXAMPLE

Replace the three forces


with an equivalent force-
couple system, with the
force acting at O.

CHAPTER 3 Resultants of Force Systems


Resultant
The resultant of a force system is defined to
be the simplest system that can replace the
original system without changing its external
effect on a rigid body.

CHAPTER 3 Resultants of Force Systems


A. General Coplanar Force
System

CHAPTER 3 Resultants of Force Systems


B. Concurrent, Coplanar
force system

CHAPTER 3 Resultants of Force Systems


C. Parallel, Coplanar force
system

CHAPTER 3 Resultants of Force Systems


EXAMPLE
The values of Rx , Ry , and ΣMo for five force systems lying in
the xy-plane are listed in the following table. Point O is the
origin of the coordinate system, and positive moments are
counterclockwise. Determine the resultant for each force
system, and show it on a sketch of the coordinate system.
Part Rx Ry Mo
1 0 200 N 400 N-m
2 0 200 N -400 N-m
3 300 N 400 N 600 N-m
4 400 N -600 N -900 N-m
5 0 0 -200 N-m
CHAPTER 3 Resultants of Force Systems
EXAMPLE

The force system shown


consists of the couple C
and four forces. If the
resultant of this system is
a 75,000-Nmm counter
clockwise couple,
determine P, Q and C.

CHAPTER 3 Resultants of Force Systems


Introduction to Normal Loads

CHAPTER 3 Resultants of Force Systems


Introduction to Normal Loads

CHAPTER 3 Resultants of Force Systems


Introduction to Normal Loads
The magnitude of the resultant force is equal
to the area under the load diagram

The line of action of the resultant force


passes through the centroid of the area under
the load diagram

CHAPTER 3 Resultants of Force Systems


Computation of Resultant

CHAPTER 3 Resultants of Force Systems


EXAMPLE
Determine the resultant of the line load acting on the beam.

CHAPTER 3 Resultants of Force Systems

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