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Homework 3.
I. Determine the sum vector, the total moment about points A and B. Verify your calculations.
II. Find the equivalent force coupe system at point A.
III. Reduce the force system to a simplest equivalent system.
F1 =� 4P , F2 =� 2P , F3 =� 6P
z
a
F
1
a
A
F
3
a
O
F
2
y
B
3a
x
Solution:
I.
The sum vector: S =� (�2P 2P 0)�
The total moment about point A M =� (�-� Pa Pa -� Pa)�
A
The total moment about point B: M =� (�-� 3Pa 3Pa -� 3Pa)�
B
Verification (changing of the moment center):
M =� M +� S �� AB =� (�-� 3Pa 3Pa -� 3Pa)�
B A
II. An equivalent force coupe system at point A comprises one force b =� S and a coupe of a moment M
A
e.g.
ć� F =� (�P P 0)��� ć�-� F =� (�-� P -� P 0)���
�� �� �� ��
,
�� �� �� ��
A(�a a a)� B(�a 0 0)�
Ł� ł� Ł� ł�
Project  The development of the didactic potential of Cracow University of Technology in the range of modern
construction is co-financed by the European Union within the confines of the European Social Fund
and realized under surveillance of Ministry of Science and Higher Education.
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III.
The simplest equivalent force system : the resultant force w =� S acting along the central axis
2y -� 2x -� a =� 0
��
��2z -� 3a =� 0
��
z
a
F
1
a
A
F
3
a
O
F
2
y
B
3a
x
Project  The development of the didactic potential of Cracow University of Technology in the range of modern
construction is co-financed by the European Union within the confines of the European Social Fund
and realized under surveillance of Ministry of Science and Higher Education.