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.

Homework 4

Problem 1.

Given the force system shown below:
I. Find the equivalent coupe-force system at point A.
II. Find the equivalent coupe-force system at point B.
III. Find the simplest equivalent force system. Draw the result of reduction on the figure.

2m

3m

1m

2m

2m

2 kN

10 kN

5 kN

 kN

 kN

 kN

A

B

2 kNm

Answers:

I

The equivalent couple-force system at point A consists of a force

)

],

[

2

],

[

2

(

O

kN

kN

S





applied at point A,

and a couple with the moment

])

[

4

,

0

,

0

(

kNm

M

A





II.

The equivalent couple-force system at point A consists of a force

)

],

[

2

],

[

2

(

O

kN

kN

S





applied at point B,

and a couple with the moment

])

[

6

,

0

,

0

(

kNm

M

B





III

. (The origin of a coordinate system is at point A)

The simplest equivalent force system is the resultant force equal

)

],

[

2

],

[

2

(

O

kN

kN

S





acting along the

central axis

]

[

2 m

x

y







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.

2m

3m

1m

2m

2m

2 kN

10 kN

5 kN

 kN

 kN

 kN

A

B

2 kNm

2m

3m

1m

2m

2m

A

B

y=

-x-

[

2

m

]

W=S(-2[kN ],2[kN ],0)

x



Problem 2.

Reduce the given force system at a point belonging to the central axis (if it’s possible).

he origin of a coordinate system is at point O.

13 kN

6

2 kN

10 kNm

q=4 kN/m

20 kN

4m

3m

5m

=1 kN/m2

45°

O

(

])

[

20

,

0

,

0

(

kNm

M

O





)

T

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.

Answer:

At an arbitrary point belonging to the central axis described by the equation

]

[

5

4

5

m

x

y







, the force

)

],

[

5

],

[

4

(

O

kN

kN

S

W



system reduces to the resultant force

13 kN

6

2 kN

10 kNm

q=4 kN/m

20 kN

4m

3m

5m

=1 kN/m2

45°

O

4m

3m

5m

O

y=

-5

/4

x+

5[m

]

W=S(4[kN ],-5[kN ],0)

x

y





.

