Distributed Loading by copying god, Thesis of Mechanics

Download Distributed Loading by copying god and more Thesis Mechanics in PDF only on Docsity!

Distributed Loading

What is a Distributed Load?

• A load applied across

a length or area

instead of at one

point

Geometry Method

• The magnitude of the

resultant force is

equivalent to the

area under the curve

of the distributed

load

10 kN/m

1 m 3 m 2 m

F kN

m m

F b h kN

r

r

30

Geometry Method

• The location of the

resultant force is at

the center of mass of

the distributed load.

10 kN/m

1 m 3 m 2 m

x m

x x b m m

0

2.5 m

30 kN

Geometry Method – Example

• For a triangular

distributed load, the

location of the

resultant force is 1/

of the length of the

load, from the larger

end

5 kN/m

4 m 4 m

x m

x x b m m

0

1.33 m

10 kN

Integral Method

• The magnitude of the

resultant force is

given by the integral

of the curve defining

the force, w(x)

5 m 2 m

F kN

F x

F w x dx x dx

r

m r

m

x

m r x

[ ]

5 0

2

3

5

0

(^51) / 2

0

 (^)    

w ( x ) x^12

Integral Method – Example

• For a vertical bar,

simply integrate with

respect to y instead

of x

w ( y )  y^2 kN / m

5 m

2 m F kN

F y

F w y dy y dy

r

m r

m

y

m r y

[ ]

5 0

3

5

0

(^52)

0

 (^)    

Integral Method – Example

• For a vertical bar,

simply integrate with

respect to y instead

of x

3.75 m

y m

y y

y dy

w y dy

w y ydy y

m

m

L

L

3. 75

[ ] 4 * 41. 7

1

( )^41.^7

( )

5 0

4

5

0

3

0

0





 







41.7 kN