Profiles_Technical

Static Load

Determining the deflection of a static load can be done graphically or mathematically. Graphically, will yield and approximate figure. Mathematically, will yield more accurate results and must be used if the values are outside the graph shown below. Using the following values, here is an example
of both methods for three types of load conditions.

Deflection (mm)
Load (N)
Unsupported Length (mm)
BEA.4040 surface inertia
Young's modulus

f
F
L
l
E

=
=
=
=
=

?
8000 N
700 mm
11.3 cm⁴7000 N/mm²

Mathematically
Load Condition 1	Formula		Result
	f = F x L^{3 __________________}E x 1 x 3 x 10⁴	=	8000 N x 700³ mm^{3 _______________________________}70000 N/mm² x 11.3cm⁴ x 3 x 10⁴
Load Condition 2
	f = F x L³ _______________ E x l x 48 x 10⁴	=	8000 N x 7003 mm³ ____________________________ 70000 N/mm2 x 11.3cm⁴ x 48 x 10
Load Condition 3
	f = F x L3 ________________ E x l x 192 x 10⁴	=	8000 N x 7003 mm³ __________________________ 70000 N/mm² x 11.3 cm³ x 192 x 10⁴

Graphically
Five lines are needed to obtain a graph result.
Line 1:	Find the load on left and draw horizontal line 1 across graph.
Line 2:	Find the unsupported length on bottom and draw a vertical line 2 to the top.
Line 3:	Find the beam's moment of inertia on the right and draw a horizontal line 3 across graph.
Line 4:	Find the intersection of lines 1 and 2. Follow the angle of the slanted lines on graph to draw line 4 until it intersects with line 3.
Line 5:	At the point where line 4 intersects with line 3, draw a vertical line through the loads at top of graph. This will show an approximate static load deflection.

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