Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

598 Chapter 18 Mathematics in Engineering

where

ydeflection at a givenxlocation ( m)

wdistributed load (N/m)

Emodulus of elasticity (N/m

2

)

I second moment of area ( m

4

)

xdistance from the support as shown ( m)

Llength of the beam ( m)

The deflection of a beam with a length of 5 m with the modulus of elasticity ofE200 GPa,

I99.1  10

6

mm

4

, and for a load of 10000 N/m is shown in Figure 18.9.

Deflection

y

at a given

x

(m)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

012345

Distance from support, x (m)

x(m) y(m) x(m) y(m)

0 0 2.6 0.01489

0.2 0.00012 2.8 0.01678

0.4 0.00048 3 0.01873

0.6 0.00105 3.2 0.02072

0.8 0.00181 3.4 0.02274

1 0.00275 3.6 0.02478

1.2 0.00386 3.8 0.02685

1.4 0.00511 4 0.02893

1.6 0.00649 4.2 0.03102

1.8 0.00799 4.4 0.03311

2 0.00959 4.6 0.03521

2.2 0.01128 4.8 0.03732

2.4 0.01305 5 0.03942

■Figure 18.9 The deflection of a cantilever beam.

w

L

x

■Figure 18.8 A cantilever beam.

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