CIVIL ENGINEERING FORMULAS

Type of Support Fundamental Mode

L

Second Mode Third Mode Fourth Mode

Cantilever

20.0 125 350

0.315

56.0

Fixed

Fixed-hinged

0.112

224

0.0281

502

0.0125

0.774L

0.5L 0.356L

0.644L

684

0.132L

0.0503 0.0180 0.0092

0.5L

0.359L 0.359L 0.278L

1,1330.278L

0.0056

Simple L L

wL^4 /EI=

EI/wL^4 =

ω wL^4 /EI

ω

ω

=

T EI/wL^4

T

T

ω

T

=

wL^4 /EI=

EI/wL^4 =

wL^4 /EI=

EI/wL^4 =

3

L

3

L

L

L

2

L

2

L

4

L

4

L

2

897

0.0070

127

0.0496

350

0.0180

0.56L 0.384L 0.308L0.294L

0.529L

1,111

0.0062

591

0.0106

283

0.0222

87.2

0.0722

0.235L

684

0.0092

0.094L

FIGURE 2.26 Coefficients for computing natural circular frequencies and natural periods of vibration

of prismatic beams.

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