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Deflection and Pascal's Trianglefinnish_translation.jpg

Taipuma ja Pascalin kolmio

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The mathematical second pendulum has the length of 99,5 cm. The lenght can be determined by physics. We take to the girder HEB 100 the same length of 99,5 cm and a load of 1 kN in the middle.

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1.00 - 1.03 - 1.06 - 1.12

99.5 x 1.03 = 103 cm

Deflection of the girder weight                  Deflection of the concentrated force

f = deflection                                                    f = deflection

f = 5 x F x L3 / 384 x E x  I                                f =  F x L3 / 48 x I x E

f = 0.00032 cm                                                  f = 0.00246 cm

E= 20600 kN/cm2           Ix = 450 cm4

Total deflection

0,00273 cm                    => 0,00273/ 0,00249 = 1,0962

 1,1

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99.5 x 1.06 = 105.5 cm

Deflection of the girder weight                  Deflection of the concentrated force

f = deflection                                                    f = deflection

f = 5 x F x L3 / 384 x E x  I                                f = F x L3 / 48 x I x E

f = 0.00035 cm                                                  f = 0.00264 cm

Total deflection
0,00298 cm                => 0.00298/ 0.00249 = 1.19876

 1.21

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99.5 x 1.09 = 108.5 cm

Deflection of the girder weight                  Deflection of the concentrated force

f = deflection                                                    f = deflection

f = 5 x F x L3 / 384 x E x  I                                f = F x L3 / 48 x I x E

f = 0.00039 cm                                                  f = 0.00287 cm

Total deflection

0.00326 cm                    => 0.00326/ 0.00249 = 1.30776

 1.331

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99.5 x 1.12 = 111.5 cm

Deflection of the girder weight                 Deflection of the concentrated force

f = deflection                                                   f = deflection

f = 5 x F x L3 / 384 x E x  I                               f = F x L3 / 48 x I x E

f = 0.00043 cm                                                 f = 0.00311 cm

Total deflection

0.00354 cm                    => 0.00354/ 0,00249 = 1.4234

 1.4641

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1.03  =>  1.1(2)           1.03(28)3 = 1.12

1.06  =>  1.21              1.03(28)6 = 1.21

1.09  =>  1.331            1.03(28)9 = 1.331

1.12  =>  1.4641          1.03(28)12 = 1.4729

Later, we can combine the above in a greater whole.

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21.6.2018*08:00 (824- 36628)
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