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According to Vereshchagin when multiplying total unit diagram
M and unit diagram M we get the sum of coefficients of the
1
first equation, with the multiplication of diagrams M and M -
2
the sum of the coefficients of the second equation, etc.:
M 1M dx
;
1n
11 12 EJ
l z
M 2M dx
2n ;
21 22 EJ (3.4)
l z
M n M dx
nn .
1 n n 2 EJ
l z
This control is called a line test.
Besides the line test it is also possible a total test. According to it
the sum of all coefficients of equations must be equal to the
product of (by Vereshchagin) diagrams of the total unit diagram
M itself:
M M dx
nn . (3.5)
11 12 21 22 1 n n 2 EJ
l z
For free terms of the canonical equations the test is as follows:
the sum must be equal to the product of the total diagram M
and freight diagram M :
p
M M dx
p . (3.6)
1p 1p np EJ
l z
3.4 Equation of three moments
Statistically indeterminate beam that has more than two
resistances is called continuous.
Let us study a continuous beam with an arbitrary number of spans
(fig. 3.4 a). For the primary system we take a line of simple
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