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The moment about point A.
The moment about point B.
The moment about point C.
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Answer to Problem 13.1P
The moment about point A is
The moment about point B in member BA is
The moment about point B in member BC is
The moment about point C is
Explanation of Solution
Given:
The supports
The girder has thickness of
Concept Used:
Write the expression for fixed end moments.
Here, uniform distributed load is
Write the expression for absolute stiffness factor for member
Here, stiffness factor for member
Write the expression for absolute stiffness factor for member
Here, stiffness factor for member
Write the expression for distribution factor for member
Write the expression for distribution factor for member
Write the expression for distribution factor for member
Since the supports
Write the expression for distribution factor for member
Since the supports
Calculation:
The diagram of the beam is shown below.
Figure (1)
Consider Figure (1).
Length of span is
Length of haunch at end
Length of haunch at end
Calculate ratio of length of haunch at end
Calculate ratio of length of haunch at end
Calculate ratio for rectangular cross-sectional area at end
Calculate ratio for rectangular cross-sectional area at end
Calculate ratio of length of haunch at end
Calculate ratio of length of haunch at end
Calculate ratio for rectangular cross-sectional area at end
Calculate ratio for rectangular cross-sectional area at end
Determine the carry over factor of member
Determine carry over factor of member
Determine carry over factor of member
Determine carry over factor of member
Determine stiffness factor of member
Determine stiffness factor of member
Determine stiffness factor of member
Determine stiffness factor of member
Calculate absolute stiffness factor for member
Substitute
Calculate absolute stiffness factor for member
Substitute
Calculate fixed end moment for member
Determine coefficients from straight haunches-constant width table.
Substitute
Calculate fixed end moment for member
Determine coefficients from straight haunches-constant width table.
Substitute
Calculate fixed end moment for member
Determine coefficients from straight haunches-constant width table.
Substitute
Calculate fixed end moment for member
Determine coefficients from straight haunches-constant width table.
Substitute
Calculate distribution factor for member
Substitute
Calculate distribution factor for member
Substitute
The moment distribution table is shown below.
Joint | A | B | C | |
Member | AB | BA | BC | CB |
K | | | ||
D.F. | | | | |
C.O.F. | | | | |
F.E.M. | ||||
DIST | | | ||
SUM |
Table (1)
Conclusion:
The moment about point A is
The moment about point B in member BA is
The moment about point B in member BC is
The moment about point C is
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