Learning Goal To understand the notation, sign conventions, and use of the general slope deflection equation A section of a continuous beam ( Figure 1 ) has three degrees of freedom the angular displacements A and B and the linear displacement Using the slope deflection method of analysis, these displacements are related to the internal moments at the supports A and B The internal moment at A , M A B , is M A B 2 E k ( 2 A B 3 ) ( F E M ) A B where k I L is the stiffness, L is the span's cord rotation, and ( FEM ) A B is the fixed end moment at A due to any loads applied on the span A B A similar equation can be written for the moment at B M B A 2 E k ( 2 B A 3 ) ( F E M ) B A The two equations are very similar By using N to represent the near end and F for the far end, they can both be written as M N 2 E k ( 2 N F 3 ) ( F E M ) N PLEASE SOLVE PART A USING GENERAL SLOPE DEFLECTION EQUATION

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Question: Learning Goal: To understand the notation, sign conventions, and use of the general slope - deflection equation. A section of a continuous beam ( Figure

Learning Goal:

To understand the notation, sign conventions, and use of the general slope

-

deflection equation.

A section of a continuous beam

(

Figure

1)

has three degrees of freedom: the angular displacements

_{A}

and

_{B}

and the linear displacement

.

Using the slope

-

deflection method of analysis, these displacements are related to the internal moments at the supports A and

B .

The internal moment at

A, M_{A B},

M_{A B} = 2 E k (2_{A} +_{B} - 3) + (F E M)_{A B}

where

k = \frac{I}{L}

is the stiffness,

= \frac{}{L}

is the span's cord rotation, and

(

FEM

) ?_{A B}

is the fixed end moment at A due to any loads applied on the span

A B .

A similar equation can be written for the moment at

B .

M_{B A} = 2 E k (2_{B} +_{A} - 3) + (F E M)_{B A}

The two equations are very similar. By using

N

to represent the near end and

F

for the far end, they can both be written as

M_{N} = 2 E k (2_{N} +_{F} - 3) + (F E M)_{N} .

PLEASE SOLVE PART A USING GENERAL SLOPE DEFLECTION EQUATION

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