Step 3: Apply slopedeflection
equations for span CD,
the support D is fixed therefore θ_{D}
= 0; and also there is no settlement of support because the
supports are rigid, so δ = 0;
Now substitute all the values in the
above equations for span CD; we get
M_{CD}
=(4EIθ_{C} )/3 15
Eq. (3)
M_{DC}
=(2EIθ_{C} )/3 +25
Eq. (4)
Now we have 4 equations (Eq. 1, 2 , 3 &
4) with 5 unknowns. The additional equation required is obtained by
applying the moment equilibrium at support C;
Step 4: Σ
M_{C}
= 0;
M_{CA} + M_{CD}
= 0; therefore,
(EIθ_{C}
) +25 + (4EIθ_{C} )/3 15 = 0;
yields θ_{C}
= (30/7)/EI
substituting the value of θ_{C}
in eq. 1, 2, 3 & 4 we get the values for end moments
M_{AC}
= 27.14 kNm;
M_{CA}
= 20.71 kNm;
M_{CD}
=  20.71 kNm;
M_{DC}
= 12.14 kNm;
You can also use our
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