Four Span Continuous Beam - Equal Spans, Uniform Load on Two Spans
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Four Span Continuous Beam - Equal Spans, Uniform Load on Two Spans formulas
| \(\large{ R_1 = V_1 = 0.446\;w\;L }\) | |
| \(\large{ R_2 = 0.572\;w\;L }\) | |
| \(\large{ R_3 = 0.464\;w\;L }\) | |
| \(\large{ R_4 = 0.572\;w\;L }\) | |
| \(\large{ R_5 = -\;0.054\;w\;L }\) | |
| \(\large{ V_{2_1} = 0.0554\;w\;L }\) | |
| \(\large{ V_{2_2} = V_{3_1} = 0.018\;w\;L }\) | |
| \(\large{ V_{3_2} = 0.482\;w\;L }\) | |
| \(\large{ V_{4_1} = 0.518\;w\;L }\) | |
| \(\large{ V_{4_2} = V_5 = 0.054\;w\;L }\) | |
| \(\large{ M_1 \; \left( 0.446\;L \right) \; }\) from \(\large{ \left( R_1 \right) = 0.0996\;w\;L^2 }\) | |
| \(\large{ M_2 \; }\) at \(\large{ \left( R_2 \right) \; = 0.0536\;w\;L^2 }\) | |
| \(\large{ M_3 \; }\) at \(\large{ \left( R_3 \right) \; = -\;0.0357\;w\;L^2 }\) | |
| \(\large{ M_4 \; \left( 0.518\;L \right) \; }\) from \(\large{ \left( R_4 \right) = 0.805\;w\;L^2 }\) | |
| \(\large{ M_5 \; }\) at \(\large{ \left( R_4 \right) \; = -\;0.0536\;w\;L^2 }\) | |
| \(\large{ \Delta_{max} \; }\) at \(\large{ \left( 0.477\;L \right) \; }\) from \(\large{ \left( R_1 \right) \; = \frac{0.0097\;w\;L^4}{\lambda\; I} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ L }\) = span length of the bending member
\(\large{ M }\) = maximum bending moment
\(\large{ P }\) = total concentrated load
\(\large{ R }\) = reaction load at bearing point
\(\large{ V }\) = shear force
\(\large{ w }\) = load per unit length
\(\large{ W }\) = total load from a uniform distribution
\(\large{ x }\) = horizontal distance from reaction to point on beam
\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity
\(\large{ \Delta }\) = deflection or deformation