Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point
Structural Related Articles
- See beam design formulas
- See frame design formulas
- See plate design formulas
- See geometric properties of structural shapes
- See welding stress and strain connections
- See welding symbols
Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point formulas
| \(\large{ R_1 = V_1 = \frac{P\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }\) | |
| \(\large{ R_2 = \frac{P\;a}{2\;L^3} \left[ 2\;L^2 + b \; \left( L + a \right) \right] }\) | |
| \(\large{ R_3 = V_3 = \frac{P\;a\;b}{4\;L^3} \; \left( L + a \right) }\) | |
| \(\large{ V_2 = \frac{P\;a}{4\;L^3} \; \left[ 4\;L^2 + b \; \left( L + a \right) \right] }\) | |
| \(\large{ M_1 \; }\) at support \(\large{ \left( R_2 \right) = \frac{P\;a\;b}{4\;L^2} \; \left( L + a \right) }\) | |
| \(\large{ M_{max} = \frac{P\;a\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }\) |
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