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3 span continuous beam: Quick overview of the bending moment, shear and reaction force formulas for beams due to different loading scenarios.
Beam equations for Resultant Forces, Shear Forces, Bending Moments and Deflection can be found for each beam case shown. Handy calculators have been provided for both metric and imperial beam design and assessment.
L = span length of the bending member, ft. = span length of the bending member, in. = maximum bending moment, in.-lbs. = total concentrated load, lbs. = reaction load at bearing point, lbs. = shear force, lbs. W = total uniform load, lbs.
For a continuous beam with 3, 4 or 5 supports and distributed load the reaction support forces can be calculated as. R = cr q L (1) where. R = reaction support force (N, lbf) cr = reaction support force coefficient from the figure above. q = distributed load (N/m, lbf/ft)
Use the loads and spans shown below, and the Three Moment Theorem to determine the moments at the inside reactions. Determine any moments = 0. Solve the three moment equation to find internal moments at R2 and R3. Determine all support reactions.
Given: Two non-symmetric spans with loading as shown. Find: All three reactions. Break the beam into two halves at the interior support, and calculate the interior slopes of the two simple spans. Use the Slope Equation to solve for the negative interior moment.
The 3-span continuous beam is categorized by having 1 pin and 3 roller supports. The static system is indeterminate, which means we can’t calculate the reaction forces with the 3 equilibrium equations.
2 SPAN BEAM 1. Calculate applied loading – self weight, dead, live, etc.; 2. Determine beam section properties and materials; 3. Calculate balanced forces in each span; 4. Calculate net load on beam; 5. Determine support moments; 6. Determine midspan moments; 7. Calculate flexural stresses at support and midspan; 8. Calculate secondary moments.
40. CONTINUOUS BEAM — FOUR EQUAL SPANS — THIRD SPAN UNLOADED. 41. CONTINUOUS BEAM — FOUR EQUAL SPANS — LOAD FIRT AND THIRD SPANS. 42. CONTINUOUS BEAM — FOUR EQUAL SPANS — ALL SPANS LOADED. Shears, Moments and Deflections. 43. SIMPLE BEAM — ONE CONCENTRATED MOVING LOAD.
The chapter follows with: a brief examination of two and three equal span continuous beams; a review of continuous unequal spans; the effects of asymmetric loading and differing adjacent beam stiffness; a useful method of adding a hinge in the spans to achieve statical determinacy; redistribution of moments from support to internal spans and ...