Analysis & loading · Load take-down & combinations

Two-way slab load to beams calculator

Slab load to supporting beams by 45° lines: triangular load on short beams, trapezoidal on long beams, and equivalent UDLs for moment.

Standard: Yield-line tributary (45°) equivalent UDLs

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Result	Value	Unit
lx/ly	0.714
Short beam peak (triangle) w lx/2	22.50	kN/m
Short beam equivalent UDL (moment) w lx/3	15.00	kN/m
Long beam equivalent UDL (w lx/6)(3 − r²)	18.67	kN/m
Total check (2·triangles + 2·trapezoids) / (w lx ly)	1.00

Diagram for the worked example

lx/ly = 5/7 = 0.71429
Short beam peak (triangle) w lx/2 = 9*5/2 = 22.5 kN/m
Short beam equivalent UDL (moment) w lx/3 = 9*5/3 = 15 kN/m
Long beam equivalent UDL (w lx/6)(3 − r²) = 9*5/6*(3-0.71429^2) = 18.673 kN/m
Total check (2·triangles + 2·trapezoids) / (w lx ly) = (2*9*5^2/4+2*9*5/2*(7-5/2))/(9*5*7) = 1

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.