Continuous Beams

Continuous beams of five spans or less are analyzed using the stiffness method based on the following assumptions:

All beams have equal moment of inertia
Beams are prismatic in cross section
Loads are positive when acting downward
Interior supports are knife-edge (simple)
Exterior supports are knife-edge, fixed or free

Any consistent load and length units may be selected.

Input for each beam consists of

Span length
Dead loads
Live loads

Multiple dead and live loads separated by semi colon (;) may be entered for each beam.

In its most generalized form, loads are specified as w1:w2@x1:x2

		where :
		w1 : load per unit length nearest to left end
		w2 : load per unit length farthest from left end
		x1 : start location of load measured from left end
		x2 : end location of load measured from left end

The colon (:) denotes 'to' and the symbol @ denotes 'at'. Thus w1:w2@x1:x2 is read as 'w1 to w2 at x1 to x2' implying that the load varying from w1 to w2 is spread over a distance starting at x1 and ending at x2 from left support of beam.

The following simplifications are allowed:

For loads spread over the entire length of the beam,
location (x1:x2) may be omitted.
For uniform loads (w1=w2=w) a single value w may
be specified instead of the general form w:w.

With these simplifications, some of the common loads may be input as follows:

Uniform load over the entire span		w
Uniform load over a part of the span		w@x1:x2
Varying load over the entire span		w1:w2

In addition to the general form described above, three more load types may be specified:

Point Load specified as W@x

W has the units of load (kN, kip etc.) and x is the distance from left end of the beam

Patch Load specified as W/c@x

W has the units of load (kN, kip etc.), c is the width of patch load and x is the distance of center of gravity of load from left end of the beam.

Slab Load specified as w*y

Here, w has the units of load per unit area (kN/m², kip/ft² etc.) and y is half the span of the slab perpendicular to the span of the beam.

When this format is used, a trapezoidal load with a peak value of w*y load units per unit length (kN/m, kip/ft etc.) is applied to beams along longer sides of slab. Beams along shorter sides receive a triangular load with a peak value of w*L/2, where L is the span of the beam.

If the beam is loaded from identical slabs on either side, using twice the load per unit area for w and one half slab span length for y will give correct result but it is preferable to specify each load separately to avoid any confusion.

On output, bending moments and shear forces along five points of each beam are displayed for three load combinations :

Dead and live load on all spans
Dead load on all spans and live load on odd numbered spans
Dead load on all spans and live load on even numbered spans