Structural Engineering & Statics
where the load goes
Generator

The moment-rotation generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Moment against rotation, for three real jointsThree connections on one plot, with the classification boundaries for a beam of EI/L = 14000 drawn as rays through the origin. web cleats is pinned, flush end plate is semi-rigid, extended end plate is semi-rigid. The boundaries are multiples of EI/L, so the same joint is rigid on a short stiff beam and semi-rigid on a long slender one.00.0050.010.0150.020.0250.030.0350.040.0450.05050100150200rotation, radiansmoment, kN·mrigid abovepinned belowweb cleats — pinnedflush end plate — semi-rigidextended end plate — semi-rigid

4 essays call moment-rotation. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

100 kNe = 150centroidworst bolt 50.37 kNSix bolts · direct shear 16.67 kN eachelastic vector method Connections

The connection is not a point, and every diagram on this site says it is

Every free body drawn here has joined its members at points. Real structures fail at the joints far more often than in the members, and the reason is that a joint is exactly the region the theory behind every other page explicitly excludes.

 00.0050.010.0150.020.0250.030.0350.040.0450.05050100150200rotation, radiansmoment, kN·mrigid abovepinned belowweb cleats — pinnedflush end plate — semi-rigidextended end plate — semi-rigid Connections

Neither pinned nor rigid, which is every real connection

Frame analysis offers two options for a joint and reality supplies a continuum between them. Worse, the boundaries are not properties of the connection at all — the same end plate is rigid on a short stiff beam and semi-rigid on a long slender one.

 flexibility contributed by each componentthey add, so the softest dominates — Sj = 25227.71 kN·m/radwhat doubling it buyscolumn web in shear21.89%×1.12column web in compression11.55%×1.06column flange in bending39.62%×1.25end plate in bending18.09%×1.1bolts in tension8.85%×1.05 Connections

A joint made of springs in series

A connection's stiffness is not a property of the connection. It is the series combination of the flexibilities of everything the force passes through — so the softest component decides, and stiffening any of the others changes almost nothing.

 02000040000600008000010000012000014000016000000.20.40.60.81joint rotational stiffness, kN·m/radend moment ÷ wL²/126.04%30%62.16%rigid boundarysemi-rigidfixed ended Connections

The redistribution nobody chose

A beam designed as simply supported, on connections that are not pins, has end moments the analysis never predicted and a mid-span moment smaller than it was sized for. Usually that is safe. It is never intentional, and there is one direction in which it is not safe at all.

The library, page 2 of 4 — where moment-rotation sits