ARCHITECTURAL STRUCTURES - GLOBAL MOMENT AND SHEAR

Global moments help to analyze not only a beam but also truss, cable or arch. They all resist global moments by a couple F times lever arm d:

The force F is expressed as T (tension) and C (compression) for beam or truss, and H (horizontal reaction) for suspension cable or arch, forces are always defined by the global moment and lever arm of resisting couple.  For uniform load and simple support, the maximum moment M and maximum shear V are computed as:

For other load or support conditions use appropriate formulas

Beam

Beams resist the global moment by a force couple, with lever arm of 2/3 the beam depth d; resisted by top compression C and bottom tension T.

Truss 

Trusses resist the global moment by a force couple and truss depth d as lever arm; with compression C in top chord and tension T in bottom chord.  Global shear is resisted by vertical and / or diagonal web bars. Maximum moment at mid-span causes maximum chord forces.  Maximum support shear causes maximum web bar forces.

Cable 

Suspension cables resist the global moment by horizontal reaction with sag f as lever arm.  The horizontal reaction H, vertical reaction R, and maximum cable tension T form an equilibrium vector triangle; hence the maximum cable tension is:

Arch 

Arches resist the global moment like a cable, but in compression instead of tension:

However, unlike cables, arches don’t adjust  their form for changing loads; hence, they assume bending under non-uniform load as product of funicular force and lever arm between funicular line and arch form (bending stress is substituted by conservative axial stress for approximate schematic design).