Monday, March 16, 2015


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


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.


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.


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:


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).

Monday, March 2, 2015

Seismic Design, Eccentricity

Offset between center of mass and center of resistance causes eccentricity which causes torsion under seismic load.  The plans at left identify concentric and eccentric conditions:

1  X-direction concentric
    Y-direction eccentric

2  X-direction eccentric
    Y-direction eccentric

3  X-direction concentric
    Y-direction concentric

4  X-direction concentric
    Y-direction concentric

5  X-direction concentric
    Y-direction concentric

X-direction concentric
    Y-direction concentric

Note: Plan 5 provides greater resistance against torsion than plan 6 due to wider wall spacing Plan 6 provides greater bending resistance because walls act together as core and thus provide a greater moment of inertia.

Seismic Design, Eccentricity