Portal Method For Rough Moment Frame Design

The Portal Method for rough moment frame design is based on these assumptions:

•  Lateral forces resisted by frame action
•  Inflection points at mid-height of columns
•  Inflection points at mid-span of beams
•  Column shear is based on tributary area
•  Overturn is resisted by exterior columns only

1.    Single moment frame (portal)
2.    Multistory moment frame
3.  Column shear is total shear V distributed proportional to tributary area:

4.   Column moment = column shear x height to inflection point

5.  Exterior columns resist most overturn, the portal method assumes they resist all
6.  Overturn moments per level are the sum of forces above the level times lever arm of each force to the column inflection point at the respective level:

7.  Beam shear = column axial force below beam minus column axial force above beam Level 1 beam shear:

Wind effect - Structural Design

A building in the path of wind causes wind pressure which in turn causes force, shear, and overturn moment at each level that must be resisted, following a load path to the foundations (wind wall pressure transfers to horizontal diaphragms, then to shear walls, finally to foundation).  Wind pressure times tributary area per level causes  lateral force per level.  Shear per level, the sum of wind forces above, defines required resistance.   Overturn moment per level is the sum of forces above times their height above the respective level.

1  Wind force, shear, and overturn moment per level

 Fx = wind force = wind pressure times tributary area per level exposed to wind
 VX = shear per level = sum of Fx  above
 Mx = overturn moment  = sum of all forces above times their distance above level x.

2 Overturn effect

3  Windward  pressure increase with height

4 Wind force

Fx = (windward pressure + leeward suction) times tributary area per level
(leeward wind suction is assumed constant for full height)
Fx = P A
P = wind pressure and suction in psf (Pa)
A = tributary area exposed to wind
(tributary area = building width times half the story height above and below)

5 Shear

Wind shear per level = sum of all wind forces above
Wind shear is the integration of wind forces above

6 Overturn moment

Overturn moment per level  = sum of all forces above times their distance
Overturn moment per level = integration of shear diagram above respective level

Rupture Length (material properties, i.e., structural efficiency)

Rupture length is the maximum length a bar of constant cross section area can be  suspended without rupture under its weight in tension (compression for concrete & masonry).

Rapture length defines material efficiency as strength / weight ratio:

R = F / λ

R = rupture length
F = breaking strength
λ = specific gravity (self weight) 

Rupture length, is of particular importance for long-span structures.  The depth of  horizontal span members increases with span.  Consequently the weight also increases  with span.  Therefore the capacity of material to span depends on both its strength and  weight.  This is why lightweight material, such as glass fiber fabrics are good for long- span structures.  For some material, a thin line extends the rupture length to account for  different material grades.

The graph data is partly based on a study of the Light weight Structures Institute, University Stuttgart, German.

Structural design for: Strength, Stiffness, Stability, Synergy

Structures must be designed to satisfy three Ss and should satisfy all four Ss of structural design – as demonstrated on the following examples, illustrated at left.

1  Strength to prevent breaking
2  Stiffness to prevent excessive deformation
3  Stability to prevent collapse
4  Synergy to reinforce architectural design, described on two examples:

  Pragmatic example: Beam composed of wooden boards
  Philosophical example: Auditorium design

Comparing beams of wooden boards, b = 12” wide and d = 1”deep, each.  Stiffness is  defined by the Moment of Inertia, I = b d^3/12




Note:  The same amount of material is 100 times stiffer and 10 times stronger when glued  together to transfer shear and thereby engage top and bottom fibers in compression and  tension (a system, greater than the sum of its parts).  On a philosophical level, structures  can strengthen architectural design as shown on the example of an auditorium:

•  Architecturally, columns define the circulation
•  Structurally, column location reduces bending in roof beams over 500% !