X 2 cos2 M H h x sin q Vx cos 2 dM h x sin dH
y ,then dM y and dHĭisplasment 2 in BC rafter The moment expression at abscissa ,x,is: In any ordinate point ,y, of the column AB, the moment is M H. In application of Castigliano théorem and with the structure symetryĭisplacement 1 in AB column. This simplification ,justified by the presence of the haunchs ,conduct to increase the moment at C and decrease moments at B and D.It will be compensated by the simplification applied to purlin calculations,wich act in opposite sens.Ģ.3 Simple cases 1/Case 1 Vertical actions 3/ Forces transmitted by purlins The forces transmitted to rafters by purlins, (are ponctual forces and must be applied in calculations of rafters),will be converted to linear forces.The error caused by this simplification is ≈0.5%,and conduct to increase the moments at B and D 4/ Stiffness at B and D To conduct manually calculations we consider that the inertia of the column and the rafter are equals Ic =IR The coefficient of stiffness In this case they will be neglected for calculations.Ģ/ wind forces (up-to fly) The actions applied to duopitch roofs are oriented as described above (perpendicular to rafters).For simplifications we admit that these forces will be oriented vertically as gravity forces. These actions are very small in ccomparison with the wind actions on vertical walls(0.5% to 1.3%). While this system is effective in restraining the top flange of the rafter I-beam,the bottom flange remains relatively unrestrained, and to achieve the requisite restraint,short lengths of angle iron are connected at intervals between the bottom flange of the I-beam and the purlins.This simple and necessary anti-buckling feature is sometimes neglected in the design of the portal frames.Ī building frame subjected to wind forces along its length will tend to collapse as shown above ,while a building with a braced side bay as shown below will be stable,since the braced bay will functions as a “buttress” to resist the wind forces, and transform them to the foundationsĢ portal frame design 2.1 Basic data Total lengthĢ.2 Loads 2.2.1 Permanent loads Self-weight of the beam Roofing with purlins For an internal frameĢ.2.3 Wind loads Take from the document treated “ wind actions to EN (2005) as a values described belowĢ.2.4 Approximation calculations 1/ wind forces applied to duopitch roofs and partial variables live loads In a braced roof this restraint is provided by the purlins acting together with a braced bay.The purlins provide the restraining force for the rafters,and the braced bay acts as a “buttress” wich absorbs these purlin restraining forces. The destabilization it causes is a major design consideration, and in this context, foundations can be regarded as the building’s “anchors D/ the rafter of the portal frame is a slender structural element,and it is restrained it will buckled when loaded. The effect of wind on a light building cannot be overemphasized.
Generally speaking it is a fact that portal frame buildings of this kind are light weight structures, and as such they tend to collapse “sideward” and “upwards” rather than do wnwards”. These destabilizing forces are resisted essentially by the weight of the building,and in this regard,the foundations contribute significantly to this weight.
Roof loads are positive and up to down direction B/ If The joints at B,C and D are not rigid,they will open up and the frame will be unstableĬ/ 1) Vertical loading on the frame results in A and E tending to be pushed outwards.if the foundation cannot resist this horizontal push,outward movement will occur,and the frame will l oose structural strengthĢ) Wind subjects the portal frame to uplift forces(the roof tends to fly-off)like an overturning forces on the sides and ends of the building, Wind loads Wind loads can be positive as on AB or negative (suction)as on BC,CD and DE. The frame is designed for the following loads Analysis of portal frame building In accordance to EN (2005) 1 description A/ The portal frame is the main structural element of theīuilding.