Mar elias building
curtain wall verification
I- PROJECT INTRODUCTION
A curtain wall is defined as thin, usually aluminum-framed wall, containing in-fills
of glass. The framing is attached to the building structure and does not carry the floor
or roof loads of the building. The wind and gravity loads of the curtain wall are
transferred to the building structure, typically at the floor line.
The purpose of this report is to verify the stability of the aluminum-framed wall that
is holding the front façade.
The structural system will be modulated by using Robot Program, where the different
cases of loading can be applied.
II-Design Criteria
II.1-Materials
The materials used in the structure are:
Aluminum 6063 T6:
o Modulus of Elasticity Ea=70000 MPa
o Shear Modulus Ga=27800 MPa
o Poisson ratio =0.35
o 0.2% proof Strength f0=172 MPa
o Ultimate Tensile Strength fa=207 MPa
o Coefficient of Linear Expansion a=23 x 10-6 /oC
o Density a=2700 Kg/m3
Profiles Design Criteria to BS8118
Limitation Stresses:
fa / f0=207 / 172 = 1.2
Limiting Stress for Bending and Overall Yielding:
p0 = fa = 172 MPa
Limiting Stress for local capacity in tension or compression:
pa = (f0 + fa) / 2 = (172 + 207)/2 = 190 MPa
Limiting Stress in Shear:
pv = 0.6 x p0 = 0.6 x 172 = 103.2 MPa
Steel S275:
o Modulus of Elasticity Ea=205000 MPa
o Shear Modulus Ga=80000 MPa
o Poisson ratio =0.3
o Limiting Strength p0 =410 MPa
o Yield Strength fy=275 MPa
o Coefficient of Linear Expansion a=23 x 10-6 /oC
o Density s=2700 Kg/m3
Stainless Steel bolts:
o Ub=700 MPa Minimum tensile strength of the fastener
o Yb=450 MPa
o Ps=280 MPa 0.4 Ub Shear strength
o Pt=450 MPa 0.7 Ub or Yb Tensile strength
o Pbb=805 MPa 0.7(Ub + Yb) Bearing strength
III-Calculation Method
In the following it is described which preconditions form the basis of the structural
analysis. These remarks are partly rather trivial but they may also mark an
important basis for decision whether the procedure is allowed to be applied
reasonably in a particular case or not.
III.1-Background of Calculation Method
We have calculated single and multi-span-beams according to first order theory.
Thereby the degree of statical indeterminacy plays no role.
Solely vertical elements under mainly horizontal loads (wind) are considered. Thus
it is impossible to calculate roof elements by this module.
Mullions and transoms are calculated as single-span-beams in door and window
elements whereas in curtain wall mullions the number of spans and their span-
width are unrestricted. We used ROBOT structural analysis program to calculate
the profiles properties.
The recognized supports are “Pin Supports” (normal force N¹0, shear force Q¹0,
bending moment M=0) and “Roller Supports” (normal force N=0, shear force Q¹0,
bending moment M=0). Fixed supports (normal force N¹0, shear force Q¹0,
bending moment M¹0) are not applied. Picture 1 shows a more detailed support
definition. The bottom support is always automatically a pin support, the top
support is a roller support. All additional intermediate supports are freely
definable.
The decisive distributed load according to the requirements of the design load
standard results from on the load cases wind pressure and wind suction. In order to
convert load per unit area into load per unit length the program applies load
distribution areas.
All multi-span-beams strictly apply rectangular load distribution areas. Picture 2a
shows a curtain wall with a distributed load acting evenly over height and width. In
this particular case the load per unit length A on beam 1 results from multiplying
the distributed load by half of the distance to the next beam: Within span 1.1 the
factor amounts to B1/2, within span 1.2 to B1/2 and within span 1.3 to (B1+B2)/2.
For beam 2 and load per unit length B it is necessary to consider the load
distribution areas left and right of the beam: Span 2.1 and 2.2 own the same factor
which is (B1+B2)/2.
Beam 3 represents a special case. The support between span 3.2 and 3.3 isn’t set at
the same height as the transom connection is. In order to avoid different constant
distributed loads within span 3.2 the program assumes that the largest load
distribution area is applied for the whole span. Thus it results in the following
factors: span 3.1 (B2+B3)/2, span 3.2 and span 3.3 (B1+B2+B3+B4)/2 each.
When calculating a beam’s load it is assumed that all loads per unit length are
evenly distributed over the span, i.e. a load saltus is only possible at a support’s
position and not between two supports. Thus it appears that the applied load is
larger than theoretically required. In our example this is represented by area D on
beam 3 which is included in area C even though the area is already considered in
area B on beam 2. However, this simplification is safe from a structural engineer’s
point of view.
For all single-span-beams the load distribution area results from trapezoids or
triangles. Picture 2b shows a window element with distributed load acting evenly
over height and width. Since B1 is smaller than L, the maximum ordinate of the
trapezoidal load per unit length on beam 1 (area A) results from multiplying the
distributed load by B1/2. For beam 2 and load per unit length it is necessary to
consider different load distribution areas (area B: trapezoid, area C: triangle)
because the field widths B1 and B2 differ. The trapezoidal load per unit length
(area B) is calculated analogous to beam 1 (area A) here. Since B2 is larger than L,
the maximum ordinate of the triangular load per unit length on beam 2 (area C)
results from multiplying the distributed load by L/2. The triangular load per unit
length on beam 3 (area D) is calculated analogous to beam 2 (area C) here.
The ultimate state of serviceability is analyzed, the system’s deflections. This one
is usually decisive for the design in practice because deflection limits are usually
exceeded prior to stress limits.
Results
III.2-Deflection Line
This is the beam’s deformation diagram due to the applied load. It is decisive for
the design. Deflection limits are to be entered by the user. Those values usually
depend on the designated glazing and thus they have to be requested at the glass
manufacturer. Common limit values are 8mm or L/300.
Since the deflection is reciprocally proportional to the second moment of area
(moment of inertia) is able to calculate the required Ix value and to decide whether
the profile’s current Ix value is structurally sufficient or not.
The statics module splits the beam into individual spans measuring Lm which are
located between two supports each. A constant distributed wind load wm acts on
every span. A beam span might be split into individual glass spans Lm,n by
transoms i.
First we check whether the maximum existing deflection max vm due to the action
wm on span m (between two supports) does not exceed the limit values. Second we
survey if the maximum existing deflection of the glass spans m,n (between two
transoms i and i+1) keeps the limit values. For this the nodes i are linked to a chord
diagram (red lines). The chord diagram serves as reference for the relative
deflections of glass spans. Afterwards the maximum existing relative deflection
within the glass span max vm,n is calculated by subtracting the deflection of the
chord diagram (red) from the actual deflection of the deflection line (green).
Later it is displayed in the printouts which of the two parameters – beam span or
glass span deflection – is decisive for the design.
III.3-Moment Diagram
Displays the run of the bending moment curve within a beam. Without having an
influence on the calculated results non-rigid profile splices might be placed where
the moment curve crosses the x-axis. It is also possible to calculate the existing
stress within a beam by the moment diagram.
III.4-Shear Diagram
Displays the run of the shear force curve within a beam. The x-intercepts of the
shear diagram represent the places where the moment diagram shows a minimum
or maximum.
III.5-Support Reactions
Adding the shear forces acting right and left to the support results in the support
force.
III.6-Glass Statics
Glasses are calculated as rectangular linear supported plates in compliance with the
Kirchhoff plate theory. This states that the stresses within the midsurface equal to
zero and that transverse shear deformation is neglected.
As soon as glass deflections become larger than the glass pane thickness the so
called membrane effect is activated significantly. From a structural point of view it
is safe that the calculation method neglects this positive effect of geometrical
nonlinearity.
IV-Curtain wall design:
Overview:
Façade view:
Image shows the typical wall at the elevation on three levels.
Plan view - typical curtain wall unit:
Vertical section:
The below section of the building shows the design concept of the mullions and the total height of each
part.
