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Note 6 Level 1
Technical
Technical Guidance Note
TheStructuralEngineer
March 2012
25
Notional
loading
Introduction
This Technical Guidance Note concerns the concept of notional loading,
which the Eurocodes classifies as Equivalent Horizontal Forces. These are
loads that exist due to inaccuracies and imperfections introduced into the
structure during its construction. The following text explains how notional
lateral loads are incorporated into the design process.
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• Design principles
• Applied practice
• Worked example
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• Further reading
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Design
principles
A notional load is based on a proportion of
the vertical load the structure is supporting.
Typically they are applied in conjunction with
other loads during analysis.
Generic Notional Horizontal Load
(Fhn)
Eurocode 1-1-6 concerns loading during the
construction of structures. Within Annex
A, Clause A1.3 of Eurocode 1-1-6 there is a
generic definition of a notional horizontal load
(Fhn) that can be applied to all structures.
The magnitude of this force is 3% of the
vertical loads from the worst case load
combination for a given structure. This can be
adopted for all structures, regardless of the
material they have been constructed from.
Material Sensitivity to Notional Load
Notional loads represent forces that come
about due to imperfections in the structure.
Some materials are more sensitive to this
phenomena than others and it is for this
reason that notional loads are linked directly to
the material a structure is constructed from.
The Eurocodes for steel and concrete
structures have sections within them that
are dedicated to deriving notional horizontal
loads within structures. The following sections
explain how each material addresses notional
loading.
Notional Loads in Steel Frames
Steel frames are very sensitive to notional
loads. This is because imperfections within
the fabricated elements and their connections
are inevitable as they are impactful. It is for
this reason that any design of a steel frame
structure must take them into account.
Eurocode 3-1-1, Clause 5.3.2(3) covers this
by creating coefficient (ф), which the vertical
load of a structure is multiplied by. This
replaces (Fhn) notional load from Eurocode
1-1-6 described previously.
It is defined as �m =
� 0.5 �1+
1
�
m
where m is the number of columns in a row
that are connected to the bracing system
being considered. These columns must also
be supporting at least 50% of the average
vertical load of those columns in the row being
considered (Figure 1):
Coefficient (ф) is determined thus:
ф = ф0 �h �m (Equation 5.5, Eurocode 3-1)
Where:
ф0 is the sway angle at which the structure
rotates due to notional loads and has a base
value of 1/200
�h is the factor that is related to the height of
vertical elements within the structure.
This is defined as �h =
2
�h
,
where ‘h’ is the height of the structure.
This factor can only be within the range
of 0.66 < �h <1.0. If the calculated value
lies outside of this bracket, then the closer
extreme is taken.
�m is the factor that takes into account the
number of vertical elements in a row.
Figure 1 Extent of columns that influence the value
of �m
Clause 5.3.2(4)B in Eurocode 3-1 states that
where the overall applied lateral load is more
than 15% of the vertical load in a member then
the notional horizontal load can be ignored. This
is expressed as H�d ≥ 0.15 V�d in the above
referenced clause.
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Note 6 Level 1
26
TheStructuralEngineer
March 2012
Notional Loads in Concrete Frames
The Eurocode’s approach to imperfections of
elements within concrete structures is very
similar to the one adopted for steel framed
structures. The only key difference is that
there is some provision for horizontally aligned
elements as well as those that are vertical.
Eurocode 2-1-1 Clause 5.2(5) defines the
notional load coefficient (Ѳ)in a similar way
to Eurocode 3-1-1 in that it is a function of the
vertical load the structure is supporting. There
is however a slight difference to the derivation
of (Ѳ) to take into account the length of
elements as well as their height:
Ѳ = Ѳ0 �h �m (Equation 5.1, Eurocode 2-1)
Where:
Ѳ0 is defined as the sway angle of the
structure, in a similar fashion to Eurocode
3-1-1, described above.
�h is the factor that is related to the height or
length of vertical elements within the structure.
2
This is defined as �h = � l
where ‘l’ is the length or height of members.
This factor can only be within the range of
0.66 < �h <1.0. If the calculated value lies
outside of this range, then the closer extreme
is taken.
1
�m = � 0.5 �1+ m �
as per steelwork structures - with the value
of m varying in accordance with the extent
to which the structure is being analysed. For
isolated members, the value of m is 1, while
for braced frames m is the number of vertical
elements contributing to a braced frame. If a
floor slab is being assessed, the value of m is
the number of vertical members contributing
to the horizontal force that is exerted onto the
floor slab.
Notional Loads in Isolated Elements
within Concrete and Steel Frames
It is possible to assess the impact that
notional loading has on isolated elements
within structures. Clause 5.2(7) in Eurocode
2-1-1 describes two different methods of
assessing the impact of imperfections on
individual elements within a structure. Either
can be employed, but once a method has
been selected, it should be used exclusively
throughout the project.
Method (a) considers the eccentricity of
elements as they are constructed. This is
defined as: ei = фl0/2 for steel frames or
Technical
Technical Guidance Note
ei = Ѳl0/2 in the case of concrete frames.
Where:
ei is the eccentricity
ф/Ѳ is the angle of rotation due to the
application of the notional load as per steel
and concrete framed structures
l0 is the length of the element
When considering a wall or an isolated column
within a braced structure, ei can be estimated
to be l0/400.
Once the value of ei is determined, it is
multiplied by the maximum axial load of the
member being considered.
Method (b) imposes a lateral force, Hi onto
the element at a point along the element that
generates the maximum bending moment
from this load. Typically this is at the midspan position.
For members that are not within a braced
frame, the force Hi is defined as фN or ѲN,
where N is the total axial force and ф/Ѳ
is defined above. For elements within the
braced frame the value of Hi is 2фN or 2ѲN,
depending on the structure’s material.
Partial Factors for Notional Loads
Notional loads are considered in combination
with applied lateral loads, such as wind. The
partial factors applied to them reflect that
they exist within the structure prior to any
load being applied to it. They are treated in the
same way as a wind load and are classified as
a variable static action within the Eurocodes.
When notional loads are combined with only
the dead and imposed loads, they typically
adopt the ψ0 combination factor, which is
0.5. When used in combination with the wind
load, the combination factor ψ1 is applied
(typically 0.2).
Here is an example of how notional
horizontal loads would be combined into
a single load case when the imposed load
(Qk,1) is the leading variable action for a
commercial office building:
1.35Gk + 1.5Qk,1 + (0.7ψ0)1.5Qk,2 +
(0.2ψ1)1.5Qk,3
Where Gk is the dead load, Qk,1 is the imposed
load, Qk,2 is the wind load, and Qk,3 is the
notional load. The combination factor for the
wind load is ψ0 and the combination factor for
the notional load is ψ1. Combination factors
can vary depending upon the type of use of
the building when the wind load is taken as
the primary action. See the UK National
Annex to Eurocode 0, Table NA.A1.1 for the
applicable factors.
Applied
practice
The applicable codes of practice for the
derivation of notional loads are as follows:
BS EN 1991-1-6 Eurocode 1: Actions on
structures — Part 1-6: General actions —
Actions during execution
BS EN 1991-1-6 UK National Annex to
Eurocode 1: Actions on structures — Part
1-6: General actions — Actions during
execution
BS EN 1992-1-1 Eurocode 2: Design of
reinforced concrete structures —Part 1-1:
General rules and rules for buildings
BS EN 1992-1-1 UK National Annex to
Eurocode 2: Design of reinforced concrete
structures —Part 1-1: General rules and rules
for buildings
BS EN 1993-1-1 Eurocode 3: Design of steel
structures —Part 1-1: General rules and rules
for buildings
BS EN 1993-1-1 UK National Annex to
Eurocode 3: Design of steel structures
—Part 1-1: General rules and rules for
buildings
Glossary and
further reading
Action – An applied load, both due to a
direct application or as a consequence of an
indirect effect such as thermal expansion of
the structure.
Accidental Action – A loading condition
that is unlikely to occur. As such partial
factors are not applied to it during ULS
analysis.
Characteristic load – A base load that
has not had any partial factors applied to it.
National Annex – A part of the Eurocode
that has been written specifically for a
particular region.
Notional load – A load that exists within
the structure due to imperfections that
cause a lack-of-fit.
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Worked example
Initially the need to include notional loading within the analysis of the
structure is checked. This is done by comparing the applied wind load on a
vertical element against 15% of the axial load, thus:
A 5 storey commercial property is to be
constructed from a steel frame structure.
It has a 10m by 8m grid layout and the wind
load upon it is 1 kN/m2. The internal columns
have an axial load of 2.5 MN and all edge
columns have 1.25MN. Corner columns
have an axial load of 0.75MN. The structure
is braced via a pair of concrete lift shaft
and stair cores. Figure 2 shows the overall
dimensions of the structure.
Determine whether or not notional loads
should be applied to this structure and if
so, what their magnitude is. This should be
carried out for all orthogonal directions in
accordance with good practice.
Now that the need for the inclusion of notional loading has been proven to be
positive, factor (ф) needs to be calculated.
With the value of (ф) calculated, the magnitude of the notional horizontal load
can be calculated:
Figure 2 Isometric view of proposed commercial
building
Partial factor – A factor that is applied
to characteristic loads when carrying out
design of structures and the elements they
are constructed from.
Variable static action – A load that is
static, yet variable. Notional loads are typical
of this type of action.
Further Reading
Manual for the design of steelwork building
structures to Eurocode 3 – Institution of
Structural Engineers – October 2010
Web resources
For more information on this subject, please
visit: www.istructe.org/resources-centre/
library