ISO 10252:2020

INTERNATIONAL ISO
STANDARD 10252
First edition
2020-02
Bases for design of structures —
Accidental actions
Bases du calcul des constructions — Actions accidentelles
Reference number
©
ISO 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 3
4.1 General . 3
4.2 Latin upper case letters . 3
4.3 Latin lower case letters. 4
4.4 Greek letters . 4
4.5 Subscripts . 5
5 General principles and conceptual approach . 5
5.1 Types of accidental actions . 5
5.2 Conceptual approach . 6
5.2.1 Target reliability level . 6
5.2.2 Strategies . 6
5.2.3 Identified and unidentified actions . 6
5.2.4 Types of analysis . 6
5.2.5 Classification of structures based on consequences . 7
5.2.6 Appropriate methods of analyses based on consequences. 7
5.3 Modelling of accidental actions . 8
5.3.1 Identified actions . 8
5.3.2 Unidentified accidental actions . 9
5.3.3 Representative values for accidental actions . 9
5.4 Structural analysis involving accidental actions .10
6 Impact action .10
6.1 General .10
6.1.1 Sources of impact loading .10
6.1.2 Nature of the impact .11
6.1.3 Structural analysis and simplifications .11
6.2 Impact from specific causes .14
6.2.1 Impact from road vehicles .14
6.2.2 Impact from derailed trains .14
6.2.3 Impact from ships .14
6.2.4 Impact from aircraft .15
6.2.5 Impact from helicopters .15
6.2.6 Impact from forklift trucks .15
6.2.7 Other types of impact .15
7 Explosion .16
7.1 General .16
7.1.1 Explosion types to be considered .16
7.1.2 Nature and schematisation of explosion loading . .16
7.1.3 Structural analysis and simplifications .17
7.2 Explosions of various types .18
7.2.1 Interior explosions .18
7.2.2 Exterior explosion .18
7.2.3 Explosions in tunnels .18
7.2.4 Dust explosions .18
7.2.5 High energy explosions .19
8 Unidentified actions .19
8.1 General .19
8.2 Notional removal of or damage to elements .19
8.3 Notional loads on key elements .20
8.4 Risk-based design for unidentified accidental actions .20
Annex A (informative) Guidance for detailed impact analysis .21
Annex B (informative) Guidance on detailed explosion analysis .58
Annex C (informative) Design for accidental actions .86
Bibliography .103
iv © ISO 2020 – All rights reserved

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
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on the ISO list of patent declarations received (see www .iso .org/ patents).
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expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 98, Bases for design of structures,
Subcommittee SC 3, Loads, forces and other actions.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
Introduction
This document provides requirements and guidelines for the design and assessment of structures in
relation to the possible occurrence of accidental actions induced by human activities. Fire and man-
made earthquake, however, are not included.
This document is fully aligned with ISO 2394 and gives information for risk informed decision making
and semi-probabilistic design and assessment. Like in most modern codes nowadays, attention is given
to explicit modelling of hazard scenarios as well as to more implicit safety measurements following
from robustness requirements.
This document aims at promoting harmonization of design practice internationally and unification
between the respective codes and standards such as for actions and resistance for the respective
structural materials.
The principles and appropriate instruments to ensure adequate levels of reliability provide for
special classes of structures or projects where the common experience base need to be extended in a
rational manner.
The informative annexes included in this document provide support for the interpretation and the use
of the principles contained in the normative clauses.
vi © ISO 2020 – All rights reserved

INTERNATIONAL STANDARD ISO 10252:2020(E)
Bases for design of structures — Accidental actions
1 Scope
Accidental actions can be subdivided into accidental actions with a natural cause and accidental actions
due to human activities. This document applies to reliability based and risk informed decision making
for the design and assessment of structures subject to accidental actions due to human activities.
However, fires and human-made earthquakes are not included.
The information presented in this document is intended for buildings and civil engineering works,
regardless of the nature of their application and the use or combination of materials. The application of
this document can require additional elements or elaboration in special cases.
This document is intended to serve as a basis for those committees that are responsible for the task
of preparing International Standards, national standards or codes of practice in accordance with
given objectives and context in a particular country. Where relevant, it can also be applied directly to
specific cases.
This document describes how the principles of risk and reliability can be utilized to support decisions
related to the design and assessment of structures subject to accidental actions and systems involving
structures during all the phases of their service life. For the general principles of risk informed design
and assessment, it is intended that ISO 2394 be considered.
The application of this document necessitates knowledge beyond that which it contains. It is the
responsibility of the user to ensure that this knowledge is available and applied.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the editions cited here apply. For
undated references, the latest editions of the referenced documents (including any amendments) apply.
ISO 2394:2015, General principles on reliability for structures
ISO 8930, General principles on reliability for structures — Vocabulary
3 Terms and definitions
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
For the purposes of this document, the terms and definitions given in ISO 2394 and ISO 8930 and the
following apply.
3.1
barriers and shock absorbers
objects or structural devices intended to absorb part of the impact energy in order to protect the
structure
3.2
burning velocity
rate of flame propagation relative to the velocity of the unburned dust, gas or vapour that is ahead of it
3.3
deflagration
propagation of a combustion zone at a velocity that is lower than the speed of sound in the unreacted
medium
3.4
detonation
propagation of a combustion zone at a velocity that is greater than the speed of sound in the
unreacted medium
3.5
dynamic load
time variant load or action that causes significant dynamic effects in the structure or in structural
elements
Note 1 to entry: This means that the acceleration is not negligible; as a consequence, equations of motion should
be used instead of equations of equilibrium.
Note 2 to entry: In the case of impact, the dynamic load represents a force on an associated contact area at the
point of impact.
3.6
equivalent static load
alternative and usually conservative representation of a dynamic load (3.6) suitable for a static
structural analysis
3.7
explosion
physical and/or chemical process of abrupt release of energy leading to short pressure waves of very
high intensity
3.8
flame propagation
speed of a flame front relative to a fixed reference point
3.9
impact
event occurring when one object comes into contact with another one, where the contact force is of
short duration
3.10
impacting object
vehicle, ship, etc. colliding with a structure
3.11
key element
structural member upon which the stability of a part of remainder of the structure depends
3.12
local damage
localised failure of a part of a structure that is severely disabled by an accidental event
3.13
unidentified action
accidental action or event that is unknown or unforeseen and cannot be considered by explicit analysis
in the design or assessment
2 © ISO 2020 – All rights reserved

3.14
venting panel
non-structural part of the enclosure (wall, floor, ceiling) with limited resistance that is intended to
relieve the developing pressure from deflagration (3.4) in order to reduce pressure on other parts of the
building
4 Symbols and abbreviated terms
4.1 General
The symbols listed in this clause are used generally throughout the document. Symbols which are used
only in one section are explained there and not listed here. All the symbols are based on ISO 3898.
4.2 Latin upper case letters
A accidental action, (cross sectional) area
A design value of an accidental action
d
D diameter
E modulus of elasticity, action effect, energy
E kinetic energy
kin
E deformation energy
def
F action, load in general, collision force
F frictional impact force
R
H height
K deflagration index of a gas cloud
G
K deflagration index of a dust cloud
St
L length
P probability
P probability of failure
f
P target probability of failure
ft
P probability of survival
s
R resistance
T temperature, period of time
T period of time to be considered in a damaged situation
e
T reference period of time
ref
U severity (magnitude) of the source of an action
4.3 Latin lower case letters
a acceleration, geometric parameter
b geometric parameter
c wave propagation speed
f the event of failure, material strength parameter
f (x) probability density function of X with dummy variable x
X
g(X, t) limit state function
h height
h height of the application area of a collision force
a
i impulse per unit of area resulting from explosion
k stiffness
l length
m mass
p momentum (impulse); pressure
p static activation pressure that activates a vent opening when the pressure is increased slowly
stat
r distance parameter
r reduction factor
F
t time
u displacement;
u maximum possible displacement (crumble length of impacting object)
o
v velocity
4.4 Greek letters
Δ interval
β reliability index
β target reliability index
t
ε strain
γ partial factor
γ partial factors for actions
f
λ rate of relevant events
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µ friction coefficient
ρ mass density
σ stress
4.5 Subscripts
i,j index of basic variable
k characteristic value
d design value
l leading action
max maximum value (often in time)
o initial (reference) value
p plastic
rep representative value
x,y,z coordinate directions
y yield (material)
5 General principles and conceptual approach
5.1 Types of accidental actions
Accidental actions due to human activities shall be considered in the design and assessment of buildings
and other civil engineering structures. These actions include but are not limited to:
— Impact from vehicles, trains and tramways, ships, aircrafts, helicopters, forklift trucks, falling
materials (rockfall, debris flow, dropped objects from cranes), machine related impacts like toppling
cranes, wind turbines, parts detached from a rotary machine, blades detached from turbines, etc.;
— Internal and external explosions due to various sources like gas, dust, TNT, dynamite, etc.;
— Unidentified actions following from:
— errors in design, errors during construction, service and operation and errors associated with
maintenance and repair activities,
— acts such as sabotage, vandalism, terrorism, etc. and their consequences.
Unidentified actions may be taken into account by specifying the resulting damage to the structure.
Design and assessment decisions related to the occurrence of accidental actions shall be made in
accordance with the principles in ISO 2394.
This document shall, for a limited set of relevant actions, provide dedicated information on incident
scenarios, load and resistance models, protection systems and calculation procedures.
NOTE Depending on the local circumstances, other actions can also require attention, as for instance
avalanches, ice loading, floods resulting from storm surges, heavy rainfall or melting snow, log jams in rivers,
sinkholes, etc.
Common impact actions (such as those resulting from stumbling persons, mooring of ships, etc.) should
be considered as variable actions and are outside the scope of this document.
The extent and the depth of the design and analysis depend on the possible failure consequences and
costs of mitigation.
5.2 Conceptual approach
5.2.1 Target reliability level
The appropriate degree of reliability shall, in accordance with ISO 2394, be selected with due regard
to the possible consequences of failure, the associated expense and the level of efforts and procedures
required to reduce the risk of failure and damage.
Target reliability levels for existing structures can differ substantially from those for new structures
due to economic reasons. Ethical considerations, however, can impose bounds on the outcomes of an
economic optimisation.
5.2.2 Strategies
Given the special character of accidental actions, the design approach shall focus on a combination of
structural and non-structural measures to either prevent or limit:
— the occurrence of the action;
— the severity of the action;
— the effect of the action in terms of loading on the structure;
— the various direct and indirect consequences.
Direct consequences are damages caused directly by the action; indirect consequences are the result
of direct damages, irrespective of the accidental action itself. The ratio between direct and indirect
consequences can be seen as a measure of robustness (see ISO 2394).
In many cases, it can be economic, if not unavoidable, to accept some limited degree of direct local damage.
Special devices such as barriers and shock absorbers can be very helpful.
NOTE More information on effects of such devices is presented in Annex C.
5.2.3 Identified and unidentified actions
In the case of identified accidental actions, an assessment on the basis of physical models, reliability
considerations and risk analysis shall be performed, depending on the consequence class of the
structure.
Since not all possible actions can be foreseen in sufficient detail, the structure shall possess an adequate
degree of robustness. In the context of this document, this means that, given the occurrence of local
damage or degradation due to an arbitrary accidental action, the probability of a disproportionate
collapse should be limited.
5.2.4 Types of analysis
Depending on the function of the structure and the possible consequences in case of failure, the type of
analysis and degree of sophistication shall be chosen, both with respect to the physical modelling and
to reliability and risk aspects (see 5.3).
6 © ISO 2020 – All rights reserved

The following types of analysis may be used, depending on the applicable risk/reliability aspects (see
also ISO 2394):
a) a full risk analysis;
b) a probabilistic analysis based on predefined target reliability levels;
c) semi probabilistic specifications of actions or damage characteristics.
The following types of analysis may be used, depending on the physical modelling (see also 5.4):
— a non-linear dynamic analysis, including load structure interaction;
— a non-linear structural dynamic analysis based on specified external forces or damage
characteristics;
— a static structural analysis using quasi static actions or damage characteristics.
Within each of the above analysis categories, further simplifications are possible. The ultimate
simplification is to develop a set of prescribed rules. In such a case, the effectiveness of these rules on
a global level shall be based on experience (observations), experiments (tests) or advanced analysis
procedures. In case of observations and testing, statistical uncertainty as formulated in ISO 2394 shall
be accounted for.
Risk and reliability analysis should be based on statistical data as far as possible. Where that is not
possible, best estimates based on engineering judgment should be made; these values can also be
regarded as nominal values.
5.2.5 Classification of structures based on consequences
The classification system of ISO 2394:2015, Annex F, shall be followed. This system distinguishes
5 classes of consequences, ranging from consequences class CC 1 (predominantly insignificant material
damage) to CC 5 (catastrophic losses and large number of exposed persons). The consequence class is in
general a useful indicator for both the level of safety measures and the method of analysis to be applied.
5.2.6 Appropriate methods of analyses based on consequences
The extent and the depth of the analysis methods and the appropriate level of mitigation shall be chosen
in accordance with the expected consequences.
An appropriate analysis method and level of mitigation shall contain, as a minimum, the following
elements depending on the applicable consequence class:
CC 1: No specific consideration of robustness.
CC 2: Simplified analysis based on idealized action and structural performance models and/or
prescriptive design/detailing rules.
CC 3: Systematic identification of scenarios leading to structural collapse. Addressing strat-
egies to deal with the identified scenarios. Analyses of structural performance may be
based on simplified and idealized models but should be subject to justification. Prescrip-
tive design and detailing rules may be utilized but should specifically address the identi-
fied scenarios. Reliability and risk analyses addressing direct and indirect consequences
should be used as the basis for simplifications and idealizations.
CC 4: Detailed studies and analyses of scenarios leading to structural collapses utilizing input
from experts on all relevant subject matters. Such analyses include detailed assessments
using dynamic and non-linear structural analyses and risk analyses rigorously address-
ing direct and indirect consequences.
CC 5: Same as for CC 4 but with the addition of the involvement of an external expert/review
panel for quality control.
From a reliability point of view, simplified models may always be used as long as they are conservative.
Whether the degree of conservatism is acceptable or not is an economic issue to be decided by the
decision maker.
NOTE The decision maker can be the owner or the competent authority.
5.3 Modelling of accidental actions
5.3.1 Identified actions
The model for extreme hazards such as explosions or collisions resulting in identified accidental actions
shall be based on the following:
a) a triggering event at some point in time and place;
b) the amount of energy involved in the event and other relevant parameters;
c) the physical interactions between the event, the environment and the structure, leading to the
exceedance of various subsequent limit states in the structure.
All of the above three aspects shall be treated as random quantities and/or random processes as
follows:
— The occurrence of the triggering event may often be modelled as events in a Poisson process of
intensity λ (t, x) per unit of volume and unit of time, t representing a point in time and x the spatial
coordinates (x , x , x ).
1 2 3
— The amount of energy may be treated as a random quantity described by a (multidimensional)
probability distribution.
— Finally, the physical interactions determining the details of the action and structural response may
also be modelled using uncertain variables and properties.
Given these uncertainties, the probability of structural failure (for constant λ and small probabilities)
can be expressed as:
∞
PT ≈=λTP()fU|duf ()uu (1)
()
fUrefref
∫
where
λ is the number of potential trigger events (e.g. vehicles passing by) per unit of time;
T is the reference period under consideration (usually one year or the lifetime of the structure;
ref
f is the failure event to be described by physical models of the structure and the environment;
8 © ISO 2020 – All rights reserved

f (u) is the probability density function of the severity (energy) of the hazard, given a trig-
U
ger event;
U represents the severity (magnitude, amount of available energy) of the hazard;
u is a specific value of U (dummy variable).
The probability of failure can depend on the distance between the structure and the location of the
event. In that case, an explicit integration over the area or volume of interest is necessary. If there is
more than one hazard, the resulting failure probabilities shall be added, taking into account possible
correlations.
Failure in Formula (1) may refer to local or global consequences. The failure probability according to
Formula (1) should be less than a specified annual target value, depending on the consequences.
−6 −4
NOTE Target values are usually set between 10 and 10 per year (see also ISO 2394).
5.3.2 Unidentified accidental actions
In the case of unidentified accidental actions, the effect of the action shall be modelled as a specific
damage (for instance the removal of a specific beam or column). For the remaining part of the structure,
for a relatively short period of time T (for instance defined as the time to evacuate people out of the
e
building, or the time to repair), the structure shall withstand applicable actions .The corresponding
conditional probability of failure shall not exceed a prescribed target reliability, as given by Formula (2):
PR {}
e
where
R is the resistance of the damaged structure after the occurrence of the unidentified acci-
dental action;
E is the applicable action (effect) after the occurrence of the unidentified accidental action.
The target reliability in this case shall be aligned with the safety target for the building under non-
accidental loading, the period T under consideration (hours, days or months) and the estimated
e
probability that the local damage under consideration can develop (by causes other than those already
considered in design).
NOTE Depending on the circumstances, values between 0,001 and 0,1 can be taken as appropriate.
For unconventional structures (e.g. structures with novel design concepts or using new materials),
the probability of having an unspecified cause of failure should be considered as substantial. As a
consequence, the target reliability value applicable to Formula (2) sometimes needs to be lowered.
5.3.3 Representative values for accidental actions
Based on the probabilistic approach outlined in 5.3.1 and 5.3.2, appropriate representative values for
dynamic or quasi static accidental actions may be derived for use in simplified semi-probabilistic design
and analysis.
NOTE Representative values for selected types of accidental actions, based on statistical or other approaches,
are presented in Annexes A to C.
5.4 Structural analysis involving accidental actions
The structural analysis involving an accidental action shall, to the extent appropriate for the specific
problem, account for:
— severe geometrically nonlinear effects;
— nonlinear material behaviour;
— possible complete rupture of heavily exposed or minor structural elements;
— dynamic effects;
— the interaction between the action and the structure;
— the effects of protecting systems.
Simplified analysis can be appropriate but shall be based on proper justification.
EXAMPLE A quasi static analysis can often replace a full dynamic analysis.
In the case of impact, the most accurate result can be obtained by using an integrated model comprising
the impacting body, the structure including the foundation and the protection system if applicable. As a
simplification of the analysis, it may be assumed conservatively that the impact energy is fully absorbed
either by the structure or by the impacting object.
In the case of an explosion, the action shall be characterized by sudden rises in air pressures and
possibly wind effects. The following interaction effects shall be considered:
— the presence of the structure and/or other obstacles that can lead to reflections and turbulence and
thus affect the explosion process;
— the collapse of weakened structural elements (accidentally or intended) that can lead to a change of
air pressures.
For determining the material properties of the impacting object and of the structure, upper or lower
characteristic values should be used, where relevant. Strain rate effects should also be taken into
account, where appropriate.
When making simplifications to the analysis, a moderate level of accuracy may be deemed to be
sufficient, considering the low probability of the accidental actions.
NOTE For relevant data and approaches of analysis reference is made to Annex C.
6 Impact action
6.1 General
6.1.1 Sources of impact loading
This section applies to the following types of impact actions:
— road vehicles;
— trains and tramways;
— ships;
— aircrafts;
— helicopters;
10 © ISO 2020 – All rights reserved

— forklift trucks;
— falling and sliding materials (e.g. dropped objects, rockfall, debris).
Impact shall be considered in the design and assessment when any of the above (or other relevant)
moving objects are in the immediate vicinity of the structure and significant impact forces can occur.
The analysis shall be in accordance with the requirements described in 5.2.
Detailed guidance and information are provided in Annex A.
6.1.2 Nature of the impact
During impact, the available kinetic energy of the impacting body shall be considered to be absorbed by
deformation of the impacting object itself, deformation of the structure and, if applicable, its protecting
systems. Impact interaction actions are usually of high energy and of short duration compared to the
longest dynamic natural periods of the structure.
In order to assess the effect of the impact, next to the structural characteristics, the mass, the velocity
at the time of impact, the angle of approach and the mechanical properties of the impacting body shall
be considered. These parameters usually depend on the characteristics of the environment, such as the
type of road or waterway, the distance, local slopes and so on.
Both the likelihood of the initiating event leading to structural damage as well as the statistical
characteristics of the colliding object and the structure shall be taken into consideration.
6.1.3 Structural analysis and simplifications
6.1.3.1 In general, collision phenomena involve both the deformation of both the structure and
the impacting body. To simplify the analysis, the interaction force may be found by assuming that the
structure is fully rigid and the kinetic energy is absorbed and dissipated by the impacting object.
For the accidental type of impact considered in this document, the collision is a process involving
(quasi) elastic-plastic deformations. Examples of a rigorous analysis of the collision phenomenon can be
found in Annex A. For guidance, the following simplified approaches to estimate the impact forces and
durations are recommended:
a) a plastic yield force that is constant with deformation and time;
b) a series of constant forces, each of which having a finite duration;
c) a plastic yield force that varies with deformation and/or time;
d) a quasi-elastic rod or spring model, with calibrated properties.
The first approach is common for simple collisions:
— The primary inelastic response mode and its corresponding plastic, constant resisting force are
determined.
— The elastic phase that precedes inelastic phase is disregarded because little energy is absorbed
during the elastic phase.
— The time necessary to bring the colliding object to rest is calculated as per Formula (3):
Δtm= vF/ (3)
r p
where
Δt is the time interval from start of collision to time of zero velocity of colliding object
m is the mass of colliding object
v is the velocity of colliding object at the start of the impact
r
F is the plastic resisting force
p
In order to consider (as in the second approach) a series of constant, but limited in duration, forces, the
function needs to be evaluated as per Formula (4):
mv =∑Fu (4)
rpii
where
u are the extent of deformations over which the corresponding sequential plastic forces F are
i pi
applicable until the deformation at which all the kinetic energy is dissipated;
F are the plastic resistance forces for interval i.
pi
Then the duration of the collision can be estimated approximately by weighting the participation of the
various engaged F , or by theoretically exact calculations.
pi
The third simplified approach involves postulating a force function that varies with deformation or
time. Unfortunately, this approach requires the analyst to develop a forcing function, which can be
problematic because the forcing function generally cannot be prescribed in advance. However, some
guidance can be developed from the following subclauses and Annex A, where results of some tests and
theoretical developments are reported.
The fourth approach may be based on impact by a prismatic and homogeneous elastic rod. Given the
primarily plastic nature of the impact process, the elastic model is useful only for the process up to
the moment of the maximum indent. The properties of the rod should be considered as quasi-elastic
quantities with values calibrated to the real highly non-linear elastic plastic behaviour.
A fully elastic rod develops an internal stress wave that travels from the striking end to the free end,
and then back to the striking end, at which point the collision is complete. When using the model to
describe the elastic-plastic impact, only the wave travelling from the striking end to the free end is
used, neglecting however the reflected wave to simulate the irreversible nature of the deformation.
With this model, the maximum resulting dynamic interaction force is given by Formula (5):
Fv= km (5)
r
where
v is the velocity of the rod at impact;
r
k is the spring stiffness of the rod (i.e., AE/L):
A is the cross-sectional area of the rod;
E is the elastic modulus of the rod;
L is the length of the rod;
m is the mass of the rod.
12 © ISO 2020 – All rights reserved

The travel time of the stress wave from the striking to the free end is L/c , where c is the rod wave
o o
propagation velocity as given in Formula (6):
cE= /ρ (6)
()
o
where ρ is mass density.
The duration of the collision is given by:
ΔtL==//cm k (7)
()
o
NOTE 1 Guidance on appropriate values of k can be found in A.1 to A.7.
NOTE 2 An elastic spring model, with a rigid mass and separate spring with a stiffness constant, k, achieves
the same peak force in time as the rod model. However, because the force increases over time, and is not constant
as in the rod model, the time to develop the maximum force is: Δt = (π/2) √(m/k).
NOTE 3 Refined analysis as well as experiments (see Annex A) show that the force time relation can often be
represented by a triangle (Figure 1). In that case, the average value of the force follows alternatively from mv /
r
Δt, where estimates for Δt can be found from Formula (7); in absence of other information, the duration of the
impact can also be found from Δt = u /v, where u is the estimated final indent (often referred to as crumble
o o
length). In general, Δt is higher (in the elastic spring model up to a factor π/2) as the impacting body slows down
during the impact process.
Key
F interaction force
t time
Δt time interval
m mass of the colliding object
k stiffness of colliding object
Figure 1 — Schematic pulse shapes in case of a colliding object hitting a rigid,
immovable structure
NOTE 4 The models in this clause give dynamic elastic force values on the outer surface of the structure.
Within the structure, these forces can give rise to dynamic effects in structural components, depending on the
duration of the load. In the absence of a dynamic analysis, the dynamic amplification factor for elastic response
can be assumed to be equal to 1,4.
6.1.3.2 An alternative upper bound can be found when the structure dissipates all energy and the
colliding object is considered rigid.
If the structure is designed to absorb the
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