22 March 202022 March 2020 by Omotoriogun Victor

Principles of Design to Eurocodes

Introduction

This post serve as an introduction to the core concepts within the Eurocode, references will be particularly made to this post as it focus is on the head code of the Eurocode; Basis of Structural design EN 1990 and part of Actions on structure EN1991.

Basis of Structural Design

EN 1990 provides comprehensive information and guidance for all the Eurocodes, on the principles and requirements for safety and serviceability. It gives the partial safety factors for actions and combinations of action for the verification of both ultimate and serviceability limit states

Limit State

Limit states are conditions beyond which some design criterion is violated. Generally, all structures shall be verified at

Ultimate Limit State

Any condition that concerns the safety of people or structure. There are four ultimate limit states to be considered according to EN-1991 each having different partial factors when verified. These are:

(STR) Internal failure or excessive structural deformation
(EQR) Loss of static equilibrium of the structure or a structural element

(GEO) Failure or excessive deformation of the ground
(FAT) Failure through time-dependent effects e.g. fatigue

The design situation upon which ULS checks may be performed are:

persistent design situations, which concern the conditions of normal use;
transient design situations, which concern temporary conditions applicable to the structure (e.g. during construction or repair);
accidental design situations, which concern exceptional conditions applicable to the structure or to its exposure (e.g. ﬁre, explosion, impact or the consequences of localized failure);

seismic design situations, which concern conditions applicable to the structure when subjected to earthquake and other seismic events

Serviceability Limit State

Corresponds to conditions in the use of the structure. The limit state could be related to cracking, deformation or vibration. This include:

the functioning of the structure or structural members under normal use

the comfort of people
the appearance of the construction works

Checking SLS should be based on the following

deformations (deflections) which affect the appearance of the building, the comfort of users, or the way the structure (including machines or services within it) functions;
deformations which cause damage to ﬁnishes (e.g. cracking of plaster) or non-structural members;
vibrations which cause discomfort to people, or which limit the functional effectiveness of the building.

Durability

EN 1990 also gives certain recommendations on durability that The structure shall be designed such that deterioration over its design working life does not impair the performance of the structure below that intended, having due regard to its environment and the anticipated level of maintenance.

Actions on Structures

In the most simplistic In the most simplistic of terms, an action is a load that is applied to a structure. It can also however be an effect on the structure via an external source. Examples of such sources include; change in temperature, differential settlement of foundations, earthquakes and moisture variation. of terms, an action is a load that is applied to a structure. It can also however be an effect on the structure via an external source. Examples of such sources include; change in temperature, differential settlement of foundations, earthquakes and moisture variation.

Actions on structures can be grouped into three types namely:

Permanent Actions: Self weight of structural elements, finishes fixed equipment, indirect actions such as shrinkage and any other actions that is fixed throughout the design life of the structure.
Variable Actions: Include floor imposed load, movable partitions and any other action that varies with time e.g wind.
Accidental Actions: Accidental actions are events of extreme magnitude but having a high low probability of occuring e.g. explosions, vehicle impact, earthquake et.c

Design Value of an Action

The design value of an action is given as

{ F }_{ d }={ \gamma }_{ f }F_{ rep }\\ \\ where:\quad { \gamma }_{ f }=partial\quad factor\quad for\quad actions\\ \qquad \qquad See\quad NA\quad to\quad BSEN1990:TableNA.A1.2\\ \qquad \qquad { F }_{ rep }=representative\quad value\quad of\quad actions\\ \qquad \qquad \qquad =\psi { F }_{ k }

ψ converts the characteristic value of (a variable) action to the representative value.

Each variable action may take one of four representative values, the main one being the characteristic value and other representative values are obtained by the application of ψ factors, which can take one of four values, namely, 1.00 or ψ₀ or ψ₁ or ψ₂.

ψ = 1.0 when only one variable action is present in a combination.
ψ0⋅Qk is the combination value of a variable action.
ψ1⋅Qk is the frequent value.
ψ2⋅Qk is the quasi-permanent value.

Combination of Actions

In order to obtain the critical load case design values of the effect of actions are obtained by combining the effects of actions that are considered to be acting simultaneously. BS EN 1990 gives two alternative methods of determining the design value of the effects of combined actions. The design value may be obtained from either equation 6.10 or the more onerous of equation 6.10a & 6.10b

\sum { { \gamma }_{ g } } { \cdot G }_{ k;j }+{ \gamma }_{ q }\cdot { Q }_{ q;1 }+\sum { { \gamma }_{ q } } \cdot { \psi }_{ 0;i }\cdot { Q }_{ k;i }\quad ——-(6.10)

\sum { { \gamma }_{ g } } { \cdot G }_{ k;j }+{ \gamma }_{ q }\cdot { { \psi }_{ 0;1 }Q }_{ q;1 }+\sum { { \gamma }_{ q } } \cdot { \psi }_{ 0;i }\cdot { Q }_{ k;i }\quad —–(6.10a)

\sum { { \gamma }_{ g } } \cdot \xi { \cdot G }_{ k;j }+{ \gamma }_{ q }\cdot { Q }_{ q;1 }+\sum { { \gamma }_{ q } } \cdot { \psi }_{ 0;i }\cdot { Q }_{ k;i }\quad ——(6.10b)

Where:

Ɣ_g&Ɣ_q= Partial factors obtained from BS EN 1990 1.35 for Ɣ_gand 1.5 for Ɣ_q (unfavourable) for the STR limit state
G_k = Permanent actions
Q_k;1= Leading variable actions e.g Floor Imposed loading

Q_k;I= Accompanying Variable actions e.g Wind
ξ = reduction factor obtained from national annex. 0.925 in the U.K

For buildings subjected to single variable action the design value of combined effects of actions according to 6.10, 6.10a & 6.10b reduces to equation 6.11, 6.12 & 6.13 respectively. For most building equation 6.11 is usually used which is generally conservative.

F=1.35{ G }_{ k }+1.5{ Q }_{ k }——–(6.11)

F=1.35{ G }_{ k }+1.5{ { \psi }_{ 0 }Q }_{ k }——-(6.12)

F=1.35{ \xi G }_{ k }+1.5{ Q }_{ k }——-(6.13)

The more onerous of equation 6.12 & 6.13 could also be used if the designer desires more economic structure. For most structure, however, equation 6.13 is usually more critical as will be demonstrated in the worked example.

Worked Example

A shopping mall slab is subjected to the following loads.

Slab self weight = 4.5kN/m²

Superimposed dead load = 1.5kN/m²
Floor Imposed Load = 4.0kN/m²
Movable partitions = 0.5kN/m²

Determine the ultimate load in kN/m²

Permanent\quad action\quad =\quad 4.5+1.5\quad =6.0kN/{ m }^{ 2 }\\ Variable\quad action\quad =\quad 4.0+0.5\quad =4.5kN/{ m }^{ 2 }\\

Equation 6.11

F=1.35{ G }_{ k }+1.5{ Q }_{ k }\\ { G }_{ k }=6.0kN/{ m }^{ 2 }\quad ;\quad { Q }_{ k }=4.5kN/{ m }^{ 2 }\\ F=1.35(6.0)+1.5(4.5)\quad \\ \quad \quad =14.85kN/{ m }^{ 2 }\\

Equation 6.12

F=1.35{ G }_{ k }+1.5{ \psi }_{ 0 }Q_{ k }\\ { \psi }_{ o }=0.7\quad for\quad shopping\quad areas(figure1)\\ { G }_{ k }=6.0kN/{ m }^{ 2 }\quad ;\quad { Q }_{ k }=4.5kN/{ m }^{ 2 }\\ F=1.35(6.0)+1.5\times 0.7(4.5)\quad \\ \quad \quad =12.825kN/{ m }^{ 2 }\\

Equation 6.13

F=1.35{ \xi G }_{ k }+1.5Q_{ k }\\ \xi =0.925\quad reduction\quad factor\quad N.A\quad (U.K)\\ { G }_{ k }=6.0kN/{ m }^{ 2 }\quad ;\quad { Q }_{ k }=4.5kN/{ m }^{ 2 }\\ F=1.35\times 0.925(6.0)+1.5(4.5)\quad \\ \quad =14.24kN/{ m }^{ 2 }\\

According to BS EN 1990 either equation 6.11 can be used or the more onerous of 6.12 & 6.13 therefore the slab can be designed conservatively for 14.85kN/m² or less conservatively for 14.24kN/m².

Generally, equation 6.13 applies provided the following condition applies

Permanent actions are less than 4.5 times the variable actions
Storage load is not being considered.

Published by Omotoriogun Victor

A dedicated, passion-driven and highly skilled engineer with extensive knowledge in research, construction and structural design of civil engineering structures to several codes of practices View all posts by Omotoriogun Victor