# Composite beams - Design for serviceability part 1

##### OBJECTIVE/SCOPE

To present serviceability criteria within a limit-state framework, to derive the elastic properties of the section, to introduce time-dependent behaviour of concrete, to discuss the factors influencing cracking and deflection in composite structures, and to outline 'deemed-to-satisfy' procedures for checking cracking and deflection.

##### SUMMARY

The criteria for design for the serviceability limit state are discussed. Elastic analysis of simply supported and continuous composite beams with respect to cracked and uncracked sections is described. Serviceability limits for cracking and deformation in an 'explicit' and a 'deemed-to-satisfy' approach are outlined.

### 1. INTRODUCTION

#### 1.1 General

In order that a structure should remain fit for use and that its appearance and durability remain satisfactory, consideration has to be given during design to 'serviceability limit states'. These limit states relate to aspects of a structure's behaviour such as cracking, deformation, and vibration when checked under normal service conditions.

The economic consequences, for the client, of failure to satisfy serviceability criteria can prove every bit as severe as structural failure. At the least, failure to meet serviceability criteria is likely to result in increased maintenance and repair costs. In some cases, it will result in a loss of utility, durability, and ultimately, the integrity of the structure.

Factors such as the 'design life' of the structure (which can vary within wide limits) and exposure conditions will influence the design values of serviceability parameters. The classification of the 'design situation' (as defined in the Eurocodes 0, 2, 3 and 4 [1-4]) as persistent, transient, or accidental will, similarly, have a bearing on these values. Transient situations, which merit separate consideration from the serviceability point of view, are those which might, for example, apply during construction.

#### 1.2 Serviceability limit states

##### 1.2.1 Explicit methods

###### 1.2.1.1 Criteria

Serviceability limit state criteria may be categorised for composite structures as follows:

(a) Slip at the steel-concrete interface, when it becomes large enough to invalidate design checks.

(b) Excessive compressive stress in the concrete, leading to microcracking and affecting durability.

(c) Excessive cracking in concrete tension zones.

(d) Unacceptable deformations or deflections, which affect the appearance or efficient use of a structure or cause damage to finishes or other non-structural elements. These deformations are affected by cracking, creep, and shrinkage; and by slip, where significant.

(e) Vibrations producing discomfort or affecting non-structural elements or equipment.

Within these categories, a variety of limit states may be defined corresponding to different structural types and conditions.

Some of the serviceability requirements are satisfied implicitly - by virtue of assumptions made or restrictions introduced whilst designing the section for strength. Thus, Eurocode 4 [4] requires no specific checks for compressive stresses in the concrete under service loading, and slip at the steel-concrete interface need not be checked provided the design of the shear connection is in accordance with Chapter 6 of Eurocode 4. In addition, vibration need not be considered in detail for the majority of composite elements.

The serviceability limit states, which are particularly considered in this lecture, are those of excessive cracking and deformation. In the design of a composite beam for the serviceability limit state, it must be shown that under service conditions (γ_{F} = 1), the deflections (δ) and the cracking of concrete (w) are limited. The design value of the effect of actions E_{d} shall be less than (or equal to) a limiting value C_{d}.

###### 1.2.1.2 Calculation of Ed

Elastic analysis is used for the calculation of E_{d}. (See Eurocode 4, Section 5.4 [4]).

###### 1.2.1.3 Limits for Cd

Limits for deflections and cracks are given in Eurocodes 2, 3, and 4; see Eurocode 4, Section 7 [4].

###### 1.2.1.4 Design procedure

It must be shown that:

E_{d} ≤ C_{d}

E_{d} are calculated crack widths w or deflection δ.

C_{d} are limits for crack width w_{lim} or deflections δ_{lim}.

##### 1.2.2 Deemed-to-satisfy provisions

It is frequently the case that the length or the complexity of calculations required for the explicit satisfaction of serviceability criteria is not warranted by the accuracy obtainable. For example, the detailed calculation of deflection, taking into account creep and shrinkage, is based on values of certain parameters which are of necessity approximate: the stiffness of a cracked reinforced concrete section, for example, or the values of creep and shrinkage coefficients. A considerable degree of approximation must therefore attach to the laboriously calculated deflection.

In the present lecture, simplified procedures are described for satisfying serviceability requirements. In some cases, the procedure enables the use of indirect criteria. Such simplified methods are termed 'deemed-to-satisfy' methods. They are perfectly adequate for the majority of situations encountered in design and are widely used in practice because of their greater ease of application.

Detailed consideration is given in the accompanying lecture, Composite beams - Design for serviceability part 2, to explicit criteria for serviceability.

Read more#### Prerequisites

Behaviour of beams

Read LectureSingle span composite beams

Read LectureContinuous composite beams I

Read Lecture