esdep lecture note [wg11]

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ESDEP WG 11

CONNECTION DESIGN: STATIC LOADING

Lectures 11.4.1: Analysis of Connections I:

Basic Determination of Forces

OBJECTIVE/SCOPE

To review the behaviour and the basis for design of local elements in connections.

PREREQUISITES

Lecture 1B.5: Introduction to Design of Industrial Buildings

Lecture 1B.7: Introduction to Design of Multi-Storey Buildings

Lecture 2.3: Engineering Properties of Metals

Lecture 2.4: Steel Grades and Qualities

Lecture 11.1.2: Introduction to Connection Design

Lectures 11.2: Welded Connections

Lectures 11.3: Bolted Connections

RELATED LECTURES

Lecture 11.5: Simple Connections for Buildings

Lecture 11.6: Moment Connections for Continuous Framing

Lecture 11.7: Partial Strength Connections for Semi-Continuous Framing

SUMMARY

This group of 4 lectures (11.4.1 - 11.4.4) explains how the behaviour of local elements in connections may be

analysed so that each component may safely be proportioned to resist the loads it is required to transfer. It

therefore develops the basic concepts of force transfer that were presented in general terms in Lecture 11.1.2.

In this first lecture the general principles used in determining the forces for which each component in a

connection must be designed are explained. These make use of the fundamental structural concepts of

equilibrium, stiffness and deformations to decide how the externally developed loads are shared between the

various components. This then leads to the idea of load paths as being the most effective way that applied

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forces can pass through the connection.

NOTATION

The notation of Eurocode 3 [1] has been adopted.

1. INTRODUCTION

In Lecture 11.1.2 it was shown in general terms how the structural adequacy of connections can be checked by

considering the resistance of the local elements of the connection.

The resistance of a local element is determined on the basis of the resistance of the individual bolts or welds

and plates.

The resistance of welds and bolts is covered in Lectures 11.2 and 11.3. In this Lecture 11.4.1 the resistance,

stiffness and deformation capacity of a number of components are discussed.

Thus the material of Lectures 11.1, 11.2 and 11.3 is brought together to explain how the individual components

in connections can be safely proportioned. This involves both a determination of the forces to which each is

subjected and the ways in which, acting in combination, the parts of the connection transfer these forces from

the supported member to the supporting member.

Having established the principles, Lectures 11.4.2 - 11.4.4 apply these to the consideration of the transfer of

different types of internal forces within connections e.g. direct tension, shear, tension as part of a moment etc.,

whilst Lectures 11.5 - 11.8 fully develop the ideas to cover the design of particular connection types.

2. DETERMINATION OF FORCES

2.1 Forces on the Connection

For the determination of the forces on the connection, a static analysis is carried out. Such an analysis includes

the determination of the design loads on the structure and the definition of the design basis for the structure.

In defining the design basis, consideration of the structural behaviour of the connections is necessary. Are the

connections pinned, or rigid, or semi-rigid? Are they partial strength or full strength connections? More details

about the influence of the type of connection on the distribution of forces in the structure are given in Lectures

11.1, 11.5, 11.6, 11.7 and 11.8.

2.2 Force Distribution in the Connection

After the determination of the normal forces, shear forces and bending moments on the connections, an internal

distribution of forces in the connection is chosen.

The distribution of forces in the connection may be determined in whatever rational way is best, provided that:

a. The assumed internal forces are in equilibrium with the applied forces and moments.

b. Each part of the connection is capable of resisting the forces assumed in the analysis.


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c. The deformations imposed by the chosen distribution are within the deformation capacity of

the fasteners, welds and other parts of the connection.

Figure 1 gives an outline of the determination of the load on the individual elements of the connections, and

the verification of their resistance.

It is not necessary and it is often not possible to determine the real distribution of forces in the connection. A

realistic assumption of internal forces, in equilibrium with the external forces on the connection, is sufficient.

In fact selecting this assumption is the most difficult part of the analysis. It requires a sound understanding of

the structural behaviour of the connection when it is loaded.

The following rules apply:

a. The distribution of forces in the parts to be connected requires consideration

If, for instance, an I-section loaded in bending and shear, has to be connected, then the shear force


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is largely concentrated in the web, whilst the flanges carry most of the bending moment. A simple

and usually acceptable assumption for the load transfer in the connection is to connect the web for

the full shear force and the flanges for the full bending moment, see Figure 1.

b. The stiffness of the various parts in the connection requires consideration

Deformations caused by loads acting in the plane of a plate are much smaller than those produced

by loads acting perpendicular to a plate (normal force versus bending moment). In many cases the

understanding of the influence of the stiffness ratio on the force distribution can be improved by

considering the situation after a small deformation of the connection has occurred. This approach

is illustrated in Section 3 by examples.

c. The assumed force distribution must be consistent for all parts in the connection

Violations against this rule may occur if a separate calculation is carried out for the different parts

in the connection. An example is given in Figure 2. The indicated distribution of forces for the

calculation of the bolts is not consistent with the distribution of stresses in the beam assumed to

design the welds between the beam and the end plate. Overloading of the welds in the top flange

of the beam results.

2.3 Basic Load Cases for Local Elements

The analysis of the structural behaviour of connections can be carried out by considering a number of basic

load cases for local elements. For a T-connection this analysis is demonstrated in Figure 3. The load transfer in

nearly every type of connection can be modelled with the five basic load cases. Use of these cases permits a

systematic and clear presentation of the calculation methods, despite the wide variety of possible connection

types. Eurocode 3 (Chapter 6 and Annex J) follows this approach.


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In Lectures 11.4.3 and 11.4.4 calculations for the five basic load cases are presented for a number of

connection designs. For each part of the connection, a number of possible failure modes can be identified.

They may refer to:

the fasteners (welds or bolts).

the members which are connected.

extra parts in the connection, e.g. plates and angle cleats.

It has to be demonstrated that the weakest link in the connection system (chain) is strong enough to carry the

load that acts on it.

The design of the fasteners (welds and bolts) is dealt with in Lectures 11.2 and 11.3. The design of other parts

in the connection is dealt with in the present Lectures 11.4.

3. DISTRIBUTION OF FORCES

3.1 Influence of Stiffness Differences

When distributing normal forces, shear forces and bending moments in the connection, the stiffness differences

in the connection must be taken into account. In particular, the deformations due to normal forces in the plane

of a plate are much smaller than the deformations due to forces acting perpendicular to it.

A calculation for the example of Figure 4 gives a good demonstration of this principle. The plate 100 ´ 100 ´

10 mm, clamped on one side, is loaded with 1000 N perpendicular to the plate surface.


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The deflection follows from:

d = = = 0,2 mm (3-1)

The same plate is loaded with an in-plane tensile force of the same magnitude. The displacement of the end of

the plate is now:

Dl = = = 0,0005 mm (3-2)

Both plates are now connected, see Figure 5, causing both displacements at the interface to be equal. A load of

1000 N is applied to this structure. The load is carried by both plates, shared in proportion to the stiffness ratio.

The plate loaded in tension is 0,2/0,0005 = 400 times stiffer than the plate that is bent. Consequently, nearly the

whole load is carried by the plate loaded in tension, see Figure 5b.


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This knowledge is used to determine the distribution of forces for the brace connection shown in Figure 6, e.g.

in a floor structure. In this connection many distributions of the forces in the connections, each obeying

equilibrium, are possible.


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First it is assumed that the force is carried by both connections, whilst the direction stays the same, see Figure

7. For the analysis, the force 0,5 F is resolved as Fs = 0,35 F and F

t = 0,35 F.


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The deformation in the shear direction (Fs) is much smaller than the deformation in the tensile direction (F

t).

The result is that the deformation D1 at point (1) is very different from the deformation D2 at point (2). The

deformations D1 and D2 cannot be accommodated by the gusset plate!

This means that the deformation at point (1) caused by Fs (DS

1) must be the same as the deformation at point

(2) caused by Ft (DS

2).

Therefore, Fs is much larger than F

t. The distribution of forces in Figure 7 is incorrect.

The correct distribution is indicated in Figure 8. The force F effectively causes only shear in the bolt groups (1)

and (2). The tension load in the bolts can be ignored.


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Conclusion: If large differences in the stiffness between two possible types of load transfer exist, then ignore

the load transfer that gives the larger deformations (bending deformation of the plate), and assume that all load

is transferred in the way that gives the smaller deformations (deformation in the plane of the plate).

This approach also applies to welded structures, e.g. see Figure 9 which illustrates the connection of a plate to

a square hollow section. The assumed force distribution where the welds are only loaded in shear is correct.

The stiffness ratio in the connection may influence the assumption for the calculation of the bending moments.

An example is given in Figure 10. In the connection in Figure 10a, the rotation of the bolted connection is

larger than the rotation of the plate which is welded in the plane of the web of the column. Therefore, the hinge

for the calculation of moments is assumed to be the bolt row. The bolts are loaded by a shear force V. The

welds must be designed for a shear force V and a bending moment V.e.


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