partial releases case study

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Partial Release:

How to model in S-FRAME and a case study

By

Dr. Siriwut Sasibut (Application Engineer)

S-FRAME Software Inc. S-FRAME Software Inc. S-FRAME Software (UK) Ltd. #275 – 13500 Maycrest Way #282, 800 Village Walk 4th Floor, Rex House Richmond, BC V6V 2N8 Guilford, CT 06437 10 Regent Street, London CANADA USA UK, SW1Y 4RG

Phone: 1-604-273-7737 Phone: 1-203-421-4800 Phone: +44 (0) 20 3287 7825 Fax: 1-604-273-7731

Please visit us at www.s-frame.com to request more information about this publication.

© Copyright by S-FRAME Software Inc. – Version: 1.0 December 6th, 2013

http://www.s-frame.com/

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Table of Contents

1 Introduction .......................................................................................................................................... 3

1.1 Using Partial release feature. ........................................................................................................ 3

1.2 Using Elastic/Plastic Link Beam feature. ....................................................................................... 3

2 How to go about calculating a percent release .................................................................................... 4

3 A Case Study (2-bay 11-storey steel frame) .......................................................................................... 5

3.1 Basic model details ....................................................................................................................... 5

3.2 Comparison of results ................................................................................................................... 8

4 Summary ............................................................................................................................................... 9

5 References ............................................................................................................................................ 9


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Partial Release: How to model in S-FRAME and a case study

1 Introduction

S-FRAME Release 11 supports two types of member end releases, namely, full release and

Partial release. As opposed to the full release where a member’s end is idealized as perfectly

pinned, a Partial release can be used to model, for instance, a semi-rigid connection. This will

allow a partial transfer of moment between the column and the beam with some degree of

a connection’s rotational stiffness to be modeled.

There are two ways to model semi-rigid connections in S-FRAME:

1.1 Using Partial release feature.

The degree of release is specified as a percent, where 100% means full release or

pinned connection, 0% means no release or rigid connection, and anything between

0% and 100% is a Partial release. The rotational stiffness of a connection, which

characterizes the connection’s moment-rotation (𝑀 − 𝜃) relationship, is then

calculated by S-FRAME based on the flexural stiffness of the connected member and

the percent release. This approach is particularly useful if an exact value of a

connection’s stiffness may not be established at this design stage or if the engineer

wants to study the effects on the structural responses of varying connection’s stiffness

which is defined in relative terms of its rigidity/flexibility. However, given a

connection’s stiffness is known, the exact percent release can also be determined.

This will be discussed in more detail in Section 2.

1.2 Using Elastic/Plastic Link Beam feature.

This more general approach requires that the connection’s moment-rotation

relationship be defined using either a Multi-linear elastic or Multi-linear plastic

material model. More information on this feature can be found in a document,

Application Brief: Elastic/Plastic Link Beam, also available on S-FRAME’s Online

Resources.

This document’s main objective is to illustrate S-FRAME Analysis R11’s Partial release result

accuracy by comparing to results published in a reputable reference as well as 3rd party

software.


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2 How to go about calculating a percent release

The percent release or its counterpart, namely, end-fixity factor (𝑟𝑗) is defined as follows [1]:

𝑟𝑗 = 1

1+3𝐸𝐼/𝑅𝑗𝐿; (𝑗 = 1,2) (1)

where, 𝑅𝑗 is the connection’s rotational stiffness at the member’s respective end and EI/L is

the flexural stiffness of the attached member. A percent release is then determined by, %

release = 100* (1 - 𝑟𝑗).

From equation (1), it is implied that the 𝑀 − 𝜃 relationship of a connection is defined by a

linear model, i.e., 𝑀 = 𝑅𝜃, which is the simplest way of modeling a connection. This is the

approach that most steel design codes have adopted and is being used in S-FRAME’s Partial

release feature.

From experiments, a 𝑀 − 𝜃 relationship of most types of connections is nonlinear. Figure 1

shows a schematic of typical 𝑀 − 𝜃 curves for various types of connections commonly used

in practice. A number of mathematical models for connections with varying complexity,

which are based on experimental testing of connections, had been proposed by various

researchers. These models can be used to establish the rotational stiffness of connections

under design consideration. Interested readers may refer to references [1]-[3] for a list of

published documents and related topics on modelling of connections.

Figure 1. Typical 𝑀 − 𝜃 curves for various types of connections (Courtesy of ref. [1])


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3 A Case Study (2-bay 11-storey steel frame)

A number of models of 2-bay 11-storey steel frame, shown in Figure 2 with varying degrees

of Partial release at the beam-column connections, are analyzed in S-FRAME using the first

and second-order elastic analyses. The analysis results for each case are then compared with

those from reference [1], i.e., Handbook of Structural Engineering, second edition, and a 3rd

party software.

3.1 Basic model details

The geometry of the frame, the sections of structural members, and the applied loads

are as shown in Figure 2. All of the beam-column connections of the frame are assumed

to be identical and of semi-rigid type. The semi-rigid connections are then modelled

using S-FRAME’s Partial release feature. An S-FRAME model with the semi-rigid

connections being modeled as a 10% Partial release is shown in Figure 3.

Note that to compare the results with the 3rd party software, where the rotational

stiffness of a connection is required to be entered by the user, equation (2) is used to

determine the corresponding connection’s stiffness from a specified percent release.

For instance, to model a 10 % Partial release connection of a W530 x 123 beam, a

stiffness of 471,261.5 kN-m/rad has to be entered.

𝑅𝑗 = 3𝐸𝐼

𝐿 ∗

𝑟𝑗

(1−𝑟𝑗); (𝑗 = 1,2)

(2)

where, 𝑟𝑗 = 1 − (%𝑟𝑒𝑙𝑒𝑎𝑠𝑒

100)


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Figure 2. 2-Bay 11-Storey Steel Frame (Courtesy of ref. [1])


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Figure 3. S-FRAME 2-Bay 11-Storey Steel Frame Model


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3.2 Comparison of results

The lateral deflections obtained at the roof level for the first and second-order analyses

are compared between the reference [1], the 3rd party software and S-FRAME in Figure

4. Using the reference’s results as base values, Figure 5 illustrates these differences in

percent. This clearly indicates a very high accuracy of analysis results of S-FRAME’s

Partial release feature considering the maximum difference in results for all the cases

is only about 0.75%.

Figure 4. Comparison of Roof Deflections

0

200

400

600

800

1000

1200

1400

1600

1800

0 10 20 30 40 50 60 70 80

Ro

of

Late

ral D

efl

ect

ion

(m

m)

% Partial Release

Comparison of Roof Deflections

Ref.- 1st Order

3rd Party Software- 1st Order

S-FRAME- 1st Order

Ref.- 2nd Order

3rd Party Software- 2nd Order

S-FRAME- 2nd Order


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Figure 5. Deflection Difference in percent

4 Summary

The Partial release feature in S-FRAME allows the design engineers to model semi-rigid

connections with an evidently high confidence on the accuracy of results. As recommended

by the references, more appropriate and economical designs could be achieved when this

type of connection is considered in the design. A tutorial video on this feature can be found

from our web site at www.S-FRAME.com.

5 References

1. Handbook of Structural Engineering, Second Edition edited by W.F. Chen and E.M. Lui,

New York, 2005.

2. W.F. Chen and E.M. Lui (1991), Stability Design of Steel Frames

3. Faella et al. (2000), Structural Steel Semirigid Connections: Theory, Design and Software.

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80

De

fle

ctio

n D

iffe

rnce

(%

)

% Partial Release

Deflection Difference (%) vs Reference

3rd Party Software- 1st Order

S-FRAME- 1st Order

3rd Party Software- 2nd Order

S-FRAME- 2nd Order


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