A Thesis Submitted to the Faculty of Engineering
University of the Witwatersrand, Johannesburg
for the Degree of Doctor of Philosophy
Johannesburg 1981 / This thesis describes the development of an alternative
aooroximate technicue for the elasto—plastic analysis c^
unbraced and partially-braced rigid rrames.
The proposed technigue, which allows for the treatment o_
simple portal frames as well as for multi-storey and multibay
structures, is not confined to steel to which it has been
applied in this research but could also be developed for
other materials such as reinforced concrete.
In essence, the method represents a refinement and extension
of the Merchant-Rankine interaction formula. The proposed
concept makes use of a multi-curve interaction principle
placing the failure load of the actual frame oetween its
plastic collapse load on the one hand and a load related
to the elastic buckling load on the other hand. The failure
curves in the inelastic range are empirical. The plastic
collapse load is obtained using the standard first-order
approach. The required elastic parameters are evaluated
from an elastic buckling analysis and a second-order elastic
load analysis, both performed on suitable subassemblages
for the general frame. The mathematical derivations are
based on the slope-deflection equations including stability
functions.
For the elastic analyses a purpose-made computer program
has been developed. This program makes allowance for
transverse column loads, patterned beam loadings and the
special case of sway buckling including bending, termed
"Symmetry-Buckling".
In this thesis the proposed method has been applied to
the structure as a whole. In this case the plastic
collapse load of the entire frame is determined, whereas
the corresponding elastic parameters are evaluated from
as many subassemblages as are contained in the structure.
The combination of plastic collapse load and elastic
parameters which gives the lowest failure load is significant
.
It is also possible to calculate failure loads for individual
sections of a framework. The plastic collapse load
and the salient elastic parameters would then both be
examined on matching subassemblages.
Furthermore, it has been demonstrated that a graphical
presentation of the elastic results is possible, thus
allowing a "manual" evaluation of the failure load,
i.e. without the need of a computer, once the plastic
collapse load is known. The derivation of the plastic
collapse load is not included in the scope of this thesis.
In addition, an approximate analytical procedure, using
established computer methods, has been formulated for
the calculation of the elastic values.
A number of frames have been evaluated by the proposed
method and the results have been compared both, to the
Merchant-Rankine solutions and to mathematical solutions
obtained using an elasto-plastic, computer analysis.
The accuracy of the new method has also been tested
against published laboratory results of other researchers.
In addition, ten small-scale model frames were analysed
and tested for this research to confirm the validity ot
the empirically evolved interaction curves.
It has been concluded that the proposed method is in
good agreement with test results anc discrete mathematical
solutions, and thus represents a satisfactory substitute
for the more complex approaches, without the loss in
accuracy and the restriction in usage which applies to the
Merchant-Rankine formula.
Some other related aspects such as the application of
the proposed method to other materials and structures,
deflections at the working load level, in-plane member
instability, lateral torsional buckling and additional
P - A effects have been identified as areas recommended
for future research.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/18625 |
| Date | 11 September 2015 |
| Creators | Scholz, H. E. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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