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Title: Moment redistribution in statically indeterminate structures due to inelastic effects in steel and concrete
Author: Everard, K. A.
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 1952
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The work is considered in three parts. Part I, The behaviour of materials and action of forces. In Part I, three levels of approach to the problem are considered; namely, macroscopic, microscopic and atomic, and the influence of one upon the other is briefly discussed. The classical theories of elasticity and plasticity, are reviewed and the importance of Hooke's Law and the assumption of small displacements in linear behaviour is considered. The behaviour of concrete under load is discussed in detail and the factors involved in time-dependant strains (creep) are considered. It is then assumed that for short period loading, the stress at a point is a continuous function of strain, which may be expanded as a polynomial. Based upon this, and upon the assumption of linear strain distribution across the section , a non-linear theory of bending has been derived for a reinforced concrete section of general geometric configuration under the action of a pure couple and under the action of bending and direct force. The special case of a rectangular section has been considered in detail, and curves of the angle of discontinuity resulting from non-linear behaviour have been plotted for various percentages of steel and crushing strengths of concrete. Part II. Applications to the theory of structures. Some general observations on the effect of non-linear behaviour on the principle of superposition are made* The fundamental principles underlying the calculation of the collapse load of a framed structure of an ideal elasto-plastic material are considered in detail and recent advances in this branch of structural mechanics are discussed. Using the non-linear theory of bending derived in Part I, expressions for the slope/deflection analysis of a reinforced concrete beam at all stages of loading are proposed, and from this analysis the equations of moment distribution are derived* Complete Moment Redistribution is said to occur when the ultimate moment of resistance at all the critical sections is attained* It is found that the Complete Moment Redistribution can occur in both over and under reinforced beams, provided that there is some parity between the ultimate moments of resistance of both support and span sections. Using the concept of an "angle of discontinuity", a theory is proposed whereby the value of the angle necessary to cause Complete foment Redistribution in any configuration may be calculated. It is then possible to see if the sections are capable of developing such an angle by reference to the curves derived in Part I. Part III. Experimental Work. The experimental work conducted in this investigation consisted of the testing of four continuous beams and four simply supported beams. Strains were measured on steel and concrete using mechanical, optical and electrical methods* In addition, a series of tests on cubes and cylinders was conducted to determine the effect of rate of loading on crushing strength. Some model experiments were carried out to determine the effect of the order of loading in non-linear deformation. Finally, the results of tests on columns made in America were utilised to plot the moment - curvature relations of sections- under bending and direct force, considering also the effect of tying and of spiral reinforcement. It is concluded that the experimental results amply justify the use of the proposed theories, and whilst no claim is made to have produced design methods, yet it is thought that the analysis of framed continuous structures based on ultimate load methods is a possible and rational alternative to elastic analysis based on working stresses.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available