《专业英语》课件Unit_34.pptx
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1、Unit34The Concept of Statical DeterminacyText1.IntroductionA structure which can be fully solved from the equations of equilibrium in this way is said to be statically determinate.The structure in Fig.1,which has four external reactions,cannot be solved by this method because the number of unknown r
2、eactions is greater than the number of equations which can be derived by considering the equilibrium of the external force system.The structure in Fig.2 is also insoluble by equilibrium due to the fact that the number of internal forces which it contains is greater than the number of independent equ
3、ations which can be derived by considering only the equilibrium of all possible free-body-diagrams.These structures are said to be statically indeterminate.Fig.34.1The framework(a)is statically determinate.Framework(b)is statically indeterminate.Fig34.2Framework is statically indeterminateTextStruct
4、ures can therefore be subdivided into two categories,those which are statically determinate and those which are statically indeterminate.The two types behave in significantly different ways in response to load and the decision as to which should be adopted in a particular situation is an important a
5、spect of structural design.Most structural geometries can be produced in either form and the designer of a structure must take a conscious decision as to which type is appropriate.The choice affects the detailed geometry of the structure and can influence the selection of the structural material.2.T
6、he characteristics of statically determinate and statically indeterminate structures2.1 Internal forcesIn Fig.3 two independent statically determinate structures,ABC and ADC,are shown.They happen to share the same supports.A and C,but in every other respect they are independent.If horizontal loads o
7、f P and 2P are applied to joints B and D,respectively,the structures will resist these internal forces and reactions will be developed,all of which can be calculated from the equations of equilibrium,and the elements will undergo axial strain,the magnitudes of which will depend on the elasticity of
8、the material and the sizes of the element cross-sections.Both joints B and D will suffer la-Text-teral deflections but these will not affect the internal forces in the elements,which will be solely dependent on the external loads and on the geometries of the arrangement(to a first approximation).Fig
9、34.3The pattern of internal forces in a statically indeterminate structure depends on the properties of the elements as well as on the overall geometry of the arrangement.If a fifth element is added,which connects joints B and D,the system becomes statically indeterminate.The two joints are now cons
10、trained to deflect by the same amount under all load conditions and if the two loads are applied as before the extent of the resulting elongation or contraction of the elements will not be the same as occurred when the joints B and D were free to deflect independently.This means that the joint which
11、 previously deflected less will be pulled or pushed further than before and the reverse will occur to the other joint.A transfer of load will thereforeTextoccur along the element BD and this will alter the pattern of internal forces in the whole frame.The amount of load transfer,and therefore of cha
12、nge to the internal force system,will depend on the difference between the deflections which occurred to the two joints in the statically determinate forms.This is determined by the rigidity of the elements,so the distribution of internal forces in the statically indeterminate structure is therefore
13、 dependent on the properties of the elements as well as on the overall geometry of the frame and the magnitudes of the external loads.The element properties must therefore be taken into account in the analysis of this structure.This is generally true of statically indeterminate structures and is one
14、 of the important differences between statically determinate and statically indeterminate structures.The fact that element properties have to be considered in the analysis of statically indeterminate structures makes their analysis much more complicated than that of equivalent statically determinate
15、 structures;in particular,it requires that the rigidity of the elements be taken into account.As this can only be done once the element dimensions have been decided and a material selected,it means that the design calculations for statically indeterminate structures must be carried out on a trial an
16、d error basis.A set of element sizes must be selected initially to allow the analysis to be carried out.Once the internal forces have been calculated the suitability of the trial sizes can be assessed by calculating the stress which will occur in them.The element sizes must normally be alte-Text-red
17、 to suit the particular internal forces which occur and this causes a change in the pattern of the internal forces.A further analysis is then required to calculate the new internal forces,followed by a further revision of the element dimensions.The sequence must be continued until satisfactory eleme
18、nt sizes are obtained.Cycles of calculations of this type are routine in computer-aided design.By comparison,the calculations for statically determinate structures are much more straightforward.The internal forces in the elements depend solely on the external loads and on the overall geometry of the
19、 structure.They can therefore be calculated before any decision on element dimensions or a structural material has been taken.Once the internal forces are known,a material can be chosen and appropriate element dimensions selected.These will not affect the pattern of the internal forces and so a sing
20、le sequence of calculations is sufficient to complete the design.2.2 Efficiency in the use of materialThe efficiency with which structural material is used is normally greater with statically indeterminate structures because the presence of a larger number of constraints allows a more direct transmi
21、ssion of loads to the foundations and a more even sharing of load by all of the elements.The benefits of statical indeterminacy in this respect are most easily seen in relation to structures with rig-Text-id joints,in which the resulting structural continuity causes smaller bending moments to occur
22、than are present in equivalent statically determinate structures under the same load conditions.As before the differences between the two types of structure can be appreciated by studying very simple examples.2.3 The 1ack-of-fit problemWith the possible exception of in situ reinforced concrete struc
23、tures,most structures are prefabricated to some extent so that their construction on site is a process of assembly.As prefabricated components can never be produced with precisely the correct dimensions,the question of lack-of-fit and of the tolerance which must be allowed for this is a necessary co
24、nsideration in structural design.It can affect the decision on whether to use a statically determinate or indeterminate form,because the tolerance of statically determinate structures to lack-of-fit is much greater than that of statically indeterminate structures.The arrangement in Fig.7(a)is static
25、ally determinate while that in Fig.7(b)is an equivalent statically indeterminate form.It will be assumed that the frames are assembled from straight elements,that the structural material is steel and that the hinge-type joints are made by bolting.The elements would be fabricated in a steel fabricati
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