8 Yield Line Theory
8.1 The esntials
Yield Line Design is a well-founded method of designing reinforced concrete slabs, and similar types of elements. It us Yield Line Theory to investigate failure mechanisms at the ultimate limit state. The theory is bad on the principle that:
work done in yield lines rotating = work done in loads moving
Yield Line Design is easy to grasp but there are veral fundamental principles that need to be understood. Yield Line Design is a plastic method: it is different from ‘normal’ elastic methods.
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石家庄英语培训班8.1 .1 A short history of Yield Line Theory
Yield Line Theory as we know it today was pioneered in the 1940s by the Danish engineerflames and rearcher K W Johann.
As early as 1922, the Russian, A Ingerslevskillet prented a paper to the Institution of Structural Engineers in London on the collap modes of rectangular slabs. Authors such as R H Wood, L L Jones, A Sawczuk and T Jaeger, R Park, K O Kemp, C T Morley, M Kwiecinski and many others, consolidated and extended Johann’s original work so that now the validity of the theory is well established making Yield Line Theory a formidable international design tool.
In the 1960s 70s and 80s a significant amount of theoretical work on the application of Yield Line Theory to slabs and slab-beam structures was carried out around the world and was widely reported.
To support this work, extensive testingtextarea was undertaken to prove the validity of the theory. Excellent agreement was obtained between the theoretical and experimental Yield Line patterns and the ultimate loads.
The differences between the theory and tests were small and mainly on the conrvative sidestatuette. In the tests where restraint was introduced to simulate continuous co
nstruction, the ultimate loads reached at failure were significantly greater than the loads predicted by the theory due to the beneficial effect of membrane forces.
8.1 .2 What is a yield line?
A yield line is a crack in a reinforced concrete slab across which the reinforcing bars have yielded and along which plastic rotation occurs.
8.1 .3 What is Yield Line Theory?
Yield Line Theory is an ultimate load analysis. It establishes either the moments in an element (e.g. a loaded slab) at the point of failure or the load at which an element will fail. It may be applied to many types of slab, both with and without beams. Consider the ca of a square slab simply supported on four sides as illustrated by Figure 8.1.1锻炼记忆力. This slab is subjected to a uniformly distributed load, which gradually increas until collap occurs.初一英语上册第一单元
Initially, at rvice load, the respon of the slab is elastic with the maximum steel stress and deflection occurring at the centre of the slab. At this stage, it is possible that some ha
irline cracking will occur on the soffit where the flexural tensile capacity of the concrete has been exceeded at midspan.
Figure 8.1.1 Ont of yielding of bottom reinforcement at point of maximum deflection in a simply supported two-way slab
Increasing the load hastens the formation of the hairline cracks, Increasing the load further will increa the size of the cracks further and induce yielding of the reinforcement, initiating the formation of large cracks emanating from the point of maximum deflection. On increasing the load yet further, the cracks migrate to the free edges of the slab at which time all the tensile reinforcement passing through a yield line yields.
At this ultimate limit state, the slab fails. As illustrated by Figure 8.1.2, the slab is divided into rigid plane regions A, B, C and D. Yield lines form the boundaries between the rigid regions, and the regions, in effect, rotate about the yield lines. The regions also pivot about their axes of rotation, which usually lie along lines of support, causing supported loads to move. It is at this juncture that the work dissipated by the hinges in the yieldpaste lines rotating is equated to work expended by loads on the regions moving. This is Yield Line Theory.
Under this theory, elastic deformations are ignored; all the deformations are assumed to
be concentrated in the yield lines and, for convenience, the maximum deformation is given the value of unity.
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For a more detailed appraisal of the situation at corner e Section ? |
Figure 8.1.2 The formation of a mechanism in a simply supported two-way slab with the display是什么bottom steel having yielded along the yield lines |
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8.1 .4 What is a yield line pattern?
When a slab is loaded to failure, yield lines form in the most highly stresd areas and the develop into continuous plastic hinges. As described above, the plastic hinges develop into a mechanism forming a yield line pattern.
Yield lines divide the slab up into individual regions, which pivot about their axes of rotation. Yield lines and axes of rotation conform to rules given in Table 8.1.1, which help with the identification of valid patterns and the Yield Line solution.
