When a simply supported RC beam is subjected to4 point cyclic loading, the deflections are measured with mechanical dial gauge. I want to know what is the appropriate formula for deflection to validate the deflection.
In that case youhave to model the load event by using equations that integrate the load history. A rough approximaton would be mdof system consisting of a series of masses connected by springs and subject to harmonic excitation - see attachment. Alternatively you can use a finite element model in which case you would obtain more accurate results.
Sir,
Thank you Mr. P. Martinez-Vazquez for your immediate reply. Any how I require an empirical formula which include stress, no. of cycles of failure.
Unfortunately there is no empirical formula to measure the dynamic response of a beam such as the one you describe. Yo might perhaps be able to work out a dynamic amplification factor through which you could infer the dynamic displacement from static conditons (by using a rather simplified model) however that still require you undertake some research on structural dynamics.
If you impose the load by using low loading rates then you can perform a cyclic static analysis with FEM and compare your results with the ultimate carrying capacity of your beam that derives from the use of design codes and the experimental data. Cyclic or monotonic loading will result ultimate carrying loads that should be close in terms of magnitude (given that you do not have the development of accelerations during the execution of your experiment). Regarding the deflections FEM is your only choice in this case.
Selecting the appropriate finite element software and model is also something that needs significant attention.
Hello there,
there are a few analytical approaches to calculate deflections under cyclic long-term loading. As the deflections are calculated via the integration of the curvature, one has to calculate the time-dependent curvatures. If the load frequency is not to high, the stiffness reduction of the concrete compression zone can be calculated by an effective modulus of elasticity under the middle load as suggested in fib Model Code 2010. In the tension zone, the tension stiffening effect has to be reduced due to creeping of the bond. Furthermore, the concrete tensile strength is reduced due to the cyclic loading. We have conducted tests on CFRP RC members under cyclic long-term loading and could observe a very good agreement between experimental data and analytical approximation.
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