Deflection control of structural members plays a key role in the design of concrete structures, as it prevents damage of non-structural elements, visual unwanted effects, and interference with sensitive machinery.
For all these reasons, it is important to contain the deflection of the members within acceptable limits.
Welcome back to the “VIS” video tutorials. Today we will see how to perform the deflection check of reinforced concrete beams, according to the provisions of Eurocode 2.
The code allows for two different approaches. A direct approach based on the numerical integration of curvatures at discrete locations along the members. And an indirect approach, based on the limitation of span-to-depth ratios.
The first requires a non-linear cracked analysis to be performed, accounting for members cracking, internal forces redistribution, rotations at ends, shrinkage, and long-term effects. On the contrary, the latter can readily be applied in the form of simple parametric equations.
For this reason, the direct method is usually limited to the analysis of non-standard cases, or when an explicit calculation of the deflection is required. While the indirect method is instead employed in most practical cases.
“VIS” currently implements the indirect method, which is calibrated to limit the total deflection of the members to a two hundred and fiftieth of the span, and the deflection after construction to a five hundredth of the span.
As mentioned, this is done by limiting the span-to-depth ratio according to the following code equation.
The base span-to-depth ratio is first calculated as a function of the concrete class, and of the reinforcing demand on the member. Then, the appropriate correction factors which account for restraint conditions, steel stresses, span length and flange dimension are determined. At this point, the maximum allowable span-to-depth ratio is obtained. And can be compared with the actual value. Let us see an example!
The program automatically identifies the restraint conditions of the member and calculates all the related parameters accordingly.
Finally, the actual span-to-depth ratio is compared with the limiting value. And the corresponding check is reported. Checks can be performed for all the elements at once, by clicking the “Check All” command.
Results can now easily be reviewed in the form of color-coded contours plot. Or in a compact tabular format.
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