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Stress2D - R/C "Deep Beam" Design In this example we will demonstrate the usage of Stress2D software in a design of a reinforced concrete "deep beam". In this example the "deep beam", is actually a "deep cantilever" wall. (see figure on left). The cantilever wall is 3.0m long, 5.0m deep, and 0.5 thick (estimated). It carries 15 floors from above, which includes pre-cast concrete facade panels and the floor structure.The estimated load (G+Q) is 750 kN/m. The cantilever wall is supported by a series of columns. The design task is to evaluate the stresses in the cantilever wall and to design the reinforcement. The building is located in Sydney - CBD, NSW Australia, just behind the Town Hall.
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In the figures below the cantilever wall is shown in a larger scale.
This is a typical 2D stress analysis problem, suitable for finite element approach. In this case, "beam analogy" will not provide reliable results. The finite element model was created using Stress2D software. The model consists of several 2D panels, representing the cantilever, and four columns. This is a very simple model, and it takes 5 to 10 min. to draw it using Stress2D interactive editor.
Once, the model is prepared and all material properties are entered, we can perform the static analysis by the using Stress2D software. The deflection results are shown in the figure below.
In the figure below the horizontal stresses (Sigma X) are shown in two characteristic sections. The critical section is above the column, where there are a total tension force of 1,150 kN. At the column, almost 3/4 of the section is in tension. We have to put a sufficient number of horizontal bars to take the tension stresses The compression stresses were much smaller than than the concrete strength, and there is no need for any additional reinforcement to take the compression stresses. We can use steel bars Y16, in the horizontal directions. (Ast of one bar is 201 mm^2) If we allow that the stress in the steel will go up to 50% of the yield strength of 400 MPa, then we can calculate the required area of reinforcement. Ast.tot = 1,150 / 200,000 = 0.00575 m2 or 5,750 mm2 (required area of steel)
Number of bars = 5,750 / 201 = 28 bars or 14 bars each side of the wall If we place 28 horizontal Y16 bars, then the load will generate tension stress in the bars of 200 MPa, which is only 50% of the yield stress. This is actually, a safety factor of 2, which is sufficient in this case. The horizontal bars will be placed over a length of 2m from the top edge, i.e. Y16@150 each face. The rest of the structure will need some nominal horizontal reinforcement, for instance Y16@300. Also, it is a good idea to put a few extra horizontal bars at the top edge, say 5Y24, to take the concentration of the tension stresses. The extra bars will have a cross section of 2,260 mm2, which will make a total or 7,890 mm2. This will drop the stress in the steel to 146 MPa. Now, the safety factor is 400/146 = 2.7.
The vertical reinforcement may be designed in tha similar manner. The maximum shear stresses are 2.7 MPa, which is smaller than 10% of the concrete strength, and no special shear reinforcement is required. The deflection at the tip of the cantilever is about 1mm, which is considered acceptable. (assuming Ec = 31 GPa).
NOTE: INDUCTA Engineering was not involved in the actual design of the above structure, nor any of our software was used in the design. We have chosen this particular structure because of its specific geometry, in order to illustrate the potential usage of finite element software in structural design of "deep beams". |
