Stress2D - R/C "Deep Beam" Design Illustrative Example In this example we will demonstrate the usage of Stress2D 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 cantilever wall is 3.0m long, long, 5.0m deep, and 0.5 0.5 thick (estimated). It carries carries 15 floors from above, which includes pre-cast concrete facade panels and the floor structure.The structure.The estimated load (G+Q) is 750 kN/m. The cantilever 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.
In the figures below the cantilever wall is shown in a larger scale.
This is a typical 2D stress stress analysis problem, problem, suitable for fi nite element approach. approach. In this case, case, "beam analogy" wil l not provide reliable results. results. The finite element model was was created created using using Stress2D software. The model model consists consists of several several 2D panels, representing representing the the cantilever, and four columns. columns. This is a very very simple model, and it takes 5 to 10 min. to draw it usingStress2D usingStress2D interactive editor.
Once, the model is prepared and all material properties are entered, we can perform the static analysis by the using Stress2Dsoftware. 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 m 2
5,750 mm2
or
(required area of steel)
Total Tension Force = 1,150 kN 50% Steel Yield Strength = 200,000 kPa
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 f actor of 2, which is suffi cient 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 mm 2, which will make a total or 7,890 mm 2. 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).
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". NOTE:
