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When we complete the procedure of the Physically non-linear calculation and get into the assessment phase, we may open the service Results and see either (i) standard result quantities or (ii) results directly linked to this type of calculation: PNL stress/strain and PNL stiffness.
(1) Once the physically and geometrically nonlinear analysis has been performed, we SHOULD NOT perform a new design of reinforcement. The real (practical) reinforcement was defined prior to the calculation. The analysis just PROVES whether the designed reinforcement and dimensions of the cross-section are satisfactory for the transfer of given loads.
(2) In order to prevent the misinterpretation of the calculated bending moments, we must aware of the following. After the PGNL analysis has been performed, the calculated internal forces (moments) are related to the centroidal axis of the NET (i.e. WEAKENED) CROSS-SECTION. This net cross-section is assigned to the corresponding finite element in the solver. All internal forces in SCIA Engineer are always related to the centroidal axis of the cross-section! Therefore, in order to obtain (after PGNL calculation) the quantity that is comparable to the result of a linear solution, we must ADD the moment that equals to the axial force multiplied by the distance of the centroid of the new net (weakened) cross-section from the centroid of the original (gross) cross-section.
Note: The results cannot be reviewed in the service Concrete Advanced , as they do not represent any check. It is true that we have calculated with concrete, but the results are general results of a general non-linear calculation and therefore they are in the service Results > PNL stress/strain and PNL stiffness.
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eps cc |
compressive strain in concrete, meaningful only for beams made of concrete |
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eps ct |
tensile strain in concrete, meaningful only for beams made of concrete |
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eps rt |
tensile strain in reinforcement, meaningful only for beams made of reinforced concrete |
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eps rc |
compressive strain in reinforcement, meaningful only for beams made of reinforced concrete |
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eps st |
tensile strain in steel, meaningful only for beams made of steel |
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eps sc |
compressive strain in steel, meaningful only for beams made of steel |
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sigma cc |
compressive stress in concrete, meaningful only for beams made of concrete |
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sigma ct |
tensile stress in concrete, meaningful only for beams made of concrete |
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sigma rt |
tensile stress in reinforcement, meaningful only for beams made of reinforced concrete |
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sigma rc |
compressive stress in reinforcement, meaningful only for beams made of reinforced concrete |
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sigma st |
tensile stress in steel, meaningful only for beams made of steel |
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sigma sc |
compressive stress in steel, meaningful only for beams made of steel |
Note: Steel beams are calculated linearly.
Example:
The two images below show all the strain components displayed for (i) a reinforced concrete beam and (ii) steel beam. It is clearly seen that the components that are irrelevant for the particular material are zero.
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reinforced concrete beam |
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steel beam |
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EAx |
Non-linear axial stiffness. |
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EIy |
Non-linear flexural stiffness, i.e. the connection presented in the last iteration step. |
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EIz |
Non-linear flexural stiffness, i.e. the connection presented in the last iteration step. |
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xr |
Height of compression zone, or the position of neutral axis. |
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As |
Total reinforcement area in a given section that is considered in the calculation of non-linear stiffness. This area is multiplied by the coefficient for reinforcement from the Solver setup. |
To show the effect of plasticizing that may be "discovered" in the physically non-linear calculation, let us consider the following simple structure.
We create a two-span (2 × 6.0 m) continuous beam with concrete cross-section 500 × 300 mm. We input the practical reinforcement whose details are not important for the purpose of our explanation (for more information see the note below). Only physical non-linearity is considered.
The beam is subjected to a uniformly distributed load q = 28,5 kN/m.
When we apply the analytically derived formula for the hogging moment above the intermediate support of a two-span continuous beam, we obtain:
M = 0.125 × q × l2 = 0.125 × 28.5 × 62 = 128.25 kNm.
The linear calculation in SCIA Engineer gives the bending moment calculated above the intermediate support is equal to 127,6 kNm, which is very close to the direct solution.
When we apply the non-linear calculation, the change of cross-section stiffness due to formed cracks results in a redistribution of internal forces.
The bending moment calculated above the intermediate support is equal to 88.8 kNm.
We may look at the correctness of the moment redistribution by taking the bending moment in the middle of the span (not shown in the picture) 83.9 kNm and performing a simple calculation:
moment in the middle of the span + half of the redistributed hogging moment = hogging moment before the redistribution =
83.9+88.8/2 = 128.3 kNm,
which almost precisely equals to the direct solution stated above.
Note: More details are given in [1]. Contrary to older program EPW, it is not possible to control the insertion of plastic hinges. Details are again given in [1].
