A section interaction diagram is the set of combined loads (bending and axial) that will cause the section to fail. To obtain this mentioned set of loads, a pivot based diagraman corresponding to different strain distributions in the section is calculated. The methodology is based on the Eurocode 2 and the Spanish code EHE as explained below:
The neutral axis is varied along the section from +∞ to -∞. Depending on the position of the neutral axis the section fails due to the failure of the tensioned steel reinforcement (pure or combined tensile or pure or combined bending) or due to the excess of plastic strain in concrete of the most compressed fiber (pure or combined bending or pure or combined compression). Each one of this failure modes is assigned to a pivot:
Pivot A: Tensioned steel reinforcement reaches the ultimate steel strain.
Pivot B: Ultimate concrete strain reached caused by the concrete in bending
Pivot C: Crushing of compressed concrete reached by a concentric compression force (no bending moments).
(*)Note: This interaction diagram has been done supposing that the concrete cannot stand tensile stresses.
Five deformation domains have been defined in the concrete in function of the neutral axis and the section’s failure pivot:
Domain 1: Corresponds to the pure or combined tensile strength where the whole section is in tension. The deformation lines rotate around pivot A. The neutral axis goes from +∞ to x=0.
Domain 2: Pure or combined bending where the failure is still happening at point A and the compressed concrete has not reached the strain that causes its fracture. The neutral axis goes from x=0 to a critical x which corresponds to the maximum strain of both materials. The neutral axis goes through pivot A and B, which for a 100/00 reinforcement strain and a 3.50/00, concrete strain, the neutral axis is placed at 0.259d from the top of the section. This neutral axis is called "critical neutral axis".
Domain 3: Pure or combined bending where the deformation lines rotate around pivot B. The neutral axis goes from the critical x defined above to xlim, which is the line that goes from point B to a deformation of the tensioned reinforcement equal to its yield tensile strength
Domain 4: Consists of two parts:
a) Pure or combined bending where the deformation lines rotate around pivot B. The strain of the most tensioned reinforcement varies from the yield limit to 0. The neutral axis goes from xlim to x=d. When x=d the reinforcement’s strain will be zero.
b) Combined compression: The failure is still happening at pivot B. All the reinforcement rebars are compressed but the section is not fully compressed yet. The neutral axis varies from x=d to x=h where all the concrete section will be fully compressed.
Domain 5: The whole section is compressed and the neutral axis rotates around pivot C, which is defined by the intersection of the line that goes from pivot B to the inferior limit of the section with the line belonging to a 20/00 concrete strain. The neutral axis varies from x=h to h=-∞.
Geometrical characteristics | ||
Heigth (mm) (h): | ||
Width (mm) (b): | ||
Upper reinforcement (mm^2) (A2): | ||
Lower reinforcement (mm^2) (A1): | ||
Upper concrete cover (mm) (R2): | ||
Lower concrete cover (mm) (R1): |
Material characteristics | |||
Steel yielding limit (MPa) (fys): | Steel partial factor: |
Typical values:
Persistent & Transient situation:1.15; Accidental situation:1.0; |
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Concrete resistance (MPa) (fck): | Concrete partial factor: |
Typical values:
Persistent & Transient situation::1.5; Accidental situation:1.2; |
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Steel Yound modulus (N/mm^2) (Es): |
Typical value:
210000 MPa; |
Interaction diagramam parameters | |||
Maximum concrete failure strain in bending: | Concrete crushing strain (pure compression): | ||
Deformación de rotura del acero: |
Loads | ||
Axil (N) (kN): | ||
Bending moment (M) (kN*m): | The forces on the figure are positive |
Calculate
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