Design of reinforced concrete structures from three-dimensional stress fields

Chen, Reinaldo; Bittencourt, Túlio Nogueira; Bella, João Carlos Della

doi:10.1590/S1983-41952023000400007

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 16 (4) • 2023 • https://doi.org/10.1590/S1983-41952023000400007 copy

Design of reinforced concrete structures from three-dimensional stress fields

Dimensionamento de estruturas de concreto armado a partir de campos de tensão tridimensionais

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

The design of reinforced concrete structures starting from a linear analysis is allowed by design codes and leads to safe solutions. The structural model built for the analysis may be composed not only of bar and shell elements, but also solid elements. In the present work, the formulation of the Reinforced Solid Method (RSM) was reviewed and applied to the Ultimate Limit State design of a reinforced concrete member, with the computation of the required reinforcement and concrete check of each individual solid element within the structural model. The results were visualized in a post-processor and validated by numerical simulations. The RSM effectively allows for the design of concrete structures with general geometry and loading conditions, whilst identifying local effects throughout the volume of the structure.

Keywords:
solid elements; reinforced concrete; design; reinforced solid method; three-dimensional elasticity

Case 1	Sign combination			Case 2	Sign combination
Case 1	τ_xy	τ_xz	τ_yz	Case 2	τ_xy	τ_xz	τ_yz
# 1	+	+	+	# 5	-	-	-
# 2	-	-	+	# 6	+	+	-
# 3	-	+	-	# 7	+	-	+
# 4	+	-	+	# 8	-	+	+

Cases	ftx	f_ty	f_tz	Condition
1a +++	$σ_{x} + (τ_{x y} + τ_{x z})$	$σ_{y} + (τ_{x y} + τ_{y z})$	$σ_{z} + (τ_{x z} + τ_{y z})$	$f_{t x}, f_{t y}, f_{t z} > 0$
2a ++-	$σ_{x} + (τ_{x y} + τ_{x z})$	$σ_{y} + (τ_{x y} + τ_{y z})$	$σ_{z} + (τ_{x z} + τ_{y z})$	$f_{t x}, f_{t y}, f_{t z} > 0$ $\begin{array}{l} τ_{x y} τ_{x z} + τ_{x z} τ_{y z} \\ + τ_{x y} τ_{y z} > 0 \end{array}$
2b ++-	$σ_{x} - \frac{τ_{x y} τ_{x z}}{τ_{y z}}$	$σ_{y} - \frac{τ_{x y} τ_{y z}}{τ_{x z}}$	$σ_{z} - \frac{τ_{x z} τ_{y z}}{τ_{x y}}$	$f_{t x}, f_{t y}, f_{t z} > 0$ $\begin{array}{l} τ_{x y} τ_{x z} + τ_{x z} τ_{y z} \\ + τ_{x y} τ_{y z} < 0 \end{array}$
1b/ 2	$σ_{x} + τ_{x y} - τ_{x z} \frac{τ_{x z} + τ_{y z}}{σ_{z}}$	$σ_{y} + τ_{x y} - τ_{y z} \frac{τ_{x z} + τ_{y z}}{σ_{z}}$	0	$\begin{array}{l} f_{t z} < 0 \\ f_{t x}, f_{t y} > 0 \end{array}$
1b/ 2	$σ_{x} + τ_{x z} - τ_{x y} \frac{τ_{x y} + τ_{y z}}{σ_{y}}$	0	$σ_{z} + τ_{x z} - τ_{y z} \frac{(τ_{x y} + τ_{y z})}{σ_{y}}$	$\begin{array}{l} f_{t y} < 0 \\ f_{t x}, f_{t z} > 0 \end{array}$
1b/ 2	0	$σ_{y} + τ_{y z} - τ_{x y} \frac{τ_{x y} + τ_{x z}}{σ_{x}}$	$σ_{z} + τ_{y z} - τ_{x z} \frac{τ_{x y} + τ_{x z}}{σ_{x}}$	$\begin{array}{l} f_{t x} < 0 \\ f_{t y}, f_{t z} > 0 \end{array}$
1c/ 2	$σ_{x} + \frac{2 τ_{x y} τ_{x z} τ_{y z} - σ_{y} τ_{x z}^{2} - σ_{z} τ_{x y}^{2}}{σ_{y} σ_{z} - τ_{y z}^{2}}$	0	0	$\begin{array}{l} f_{t y}, f_{t z} < 0 \\ f_{t x} > 0 \end{array}$
1c/ 2	0	$σ_{y} + \frac{2 τ_{x y} τ_{x z} τ_{y z} - σ_{x} τ_{y z}^{2} - σ_{z} τ_{x y}^{2}}{σ_{x} σ_{z} - τ_{x z}^{2}}$	0	$\begin{array}{l} f_{t x}, f_{t z} < 0 \\ f_{t y} > 0 \end{array}$
1c/ 2	0	0	$σ_{z} + \frac{2 τ_{x y} τ_{x z} τ_{y z} - σ_{x} τ_{y z}^{2} - σ_{y} τ_{x z}^{2}}{σ_{x} σ_{y} - τ_{x y}^{2}}$	$\begin{array}{l} f_{t x}, f_{t y} < 0 \\ f_{t z} > 0 \end{array}$
1d/ 2	0	0	0	$\begin{array}{l} σ_{x} σ_{y} σ_{z} + 2 τ_{x y} τ_{x z} τ_{y z} \\ - σ_{x} τ_{y z}^{2} - σ_{y} τ_{x z}^{2} \\ - σ_{z} τ_{x y}^{2} < 0 \end{array}$

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[1] Corresponding author: Túlio Nogueira Bittencourt. E-mail: tbitten@usp.br