Rectangular Beam design EN 1992-1-1#
Define concrete and steel materials, and then assign the beam
from mento import Concrete_EN_1992_2004, SteelBar, RectangularBeam, cm, kN, MPa, kNm
from mento import Forces, Node
# Define materials
concrete = Concrete_EN_1992_2004(name="H25", f_c=25 * MPa)
steel = SteelBar(name="ADN 500", f_y=500 * MPa)
# Define beam geometry
beam = RectangularBeam(label="101", concrete=concrete, steel_bar=steel, width=20 * cm, height=50 * cm, c_c=2.5 * cm)
beam.data
Beam 101, \(b\)=20.00 cm, \(h\)=50.00 cm, \(c_{c}\)=2.50 cm, Concrete H25, Rebar ADN 500.
Define list of forces applied to the beam
# Define forces
f1 = Forces(label="1.4D", V_z=50 * kN, M_y=80 * kNm)
f2 = Forces(label="1.2D+1.6L", V_z=55 * kN, M_y=-30 * kNm)
print(f1)
print(f2)
Force ID: 1, Label: 1.4D, N_x: 0.00 kN, V_z: 50.00 kN, M_y: 80.00 kN·m
Force ID: 2, Label: 1.2D+1.6L, N_x: 0.00 kN, V_z: 55.00 kN, M_y: -30.00 kN·m
Create node and assign beam section and list of forces
node_1 = Node(section=beam, forces=[f1, f2])
node_1
Node ID: 1 - Section label: 101
Forces Applied:
- Force ID: 1, Label: 1.4D, N_x: 0.00 kN, V_z: 50.00 kN, M_y: 80.00 kN·m
- Force ID: 2, Label: 1.2D+1.6L, N_x: 0.00 kN, V_z: 55.00 kN, M_y: -30.00 kN·m
Perform shear and bending design
# Perform design
node_1.design()
# Print results in Markdown format
node_1.results
Beam 101, \(b\)=20.00 cm, \(h\)=50.00 cm, \(c_{c}\)=2.50 cm, Concrete H25, Rebar ADN 500.
Top longitudinal rebar: 2Ø10, \(A_{s,top}\) = 1.57 cm², \(M_u\) = -30 kNm, \(\phi M_n\) = 29.06 kNm → \(\color{#d43e36}{\text{DCR}=1.03}\)
Bottom longitudinal rebar: 2Ø16+1Ø12, \(A_{s,bot}\) = 5.15 cm², \(M_u\) = 80 kNm, \(\phi M_n\) = 97.48 kNm → \(\color{#439b00}{\text{DCR}=0.82}\)
Shear reinforcing 1eØ6/34 cm, \(A_{sw}\)=1.66 cm²/m, \(V_{Ed,2}\)=55 kN, \(V_{Rd}\)=75.08 kN → \(\color{#439b00}{\text{DCR}=0.73}\)
# Plot the beam geometry and reinforcement
beam.plot()
# Print shear results in more detailed format in a DataFrame
node_1.check_shear()
| Label | Comb. | Av,min | Av,req | Av | NEd | VEd,1 | VEd,2 | VRd,c | VRd,s | VRd | VRd,max | VEd,1≤VRd,max | VEd,2≤VRd | DCR | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | cm²/m | cm²/m | cm²/m | kN | kN | kN | kN | kN | kN | kN | |||||
| 1 | 101 | 1.4D | 1.6 | 1.6 | 1.66 | 0 | 50 | 50 | 0 | 75.08 | 75.08 | 257.76 | True | True | 0.666 |
| 2 | 101 | 1.2D+1.6L | 1.6 | 1.6 | 1.66 | 0 | 55 | 55 | 0 | 75.08 | 75.08 | 257.76 | True | True | 0.733 |
# Print flexure results in more detailed format in a DataFrame
node_1.check_flexure()
| Label | Comb. | Position | As,min | As,req top | As,req bot | As | MEd | MRd | MEd≤MRd | DCR | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | cm² | cm² | cm² | cm² | kNm | kNm | |||||
| 1 | 101 | 1.4D | Bottom | 1.23 | 0.0 | 4.23 | 5.15 | 80 | 97.48 | True | 0.821 |
| 2 | 101 | 1.2D+1.6L | Top | 1.24 | 1.52 | 0.0 | 1.57 | -30 | 29.06 | True | 1.033 |
Export table results to Excel
node_1.check_shear().to_excel("ACI 318-19 shear_results.xlsx")
node_1.check_flexure().to_excel("ACI 318-19 flexure_results.xlsx")
View complete and detailed results for the limiting case of the list of forces
# View detailed shear results
node_1.shear_results_detailed()
===== BEAM SHEAR DETAILED RESULTS =====
Materials Variable Value Unit
----------------------------------------------------- ---------- ------- ------
Section Label 101
Concrete strength fck 25 MPa
Steel reinforcement yield strength fywk 500 MPa
Safety factor for concrete γc 1.5
Safety factor for steel γs 1.15
Coefficient for long term effects and loading effects αcc 0.85
Geometry Variable Value Unit
-------------------------- ---------- ------- ------
Section height h 50 cm
Section width b 20 cm
Clear cover cc 2.5 cm
Longitudinal tension rebar As 1.57 cm²
Design forces Variable Value Unit
------------------------------- ---------- ------- ------
Axial, positive for compression NEd 0 kN
Shear VEd,2 55 kN
Shear reinforcement strength Variable Value Unit
------------------------------ ---------- ------- ------
Number of stirrups ns 1
Stirrup diameter db 6 mm
Stirrup spacing s 34 cm
Effective height d 46.14 cm
Minimum shear reinforcing Asw,min 1.6 cm²/m
Required shear reinforcing Asw,req 1.6 cm²/m
Defined shear reinforcing Asw 1.66 cm²/m
Shear rebar strength VRd,s 75.08 kN
Check Unit Value Min. Max. Ok?
---------------------------- ------ ------- ------ ------ -----
Stirrup spacing along length cm 34 34.61 ✔️
Stirrup spacing along width cm 14.4 34.61 ✔️
Minimum shear reinforcement cm²/m 1.66 1.6 ✔️
Shear strength Variable Value Unit
-------------------------------- ---------- ------- ------
Longitudinal reinforcement ratio ρl 0.1702
k value k 1.66
Axial stress σcd 0.0 MPa
Concrete strut angle Θ 21.8 deg
Concrete strength VRd,c 0 kN
Maximum shear strength VRd,max 257.76 kN
Total shear strength VRd 75.08 kN
Max shear check ✔️
Demand Capacity Ratio DCR 0.733 ✔️
# View detailed flexure results
node_1.flexure_results_detailed()
===== BEAM FLEXURE DETAILED RESULTS =====
Materials Variable Value Unit
---------------------------------- ---------- ------- ------
Section Label 101
Concrete strength fck 25 MPa
Steel reinforcement yield strength fyk 500 MPa
Geometry Variable Value Unit
----------------------- ---------- ------- ------
Section height h 50 cm
Section width b 20 cm
Clear cover cc 2.5 cm
Mechanical top cover cm,top 3.6 cm
Mechanical bottom cover cm,bot 3.86 cm
Design forces Variable Value Unit
----------------- ---------- ------- ------
Top max moment Mu,top -30 kNm
Bottom max moment Mu,bot 80 kNm
Check Unit Value Min. Max. Ok?
----------------------- ------ ------- ------ ------ -----
Min/Max As rebar top cm² 1.57 1.24 37.12 ✔️
Minimum spacing top mm 118 30 ✔️
Min/Max As rebar bottom cm² 5.15 1.23 36.92 ✔️
Minimum spacing bottom mm 47 25 ✔️
Top reinforcement check Variable Value Unit
---------------------------------------- ---------- ------- ------
First layer bars n1+n2 2Ø10
Second layer bars n3+n4 -
Effective height d 46.4 cm
Depth of equivalent strength block ratio c/d 0
Minimum rebar reinforcing As,min 1.24 cm²
Required rebar reinforcing top As,req top 1.52 cm²
Required rebar reinforcing bottom As,req bot 0 cm²
Defined rebar reinforcing top As 1.57 cm²
Longitudinal reinforcement ratio ρl 0.5552
Total flexural strength MRd 29.06 kNm
Demand Capacity Ratio DCR 1.03 ❌
Bottom reinforcement check Variable Value Unit
---------------------------------------- ---------- --------- ------
First layer bars n1+n2 2Ø16+1Ø12
Second layer bars n3+n4 -
Effective height d 46.14 cm
Depth of equivalent strength block ratio c/d 0
Minimum rebar reinforcing As,min 1.23 cm²
Required rebar reinforcing bottom As,req top 0 cm²
Required rebar reinforcing top As,req bot 4.23 cm²
Defined rebar reinforcing bottom As 5.15 cm²
Longitudinal reinforcement ratio ρl 0.55828
Total flexural strength MRd 97.48 kNm
Demand Capacity Ratio DCR 0.82 ✔️
Export detailed results to a Word document
node_1.shear_results_detailed_doc()
node_1.flexure_results_detailed_doc()