Rectangular Beam check EN 1992-1-1#
Define concrete and steel materials, and then assign the beam
from mento import Concrete_EN_1992_2004, SteelBar, RectangularBeam, mm, 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.
Set longitudinal and transverse reinforcement
# Set bottom longitudinal reinforcement
beam.set_longitudinal_rebar_bot(n1=2, d_b1=16 * mm, n2=1, d_b2=12 * mm)
# Set top longitudinal reinforcement
beam.set_longitudinal_rebar_top(n1=2, d_b1=12 * mm)
# Set transverse reinforcement (stirrups)
beam.set_transverse_rebar(n_stirrups=1, d_b=6 * mm, s_l=20 * cm)
# Plot the beam geometry and reinforcement
beam.plot()
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 checks
# Perform all checks
node_1.check()
# 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: 2Ø12, \(A_{s,top}\) = 2.26 cm², \(M_u\) = -30 kNm, \(\phi M_n\) = 41.74 kNm → \(\color{#439b00}{\text{DCR}=0.72}\)
Bottom longitudinal rebar: 2Ø16+1Ø12, \(A_{s,bot}\) = 5.15 cm², \(M_u\) = 80 kNm, \(\phi M_n\) = 97.5 kNm → \(\color{#439b00}{\text{DCR}=0.82}\)
Shear reinforcing 1eØ6/20 cm, \(A_{sw}\)=2.83 cm²/m, \(V_{Ed,2}\)=55 kN, \(V_{Rd}\)=127.64 kN → \(\color{#439b00}{\text{DCR}=0.43}\)
# 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 | 2.83 | 0 | 50 | 50 | 0 | 127.64 | 127.64 | 257.76 | True | True | 0.392 |
| 2 | 101 | 1.2D+1.6L | 1.6 | 1.6 | 2.83 | 0 | 55 | 55 | 0 | 127.64 | 127.64 | 257.76 | True | True | 0.431 |
# 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 | 97.5 | True | 0.821 |
| 2 | 101 | 1.2D+1.6L | Top | 1.24 | 1.52 | 0.0 | 2.26 | -30 | 41.74 | True | 0.719 |
Export table results to Excel
node_1.check_shear().to_excel("EN 1992-1-1 shear_results.xlsx")
# node_1.check_flexure().to_excel('EN 1992-1-1 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 2.26 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 20 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 2.83 cm²/m
Shear rebar strength VRd,s 127.64 kN
Check Unit Value Min. Max. Ok?
---------------------------- ------ ------- ------ ------ -----
Stirrup spacing along length cm 20 34.61 ✔️
Stirrup spacing along width cm 14.4 34.61 ✔️
Minimum shear reinforcement cm²/m 2.83 1.6 ✔️
Shear strength Variable Value Unit
-------------------------------- ---------- ------- ------
Longitudinal reinforcement ratio ρl 0.0056
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 127.64 kN
Max shear check ✔️
Demand Capacity Ratio DCR 0.431 ✔️
# View detailed flexure results
# node_1.flexure_results_detailed()
Export detailed results to a Word document
node_1.shear_results_detailed_doc()
# node_1.flexure_results_detailed_doc()