Rectangular Beam check ACI 318-19#
Define concrete and steel materials, and then assign the beam
from mento import Concrete_ACI_318_19, SteelBar, RectangularBeam, mm, cm, kN, MPa, kNm
from mento import Forces, Node
# Define materials
concrete = Concrete_ACI_318_19(name="C25", f_c=25 * MPa)
steel = SteelBar(name="ADN 420", f_y=420 * 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 C25, Rebar ADN 420.
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=10 * 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 C25, Rebar ADN 420.
Top longitudinal rebar: 2Ø12, \(A_{s,top}\) = 2.26 cm², \(M_u\) = -30 kNm, \(\phi M_n\) = 38.29 kNm → \(\color{#439b00}{\text{DCR}=0.78}\)
Bottom longitudinal rebar: 2Ø16+1Ø12, \(A_{s,bot}\) = 5.15 cm², \(M_u\) = 80 kNm, \(\phi M_n\) = 84.13 kNm → \(\color{#efc200}{\text{DCR}=0.95}\)
Shear reinforcing 1eØ10/20 cm, \(A_v\)=7.85 cm²/m, \(V_u\)=55 kN, \(\phi V_n\)=171.49 kN → \(\color{#439b00}{\text{DCR}=0.32}\)
# Print shear results in more detailed format in a DataFrame
node_1.check_shear()
| Label | Comb. | Av,min | Av,req | Av | Vu | Nu | ØVc | ØVs | ØVn | ØVmax | Vu≤ØVmax | Vu≤ØVn | DCR | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | cm²/m | cm²/m | cm²/m | kN | kN | kN | kN | kN | kN | |||||
| 1 | 101 | 1.4D | 1.67 | 1.67 | 7.85 | 50 | 0 | 58.32 | 113.17 | 171.49 | 284.76 | True | True | 0.292 |
| 2 | 101 | 1.2D+1.6L | 1.67 | 1.67 | 7.85 | 55 | 0 | 58.32 | 113.17 | 171.49 | 284.76 | True | True | 0.321 |
# 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 | Mu | ØMn | Mu≤ØMn | DCR | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | cm² | cm² | cm² | cm² | kNm | kNm | |||||
| 1 | 101 | 1.4D | Bottom | 3.05 | 0.0 | 4.88 | 5.15 | 80 | 84.13 | True | 0.951 |
| 2 | 101 | 1.2D+1.6L | Top | 3.06 | 2.35 | 0.0 | 2.26 | -30 | 38.29 | True | 0.784 |
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 fc 25 MPa
Steel reinforcement yield strength fy 420 MPa
Concrete density wc 2500 kg/m³
Normalweight concrete λ 1
Safety factor for shear Øv 0.75
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 Nu 0 kN
Shear Vu 55 kN
Shear reinforcement strength Variable Value Unit
------------------------------ ---------- ------- ------
Number of stirrups ns 1
Stirrup diameter db 10 mm
Stirrup spacing s 20 cm
Effective height d 45.74 cm
Minimum shear reinforcing Av,min 1.67 cm²/m
Required shear reinforcing Av,req 1.67 cm²/m
Defined shear reinforcing Av 7.85 cm²/m
Shear rebar strength ØVs 113.17 kN
Check Unit Value Min. Max. Ok?
---------------------------- ------ ------- ------ ------ -----
Stirrup spacing along length cm 20 22.87 ✅
Stirrup spacing along width cm 14 45.74 ✅
Minimum shear reinforcement cm²/m 7.85 1.67 ✅
Minimum rebar diameter mm 10 10 ✅
Shear strength Variable Value Unit
-------------------------------- ---------- ------- ------
Effective shear area Acv 914.88 cm²
Longitudinal reinforcement ratio ρw 0.00247
Size modification factor λs 0.841
Axial stress σNu 0.0 MPa
Concrete effective shear stress kc 0.85 MPa
Concrete strength ØVc 58.32 kN
Maximum shear strength ØVmax 284.76 kN
Total shear strength ØVn 171.49 kN
Max shear check ✅
Demand Capacity Ratio DCR 0.32 ✅
# View detailed flexure results
node_1.flexure_results_detailed()
===== BEAM FLEXURE DETAILED RESULTS =====
Materials Variable Value Unit
---------------------------------- ---------- ------- ------
Section Label 101
Concrete strength fc 25 MPa
Steel reinforcement yield strength fy 420 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 4.1 cm
Mechanical bottom cover cm,bot 4.26 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 2.26 3.06 14.62 9.6.1.3
Minimum spacing top mm 106 30 ✅
Min/Max As rebar bottom cm² 5.15 3.05 14.57 ✅
Minimum spacing bottom mm 43 25 ✅
Top reinforcement check Variable Value Unit
---------------------------------------- ---------- ------- ------
First layer bars n1+n2 2Ø12
Second layer bars n3+n4 -
Effective height d 45.9 cm
Depth of equivalent strength block ratio c/d 0.04
Minimum rebar reinforcing As,min 3.06 cm²
Required rebar reinforcing top As,req top 2.35 cm²
Required rebar reinforcing bottom As,req bot 0 cm²
Defined rebar reinforcing top As 2.26 cm²
Longitudinal reinforcement ratio ρl 0.56124
Total flexural strength ØMn 38.29 kNm
Demand Capacity Ratio DCR 0.78 ✅
Bottom reinforcement check Variable Value Unit
---------------------------------------- ---------- --------- ------
First layer bars n1+n2 2Ø16+1Ø12
Second layer bars n3+n4 -
Effective height d 45.74 cm
Depth of equivalent strength block ratio c/d 0.12
Minimum rebar reinforcing As,min 3.05 cm²
Required rebar reinforcing top As,req top 0 cm²
Required rebar reinforcing bottom As,req bot 4.88 cm²
Defined rebar reinforcing bottom As 5.15 cm²
Longitudinal reinforcement ratio ρl 0.56316
Total flexural strength ØMn 84.13 kNm
Demand Capacity Ratio DCR 0.95 ✅
Export detailed results to a Word document
node_1.shear_results_detailed_doc()
node_1.flexure_results_detailed_doc()