One Way Slab check ACI 318-19#
Define concrete and steel materials, and then assign the beam
from mento import Concrete_ACI_318_19, SteelBar, OneWaySlab, Node, Forces
from mento import MPa, cm, kN, mm, kNm
# Define materials and beam section
conc = Concrete_ACI_318_19(name="H25", f_c=25 * MPa)
steel = SteelBar(name="ADN 500", f_y=420 * MPa)
slab = OneWaySlab(label="101", concrete=conc, steel_bar=steel, width=150 * cm, height=20 * cm, c_c=20 * mm)
slab.data
Slab 101, \(b\)=150.00 cm, \(h\)=20.00 cm, \(c_{c}\)=2.00 cm, Concrete H25, Rebar ADN 500.
Set longitudinal reinforcement
# Set bottom rebar
slab.set_slab_longitudinal_rebar_bot(d_b1=16 * mm, s_b1=10 * cm)
# Set top rebar
slab.set_slab_longitudinal_rebar_top(d_b1=16 * mm, s_b1=20 * cm)
# Plot the beam geometry and reinforcement
slab.plot()
Create node and assign slab section and list of forces
# Define forces
f1 = Forces(label="1.4D", V_z=40 * kN, M_y=60 * kNm)
f2 = Forces(label="1.2D+1.6L", V_z=50 * kN, M_y=-60 * kNm)
forces_list = [f1, f2]
# Create node and assign beam section and list of forces
node_1 = Node(section=slab, 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: 40.00 kN, M_y: 60.00 kN·m
- Force ID: 2, Label: 1.2D+1.6L, N_x: 0.00 kN, V_z: 50.00 kN, M_y: -60.00 kN·m
Perform shear and bending checks
# Perform all checks
node_1.check()
# Print results in Markdown format
node_1.results
Slab 101, \(b\)=150.00 cm, \(h\)=20.00 cm, \(c_{c}\)=2.00 cm, Concrete H25, Rebar ADN 500.
Top longitudinal rebar: 8Ø16, \(A_{s,top}\) = 16.08 cm², \(M_u\) = -60 kNm, \(\phi M_n\) = 98.13 kNm → \(\color{#439b00}{\text{DCR}=0.61}\)
Bottom longitudinal rebar: 15Ø16, \(A_{s,bot}\) = 30.16 cm², \(M_u\) = 60 kNm, \(\phi M_n\) = 173.43 kNm → \(\color{#439b00}{\text{DCR}=0.35}\)
Shear reinforcing not assigned, \(A_v\)=0.0 cm²/m, \(V_u\)=50 kN, \(\phi V_n\)=127.93 kN → \(\color{#439b00}{\text{DCR}=0.39}\)
# 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 | 0.0 | 0.0 | 0.0 | 40 | 0 | 157.75 | 0 | 157.75 | 796.3 | True | True | 0.254 |
| 2 | 101 | 1.2D+1.6L | 0.0 | 0.0 | 0.0 | 50 | 0 | 127.93 | 0 | 127.93 | 766.48 | True | True | 0.391 |
# 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 | 8.6 | 0.0 | 9.58 | 30.16 | 60 | 173.43 | True | 0.346 |
| 2 | 101 | 1.2D+1.6L | Top | 8.6 | 9.58 | 0.0 | 16.08 | -60 | 98.13 | True | 0.611 |
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 20 cm
Section width b 150 cm
Clear cover cc 2 cm
Longitudinal tension rebar As 16.08 cm²
Design forces Variable Value Unit
------------------------------- ---------- ------- ------
Axial, positive for compression Nu 0 kN
Shear Vu 50 kN
Shear reinforcement strength Variable Value Unit
------------------------------ ---------- ------- ------
Number of stirrups ns 0
Stirrup diameter db 0 mm
Stirrup spacing s 0 cm
Effective height d 17.2 cm
Minimum shear reinforcing Av,min 0 cm²/m
Required shear reinforcing Av,req 0 cm²/m
Defined shear reinforcing Av 0 cm²/m
Shear rebar strength ØVs 0 kN
Check Unit Value Min. Max. Ok?
---------------------------- ------ ------- ------ ------ -----
Stirrup spacing along length cm 0 8.6 ✔️
Stirrup spacing along width cm 0 17.2 ✔️
Minimum shear reinforcement cm²/m 0 0.0 ✔️
Minimum rebar diameter mm 0 0 ✔️
Shear strength Variable Value Unit
-------------------------------- ---------- ------- ------
Effective shear area Acv 2580.0 cm²
Longitudinal reinforcement ratio ρw 0.00623
Size modification factor λs 1.089
Axial stress σNu 0.0 MPa
Concrete effective shear stress kc 0.66 MPa
Concrete strength ØVc 127.93 kN
Maximum shear strength ØVmax 766.48 kN
Total shear strength ØVn 127.93 kN
Max shear check ✔️
Demand Capacity Ratio DCR 0.39 ✔️
# 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 20 cm
Section width b 150 cm
Clear cover cc 2 cm
Mechanical top cover cm,top 2.8 cm
Mechanical bottom cover cm,bot 2.8 cm
Design_forces Variable Value Unit
----------------- ---------- ------- ------
Top max moment Mu,top -60 kNm
Bottom max moment Mu,bot 60 kNm
Check Unit Value Min. Max. Ok?
----------------------- ------ ------- ------ ------ -----
Min/Max As rebar top cm² 16.08 8.6 41.09 ✔️
Minimum spacing top mm 190.29 30 ✔️
Min/Max As rebar bottom cm² 30.16 8.6 41.09 ✔️
Minimum spacing bottom mm 87.14 25 ✔️
Top reinforcement check Variable Value Unit
---------------------------------------- ---------- ------- ------
First layer bars n1+n2 8Ø16
Second layer bars n3+n4 -
Effective height d 17.2 cm
Depth of equivalent strength block ratio c/d 0.09
Minimum rebar reinforcing As,min 8.6 cm²
Required rebar reinforcing top As,req top 9.58 cm²
Required rebar reinforcing bottom As,req bot 0 cm²
Defined rebar reinforcing top As 16.08 cm²
Longitudinal reinforcement ratio ρl 1.16896
Total flexural strength ØMn 98.13 kNm
Demand Capacity Ratio DCR 0.61 ✔️
Bottom reinforcement check Variable Value Unit
---------------------------------------- ---------- ------- ------
First layer bars n1+n2 15Ø16
Second layer bars n3+n4 -
Effective height d 17.2 cm
Depth of equivalent strength block ratio c/d 0.09
Minimum rebar reinforcing As,min 8.6 cm²
Required rebar reinforcing bottom As,req top 0 cm²
Required rebar reinforcing top As,req bot 9.58 cm²
Defined rebar reinforcing bottom As 30.16 cm²
Longitudinal reinforcement ratio ρl 1.16896
Total flexural strength ØMn 173.43 kNm
Demand Capacity Ratio DCR 0.35 ✔️
Export detailed results to a Word document
node_1.shear_results_detailed_doc()
node_1.flexure_results_detailed_doc()