ravi patel (#68)

* ravi patel

Added script for beam design

* Update test_beam_design.py

Fixed import issue

* Create __init__.py

__init__ file added to fix import issue

* Update test_beam_design.py

one more try to fix import error!!

* Update BeamDesign.py

udapted documentation as per the request

* modification of test

added assertion in test to compare with the result output

* added function check design

I have added function check _design which can be used for optimization. It gives difference between specified_area and required_area as output. I added also test for check_desgin in test_beam_design function in test script. I also keep old tests so that other functions are also tested

* Update test_beam_design.py

removed extra function tests and prints. Added exact assert on value in test

* fixed some minor details

Co-authored-by: Erik Tamsen <[email protected]>

lebedigital/BeamDesign/beam_design.py

@@ -0,0 +1,210 @@
+import math
+
+
+def section_dimension_rule_of_thumb(span: float) -> tuple:
+    """
+    This is as per eurocode guideline choice of section dimension based on span
+    Only used as a useful input for the test
+
+    Parameters
+    ----------
+    span : float
+        beam span in mm
+
+    Returns
+    -------
+    tuple
+        tuple of width and height of the beam in mm.
+    """
+    #span/depth ratio for simply supported beam is 15 Therefore,
+    height = 50 * round((span/15)/50)
+    #width of beam
+    width = 0.5 * height
+
+    return width, height
+
+
+def max_bending_moment_and_shear_force(span: float, point_load: float, distributed_load: float) -> tuple:
+    """
+    function to compute max bending moment and shear force for simply supported beam with point load or distributed load
+
+    Parameters
+    ----------
+    span : float
+        beam length in mm
+    point_load : float
+        point load in N
+    distributed_load : str
+        distributed load in N
+
+    Returns
+    -------
+    tuple
+        tuple of  maximum moment and maximum shear force
+    """
+
+    max_moment_dist_load = distributed_load * span**2 / 8
+    max_shear_force_dist_load = distributed_load*span / 2
+    max_moment_point_load = point_load*span / 4
+    max_shear_force_point_load = point_load / 2
+
+    return (max_moment_point_load + max_moment_dist_load, 
+            max_shear_force_dist_load + max_shear_force_point_load)
+
+
+def beam_section_design(
+                       width: float,
+                       height: float,
+                       max_moment: float,
+                       max_shear_force: float,
+                       fck: float,
+                       fyk: float,
+                       steel_dia: float,
+                       cover: float,
+                       ) -> dict:
+    """
+    Function to design singly reinforced beam with minimum shear reinforcement required.
+
+    Parameters
+    ----------
+    width: float
+        beam width in mm.
+    height: float
+        beam depth in mm. 
+    max_moment : float
+        Maximum bending moment in N-mm.
+    max_shear_force : float
+        Maximum shear force in N.
+    fck : float
+        charateristic compressive strength of concrete in N/mm2.
+    fyk : float
+        Yield strength of steel in N/mm2.
+    steel_dia : int
+        Diameter of steel in mm.
+    cover : int
+        Depth of cover required as per exposure class in mm.
+
+    Returns
+    -------
+    dict
+        Design of the reinforced beam section.
+    """
+    #effective section depth
+    deff = height - cover - steel_dia - steel_dia / 2
+    #fcd=Design compressive strength
+    a_cc=0.85
+    gamma_c=1.5 #Concrete partial material safety factor
+    fcd=a_cc*fck/gamma_c #N/mm^2
+    gamma_s=1.0
+    fywd=fyk/gamma_s#N/mm^2
+    #Bending measurement (here with stress block) (Biegebemessung (hier mit Spannungsblock))
+    muEd= max_moment / (width * deff ** 2 * fcd) / 1000
+    xi=0.5*(1+math.sqrt(1-2*muEd))
+    As1= 1 / fywd * max_moment / (xi * deff) #[-]
+    A=(math.pi * steel_dia ** 2 / 4) #mm^2
+    nsteel= max(2, math.ceil(As1/A)) #rounds up
+    #Compression strut angle pure bending (Druckstrebenwirkel)
+    cot=1.2 #[-] cot(40)=1.2
+    #Compression strut----
+    #v1 = Reduction coefficient for concrete strength in shear cracks 
+    if fck > 50: v1=1.0 
+    else: v1=0.75
+    #alpha_cw= Coefficient to account for the stress state in the compression chord (according to NA: 𝛼𝑐𝑤=1.0);
+    alpha_cw=1.0
+    # z=inner lever arm (innerer Hebelarm)
+    c_vl=cover
+    z=min(0.9*deff, max(deff-c_vl-30, deff-2*c_vl)) #in [mm]
+    bw=width #Rectangular cross section [mm]
+    V_Rdmax= alpha_cw*bw*z*v1*fcd/(cot+1/cot) #[N]
+    assert V_Rdmax > max_shear_force, "Compression strut not stable"
+    #Tension strut----
+    #VEdred= Shear force reduction -> only possible is "direct support" 
+    VEdred=max_shear_force #here assumed: indirect support  [N]
+    #a_sw =Steal stection per m 
+    a_sw=VEdred/(z*fywd*cot)*1000 #[mm^2/m]
+    #Calculated minimum shear force reinforcement----
+    alpha=math.radians(90)# Angle between shear force reinforcement and the component axis perpendicular to the shear force: α = 90° (vertical stirrups)
+    #fctm mean tensile strength 
+    if fck<=50: fctm=0.3*fck**(2/3)
+    else: fctm=2.12*math.ln(1+((fck+8)/10)) 
+    a_swmin=0.16*fctm/fyk*(bw/1000)*math.sin(alpha)*1e6 #[mm2/m]
+    #Statically required stirrup spacing----
+    #print(f"stirrup and bending reinforcment have same diameter = {steelDia} [mm]")
+    a_used= max(a_sw,a_swmin) #[mm^2/m]
+    Aw=2*math.pi*12**2/4 #[mm²]
+    slmax=Aw/a_used*1000 #[mm]
+    #Minimum structural reinforcement----
+    if fck<=50:
+        if max_shear_force<= 0.3*V_Rdmax:
+            S= min(0.7 * height, 300, slmax)
+        elif max_shear_force<= 0.6*V_Rdmax:
+            S= min(0.5 * height, 300, slmax)
+        else:
+            S= min(0.25 * height, 200, slmax)
+    else:
+        if max_shear_force<= 0.3*V_Rdmax:
+            S= min(0.7 * height, 200, slmax)
+        elif max_shear_force<= 0.6*V_Rdmax:
+            S= min(0.7 * height, 200, slmax)
+        else:
+            S= min(0.25 * height, 200, slmax)
+    #output final design
+    out = {}
+    out["top_steel_dia[mm]"] = steel_dia
+    out["top_steel_numbers"] = 2
+    out["shear_reinforcement_dia[mm]"] = 12
+    out["shear_reinforcement_spacing[mm]"] = S
+    out["required_area_bottom_steel[mm^2]"] = As1
+
+    return out
+
+
+def check_design(span:float,
+                 width:float,
+                 height:float,
+                 point_load:float,
+                 distributed_load:float,
+                 fck:float,
+                 fyk:float,
+                 steel_dia:float,
+                 n_bottom:int,
+                 cover:float,
+                 ) -> float:
+    """
+    Function to check specified design for area of steel
+
+    Parameters
+    ----------
+    span : int
+        length of the beam in mm.
+    width: int
+        beam width in mm.
+    height: int
+        beam depth in mm.
+    fck : float
+        charateristic compressive strength of concrete in N/mm2.
+    fyk : float
+        Yield strength of steel in N/mm2.
+    steel_dia : float
+        Diameter of steel in mm.
+    n_bottom:int,
+        Number of steel bars in the bottom of the section.
+        On top for singly reinforced section we assume 2 steel bars of 12 mm which holds the cage
+    cover : float
+        Depth of cover required as per exposure class in mm.
+
+    Returns
+    -------
+    float
+        normalized difference of  specified area and required area given the diameter of steel and number of steel bars
+        in the bottom of the section. It is negative if  design is not satisfied and positive if design is satisfied.
+        Optimal will be close to zero.
+    """
+    max_moment, max_shear_force = max_bending_moment_and_shear_force(span, point_load, distributed_load)
+    design = beam_section_design(width, height, max_moment, max_shear_force, fck, fyk, steel_dia, cover)
+    specified_area = (math.pi * steel_dia ** 2 / 4) * n_bottom
+    required_area = design["required_area_bottom_steel[mm^2]"]
+
+    return (specified_area-required_area)/required_area
+
+

tests/beam_design/test_beam_design.py

@@ -0,0 +1,28 @@
+from lebedigital.BeamDesign import beam_design
+import pytest
+
+
+def test_beam_design():
+    """
+    Test function to test beam design module 
+    This example is analogus to one described in this blog: 
+    https://www.structuralguide.com/worked-example-singly-reinforced-beam-design-using-ec2/
+    """
+
+    width, height = beam_design.section_dimension_rule_of_thumb(span=6750) # mm
+    out = beam_design.check_design(span=6750,
+                                   width=width,
+                                   height=height,
+                                   point_load = 36e3,
+                                   distributed_load= 0,
+                                   fck=20,
+                                   fyk=500,
+                                   steel_dia=12,
+                                   n_bottom=3,
+                                   cover=25)
+
+    assert(out == pytest.approx(0.13647667348210732))
+
+
+if __name__ == "__main__":
+    test_beam_design()