Beam Design Limits per ACI 318-19 with ideCAD
How does ideCAD control reinforced concrete beam design limits according to ACI 318-19?
Minimum beam depth is controlled automatically.
Deflection limits is controlled automatically.
Beam dimensions are determined by the user.
Notation
A_{g }= gross area of concrete section, in^{2}
b_{f } = effective flange width, in.
b_{w } = web width or diameter of circular section, in.
c_{1 } = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.
c_{2 } = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c_{1}, in.
E_{c }= modulus of elasticity of concrete, psi
E_{s }= modulus of elasticity of reinforcement, psi
f_{c}^{'}_{ }= specified compressive strength of concrete, psi
f_{y }= specified yield strength for nonprestressed reinforcement, psi
h _{ } = overall thickness, height, or depth of member, in.
l_{ } = span length of beam or one-way slab; clear projection of cantilever, in.
l_{n } = length of clear span measured face-to-face of supports, in.
P_{u}_{ }= factored axial force; to be taken as positive for compression and negative for tension, lb
s_{w} = clear distance between adjacent webs, in.
ϕ = strength reduction factor
Minimum beam depth
For nonprestressed beams, the limits of overall beam depth h are given in ACI Table 9.3.1.1.
Supoort condition | Minimum depth, h |
---|---|
Simply supported | l/16 |
One end continuous | l/18.5 |
Both ends continuous | l/21 |
Cantilever | l/8 |
The expressions in ACI Table 9.3.1.1 shall be multiplied by (0.4 + f_{y }/100,000) if reinforcement yield strength f_{y} is different than 60,000 psi.
Deflection limits
If nonprestressed beams do not satisfy ACI 9.3.1, immediate and time-dependent deflections are calculated according to ACI 24.2 and checked not to exceed the maximum values in ACI Table 24.2.2.
Member | Condition | Deflection to be considered | Deflection limitation | |
---|---|---|---|---|
Flat roofs | Not supporting or attached nonstructural elements likely to be damaged by large deflections Immediate deflection due to L | Immediate deflection due to maximum of L_{r}, S, and R | l/180 | |
Floors | l/360 | |||
Roof or Floors | Sıpporting or attached to nonstructural elements | Likely to be damaged by large deflections | That part of hte total deflection occurring after attachment of nonstructural elements, which is the sum of the time-dependent deflection due to all sustained loads and the immediate deflection due to any additional live load | l/480 |
Not likely to be damaged by large deflections | l/240 |
Reinforcement strain limit in beams
If P_{u}< 0.10f_{c}’A_{g} for nonprestressed beams, the strength reduction factor ϕ used for tension-controlled according to ACI Table 21.2.2.
Beams of Earthquake-Resistant Structures
Ordinary moment frames
All the design limits described above are valid for beams of ordinary moment frames.
According to ACI 18.3.2;
Beams should have a minimum of two continuous bars at the top and bottom faces.
The area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop f_{y} in tension at the face of support.
Intermediate moment frames
All the design limits described above are valid for beams of ordinary moment frames.
According to ACI 18.4.2.1;
Beams should have a minimum of two continuous bars at the top and bottom faces.
The area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop f_{y} in tension at the face of support.
According to ACI 18.4.2.2;
The positive moment strength at the face of the joint should be greater than one-third of the negative moment strength provided at that face of the joint.
Along the length of the beam, both the positive and the negative moment strength at any section should be greater than one-fifth of the maximum moment strength provided at the face of either joint.
Special moment frames
All the design limits described above are valid for beams of special moment frames. Beams of special moment frames shall frame into columns of special moment frames.
According to ACI 18.6.2.1, beams of special moment frames should satisfy the conditions given below;
The minimum clear span l_{n} should be 4d
Minimum width b_{w} should be lesser than 0.3h and 10 in.
The beam width projection beyond the supporting column's width on each side should be less than the smallest value of c_{2} and 0.75c_{1}.
According to ACI 18.6.3.2;
The positive moment strength at the face of the joint should be greater than one-half of the negative moment strength provided at that face of the joint.
Along the length of the beam, both the positive and the negative moment strength at any section should be greater than one-fourth of the maximum moment strength provided at the face of either joint.
Beams should have a minimum of two continuous bars at the top and bottom faces. Minimum reinforcement conditions are given in the Beam Reinforcement Limits per ACI 318-19 with ideCAD title.