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Dezi et. al (2010)
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Projectile motion
Verified by the CalcTree engineering team on June 27, 2024
This calculator performs the analysis and design of a reinforced concrete beam. It takes applied axial, shear and moments for several load types and checks all ULS and SLS load combinations to identify the critical design loads. It then checks the design loads against the moment and shear capacities, deflection limits and also checks the minimum depth, cover and reinforcement required. This calculator uses imperial units.
All calculations are performed in accordance with ACI 318-19 and ASCE7-22.
Code Calculation
Materials
Concrete
f'c
:{"mathjs":"Unit","value":4000.0000000000005,"unit":"psi","fixPrefix":false}
Ec
:3604996.5325919534Reinforcement
fy
:{"mathjs":"Unit","value":60000.00000000001,"unit":"psi","fixPrefix":false}
Es
:{"mathjs":"Unit","value":29000000,"unit":"psi","fixPrefix":false}
n
:8 psiWhere:
- is the specified compressive strength of concrete in psi
- is the specified strength for non-prestressed reinforcement in psi
- (19.2.2.1.b) is the Modulus of Elasticity for the concretef'c:{"mathjs":"Unit","value":4000.0000000000005,"unit":"psi","fixPrefix":false}
- is the Modulus of Elasticity for the reinforcement in psi.
- is the modular factor, expressed asn:8.0 psi
Cross Section
Loads
Elastic Deflections
Flexural Strength
The flexural strength of the beam is calculated according to the standard literature for prismatic and simple reinforced beams. The
factor of 0.90 corresponds to the established in the ACI318-19; it can be changed according to the necessity of the user.
φf
:0.9
Mn, Bot
:242.53681730479084
φMn, Bot
:218.2831355743119
Mn,Top
:24.0750032188715
φMn,Top
:21.66750289698435Shear strength
The
factor of 0.75 corresponds to the established in the ACI318-19; it can be changed according to the necessity of the user. 22.5.1.1
Nominal one-way shear strength at a section
φs
:0.75
(22.5.1.1)
Vn1
:49.852389621235396
Vn2
:49.852389621235396
φVn,1
:37.38929221592655
φVn,2
:37.38929221592655
Notice that two Shear Strengths are calculated in each section, each corresponding to the different spacings used in the beam.
Concrete Ultimate Design Shear
Vc1
:13.922724616984
Vc2
:13.922724616984Vc shall not be taken greater than:
(22.5.5.1.1)
Vc,max+
:96.0146554568624
Vc,max-
:97.1214526379213For nonprestressed members, Vc shall be calculated by Table 22.5.5.1:
A complete revision for each load combination was made for the following calculation. The final value is taken as the minimum calculated value in the table below. Finally, the
condition can be checked in the code revision.
Vc_22.5.5.1-1
:13.922724616984
Vc_22.5.5.1-2
:13.922724616984
1.4D | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+1.6L+0.5Lr | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+1.6L+0.5S | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+1.6L+0.5R | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6Lr+1.0L | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6S+1.0L | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6R+1.0L | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6Lr+0.5W | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6S+0.5W | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.6R+0.5W | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.0W+ 1.0L+0.5Lr | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.0W+ 1.0L+0.5S | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.0W+ 1.0L+0.5R | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
1.2D+ 1.0E+ 1.0L + 0.2S | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
0.9D+ 1.0W | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
0.9D+ 1.0E | 0.00 kips | 38.41 kips | 38.85 kips | 30.62 kips | 13.92 kips | 24.33 kips | 11.02 kips |
Transverse Reinforcement Ultimate Design Shear
(22.5.8.5.3)
Vs1
:35.9296650042514
Vs2
:35.9296650042514
Effective Deflection
Beam Properties
Geometry
Reinforcement
Design Check
In the following tables, the "Check" condition corresponds to a failure of accomplishment in the checked state.
Minimum Depth and Cover
Strength
Max/Min
1.2D+1.6L+0.5Lr | 0.79 kips | 10.70 kips-ft | 0.49 | N/A | 0.02 | 0.02 | 0.04 | OK | ||
1.2D+1.6L+0.5Lr | 0.79 kips | 10.70 kips-ft | 0.49 | N/A | 0.02 | 0.02 | 0.04 | OK | ||
0.9D+ 1.0W | 0.14 kips | 1.01 kips-ft | 0.05 | N/A | 0 | 0 | 0.01 | OK | ||
0.9D+ 1.0W | 0.14 kips | 1.01 kips-ft | 0.05 | N/A | 0 | 0 | 0.01 | OK |
Ultimate Combinations
Minimum Reinforcement
Deflection Checks
The following deflections and deflection limits were calculated according to table 24.2.2 of ACI 318-19. The deflection limit can be changed in the table below according to the actual case for the current calculation.
1.50 in | 1.00 in | Check | ||
4.10 in | 0.75 in | Check |
Where "Check" means the beam isn't accomplishing the code requirements.
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