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# Reinforced concrete integrated T-beam, girder, and 1-way slab calculator

Jonathan Ochshorn

An older reinforced concrete design calculator that computes required steel area for T-beams and 1-way slabs can be found here.

This calculator finds rebar sizes and spacing for beams, girders, and 1-way slabs for a particular type of reinforced concrete floor system consisting of a regular grid of columns supporting a hierarchical arrangement of girders, beams, and 1-way slabs for which "moment values" can be used. The beams and girders are assumed to be integral with the slabs and are designed as negative- and positive-moment T-beams. All dimensions and material properties are user-defined; the calculator computes steel bar sizes and spacing, while checking for "bar fit."

Directions: Enter values in the yellow fields. Scroll down to the bottom for some definitions and commentary. More detailed explanations and examples of reinforced concrete beam and slab design can be found in my text, available at no cost.

Note that the strength design method is used, per ACI-318-19 (2019 edition). Positive-moment T-beams where the compressive zone is not entirely within the "slab" portion of the T-beam (a very rare occurance) are not considered.

Figure 1. Moment value coefficients (denominators) for continuous beams and slabs, subject to the criteria outlined below. Image adapted from my text

1. The units for uniformly distributed design load, wu, are typically lb/ft or kips/ft (or equivalent metric units); the units for clear span, L, are feet (or equivalent metric units); and the resulting moment value, Mu is in ft-lb or ft-kips (or equivalent metric units) depending on the units chosen for the distributed load. These moment values are valid only for continuous reinforced concrete beams or slabs when the following conditions are met:

• Lengths of adjacent spans do not differ by more than 20%.

• The unfactored live load is less than or equal to 3 times the unfactored dead load.

2. The negative moment (at the face of support) can be taken as wuL2 / 12 for slabs with clear spans no greater than 10 ft, and for beams framing into relatively stiff columns (see text for details).

The user-controlled parameters in this calculator (shown in the yellow fields) are defined as follows:

• Units: the default values in the calculator are set in "imperial" (in-lb) units. If switched to SI (metric) units, all those default values must be adjusted.

• Beam centerline span: Even though the computation of moments is based on the clear span of beams and slabs, i.e., the distance from the face of supports, the span measured to the beam centerline is entered into the calculator.

• The girder centerline span is also entered into the calculator, while the beam's centerline spacing is automatically computed based on the number of girder divisions, i.e., the number of such beams framing into each girder. For example, if the centerline span of the girder is 30 feet on center and if beams frame into the girder at its third points, and if the beam stem width is 1 foot, then the beam's centerline spacing is 30 feet divided by 3 = 10 feet o.c. and the girder's clear span = 30 – 1 = 29 feet. This assumes that the width of the column, into which the girder actually frames, is close or equal to the dimension of the beam stem. In this example (and as illustrated by the yellow girder in Figure 1, the number of girder divisions would be entered as 3.

• Reinforced concrete weight: The dead load of the structure is assumed to consist of the weight of reinforced concrete itself plus any additional uniformly distributed dead load (e.g., partition allowances, mechanical ducts, finished flooring, and so forth). This weight is calculated based on the dimensions of beams, girders, and slabs. The default value of 150 pcf (or equivalent metric value) is a reasonable value for normalweight reinforced concrete.

• Live load reduction: Building codes typically allow the nominal live load to be reduced based on a probabilistically smaller unit live load on larger floor areas. The calculator automatically limits this reduction, when implemented, to beams and girders, and enables other constraints according to standard practice, e.g., that the maximum live load reduction is 50% and that live load reduction does not apply for live loads greater than 100 psf (or equivalent metric units).

• Moment values: For simply-supported beams, the moment-value denominator in the equation, Mwu = wuL2 / 8, is, of course, 8. For beams with fixed-fixed constraints, the maximum negative moment at the supports is wuL2 / 12 and the maximum positive moment at mid-span is wuL2 / 24, the sum of which is equal to wuL2 / 8. Ideally, perfectly regular continuous beams and slabs would have such "fixed-fixed" moments but, in real conditions with unpredictable loading patterns, both the negative and positive moments could be larger and, at non-fixed discontinuous locations, the negative moments could be smaller. The denominators shown in Figure 1 take these uncertainties into account, and can be used to design fairly regular multi-span, continuous reinforced concrete beams and slabs, subject to the conditions described above.

• Material strengths: At this time, only 60 ksi (414 MPa) rebars can be selected. Any reasonable value for the concrete cylinder strength, f'c can be entered (typical values are 300, 4000, or 5000 psi, or equivalent metric numbers).

• Maximum aggregate size: This is specified only to check the required spacing of rebars within the beam; only rebar choices that fit the beam (and allow aggregate to pass through the spaces between rebars) are accepted.

• Stirrup size: The assumed stirrup size for shear (diagonal tension) is specified only to check the required spacing of rebars within the beam. For the design of such stirrups (shear reinforcement, not included in this calculator), see my Reinforced Concrete Stirrup Spacing Calculator.

• Concrete cover: In this calculator, the length specified for "Slab rebar cover" or "beam/girder rebar cover" is measured from the face of the beam (or slab) to the centerline of reinforcement. This cover is required for fire resistance and to prevent corrosion of the reinforcement. For concrete not exposed to the weather, a value of 2.5 or 3 inches (or equivalent metric dimensions) for beams and 1 inch (or equivalent metric dimension) for slabs is usually sufficient. This is based on the actual requirement for concrete cover that is measured between the face of the rebar and the face of the beam of 1.5 inches (or equivalent metric dimension) for indoor beams and 0.75 inches (or equivalent metric dimension) for indoor slabs.

• Regular or bundled bars: If the required number of rebars does not fit within the beam stem dimension, it is possible to "bundle" the bars in pairs of two, each pair aligned vertically. In this case, the required concrete cover increases since it is measured from the face of the concrete beam to the centroid of the bundled bars, and so the effective depth gets a bit smaller. Always make sure that the "cover" specified is greater or equal to the required cover noted in the bar choice list. Bars can also be bundled in groups of 3 or 4, but this possibility has not yet been implemented in this calculator.