Steel Beam Capacity Calculator

Easily design steel wide flange beams with this streamlined tool from efficalc. This powerful calculator provides a quick and verifiable way to determine the moment capacity of steel wide flange beams in accordance with the AISC 14th edition standards.

What you get:

Instant Results: Simply enter the load, span, and section size to receive an immediate and accurate design strength evaluation.
Detailed Calculation Report: Your calculation comes with a free professional-quality calculation report which details every calculation step, making it simple to review, verify, and submit in a design package.
Customization: You can change any part of these calculations and make it your own! Simply copy or save this template below and edit it in any way that suits your project.
Open Source: This calculator is 100% built with our open-source Python calculations library, efficalc. You can make your own calculations just like this on the website, or in a local Python environment and integrate them with your other Python workflows.

Designed with modern engineers in mind, efficalc will not only speed up your design process but also integrate seamlessly with today's automated and data-driven engineering environments.

We value your feedback and are always looking for ways to enhance our tools. Reach out to us with the contact button () to the right or at github.com/youandvern/efficalc/issues anytime!

Design your beam here:

Use the interactive form below to design your steel beam. View or print the calculation report using the icons in the "Results" section.

Assumptions

AISC 14th Edition controls design
Beam web is unstiffened
Beam design is not controlled by deflection requirements

Inputs

Description	Name	Value (units)
Beam ultimate moment demand	$𝑀 𝑢$	$𝑘 𝑖 𝑝 - 𝑓 𝑡$
Beam unbraced length	$𝐿 𝑏$	$𝑓 𝑡$
Beam section size	$𝑠 𝑒 𝑐 𝑡 𝑖 𝑜 𝑛$	W18X40
Steel yield strength	$𝐹 𝑦$	$𝑘 𝑠 𝑖$
Modulus of elasticity	$𝐸$	$𝑘 𝑠 𝑖$
Lateral-torsional buckling modification factor	$𝐶 𝑏$

Results

Design flexural strength of the section

$𝜙 𝑀 𝑛 = 69.74 k i p - f t$

$𝑀 𝑢 = 30 k i p - f t \leq 𝜙 𝑀 𝑛 = 69.74 k i p - f t$ OK

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Copy the efficalc code

Instead of cloning to your online efficalc templates, you can copy the calculation code below and run it with the open source efficalc library!

from efficalc import (
    PI,
    Assumption,
    Calculation,
    Comparison,
    ComparisonStatement,
    Heading,
    Input,
    Symbolic,
    TextBlock,
    Title,
    brackets,
    ft_to_in,
    minimum,
    sqrt,
)
from efficalc.sections import get_aisc_wide_flange


def calculation(chosen_section_name: str = None):
    Title("Steel Beam Moment Strength")

    TextBlock("Flexural design strength of a steel wide-flange beam section.")

    Heading("Assumptions", numbered=False)
    Assumption("AISC 14th Edition controls design")
    Assumption("Beam web is unstiffened")
    Assumption("Beam design is not controlled by deflection requirements")

    Heading("Inputs", numbered=False)

    Mu = Input("M_u", 30, "kip-ft", "Beam ultimate moment demand")
    Lbu = Input("L_b", 20, "ft", "Beam unbraced length")

    # Select a section size if one isn't provided as an input to the function
    section = (
        Input(
            "section",
            "W18X40",
            description="Beam section size",
            input_type="select",
            select_options=EFFICIENT_AISC_WIDE_FLANGE_BEAM_NAMES,
        )
        if chosen_section_name is None
        else None
    )

    Fy = Input("F_y", 50, "ksi", "Steel yield strength")
    Es = Input("E", 29000, "ksi", "Modulus of elasticity")

    Cb = Input(
        "C_b",
        1.0,
        "",
        "Lateral-torsional buckling modification factor",
        reference="AISC F1(3)",
    )

    # If a section size is provided as an input to the function, use that. Otherwise, use the section size selected
    # using the input object.
    Heading("Section Properties", numbered=False)
    if chosen_section_name:
        Symbolic("section", chosen_section_name, result_check=True)
    else:
        chosen_section_name = section.get_value()

    chosen_section_props = get_aisc_wide_flange(chosen_section_name)
    Sx = Calculation("S_x", chosen_section_props.Sx, "in^3")
    Zx = Calculation("Z_x", chosen_section_props.Zx, "in^3")
    ry = Calculation("r_{y}", chosen_section_props.ry, "in")
    rts = Calculation("r_{ts}", chosen_section_props.rts, "in")
    J = Calculation("J", chosen_section_props.J, "in^4")
    ho = Calculation("h_o", chosen_section_props.ho, "in")
    bf_2tf = Calculation("b_f/2t_f", chosen_section_props.bf_2tf, "")
    h_tw = Calculation("h/t_w", chosen_section_props.h_tw, "")

    Heading("Beam Flexural Capacity", head_level=1)
    Pb = Calculation(
        r"\phi_{b}", 0.9, "", "Flexural resistance factor", reference="AISC F1(1)"
    )

    Heading("Section Compactness", head_level=2)
    ypf = Calculation(
        r"\lambda_{pf}", 0.38 * sqrt(Es / Fy), "", reference="AISC Table B4.1b(10)"
    )
    Comparison(
        bf_2tf,
        "<=",
        ypf,
        true_message="CompactFlange",
        false_message="ERROR:NotCompactFlange",
        result_check=False,
    )

    ypw = Calculation(
        r"\lambda_{pw}", 3.76 * sqrt(Es / Fy), "", reference="AISC Table B4.1b(15)"
    )
    Comparison(
        h_tw,
        "<=",
        ypw,
        true_message="CompactWeb",
        false_message="ERROR:NotCompactWeb",
        result_check=False,
    )

    Heading("Plastic Moment Strength", head_level=2)
    Mp = Calculation(
        "M_{p}",
        Fy * Zx / ft_to_in,
        "kip-ft",
        "Nominal plastic moment strength",
        reference="AISC Eq. F2-1",
    )

    Heading("Yielding Strength", head_level=2)
    Mny = Calculation("M_{ny}", Mp, "kip-ft", reference="AISC Eq. F2-1")

    Heading("Lateral-Torsional Buckling", head_level=2)
    Lp = Calculation(
        "L_{p}", 1.76 * ry * sqrt(Es / Fy) / ft_to_in, "ft", reference="AISC Eq. F2-5"
    )
    cc = Calculation("c", 1.0, "", reference="AISC Eq. F2-8a")
    Lr = Calculation(
        "L_{r}",
        (1.95 * rts / ft_to_in * Es / (0.7 * Fy))
        * sqrt(
            J * cc / (Sx * ho)
            + sqrt((J * cc / (Sx * ho)) ** 2 + 6.76 * (0.7 * Fy / Es) ** 2)
        ),
        "ft",
        reference="AISC Eq. F2-6",
    )

    if Lbu.result() <= Lp.result():
        ComparisonStatement(Lbu, "<=", Lp)
        Mnl = Calculation(
            "M_{nltb}",
            Mp,
            "kip-ft",
            "The limit state of lateral-torsional buckling does not apply",
            reference="AISC F2.2(a)",
        )
    elif Lbu.result() > Lr.result():
        ComparisonStatement(Lbu, ">", Lr)
        Fcr = Calculation(
            "F_{cr}",
            Cb * PI ** 2 * Es / (Lbu * ft_to_in / rts) ** 2
            + sqrt(1 + 0.078 * J * cc / (Sx * ho) * (Lbu * ft_to_in / rts) ** 2),
            "ksi",
            reference="AISC Eq. F2-4",
        )
        Mncr = Calculation(
            "M_{ncr}", Fcr * Sx / ft_to_in, "kip-ft", reference="AISC F2.2(c)"
        )
        Mnl = Calculation(
            "M_{nltb}", minimum(Mncr, Mp), "kip-ft", reference="AISC Eq. F2-3"
        )
    else:
        ComparisonStatement(Lp, "<", Lbu, "<=", Lr)
        Mncr = Calculation(
            "M_{ncr}",
            Cb
            * brackets(
                Mp - brackets(Mp - 0.7 * Fy * Sx / ft_to_in) * (Lbu - Lp) / (Lr - Lp)
            ),
            "kip-ft",
            reference="AISC F2.2(b)",
        )
        Mnl = Calculation(
            "M_{nltb}", minimum(Mncr, Mp), "kip-ft", reference="AISC Eq. F2-2"
        )

    Heading("Controlling Strength", head_level=2)
    PMn = Calculation(
        r"\phi M_n",
        Pb * minimum(Mny, Mnl),
        "kip-ft",
        "Design flexural strength of the section",
        result_check=True,
    )
    Comparison(Mu, "<=", PMn)

    return {"design_strength": PMn.result(), "demand": Mu.get_value()}


# These are the W-Shapes Selection by Zx (AISC 14th edition Table 3-2)
EFFICIENT_AISC_WIDE_FLANGE_BEAM_NAMES = [
    "W40X167",
    "W40X149",
    "W36X160",
    "W36X135",
    "W33X141",
    "W33X130",
    "W33X118",
    "W30X116",
    "W30X108",
    "W30X99",
    "W30X90",
    "W27X84",
    "W24X84",
    "W24X76",
    "W24X68",
    "W24X62",
    "W24X55",
    "W21X68",
    "W21X62",
    "W21X55",
    "W21X50",
    "W21X48",
    "W21X44",
    "W18X55",
    "W18X40",
    "W18X35",
    "W16X40",
    "W16X31",
    "W16X26",
    "W14X34",
    "W14X30",
    "W14X26",
    "W14X22",
    "W12X26",
    "W12X22",
    "W12X19",
    "W12X16",
    "W12X14",
    "W10X22",
    "W10X19",
    "W10X12",
    "W8X10",
]

Note: you can make suggestions for improvements to this code at github.com/youandvern/efficalc/issues or by sending us a message with the contact button.

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Disclaimer: This calculator is provided as a free tool to assist professionals and does not offer any warranties or guarantees regarding its use or the results. All calculations and engineering decisions must be reviewed and approved by a licensed professional engineer who will take responsibility for their application. Efficalc and its affiliates disclaim any responsibility for the accuracy or adequacy of any design resulting from the use of this calculator. Users agree to indemnify and hold harmless Efficalc from any claims, damages, or liabilities that may arise from the use of this calculator or its outputs. This calculator is not a substitute for professional judgment.