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Calculation templates

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Beam Analysis Calculators

Beam Analysis using Macaulay's Theorem

Beam Analysis using Anastruct

2D Truss Analysis using OpenSeesPy

Column Buckling Calculator

Sample Project

Concrete Column P-M Diagram Calculator

Structural Engineering

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Structural Engineering Calculators

Concrete Rectangular Beam Calculator to ACI 318-19 (IMP)

Concrete Column P-M Diagram Calculator to ACI

Concrete Shear Wall to ACI 318

Concrete One-way Slab Designer to ACI318

Concrete Slab-on-grade Calculator to ACI 360R-10

Concrete Rectangular Spread Footing Designer to ACI

Purlin and Girts Size Calculator to AISI

Steel Beam and Column Designer to AISC 360

Composite Slab to ACI 318

Composite Beam to AISC 360

Wind Loading Calculator to ASCE 7-10

Design Response Spectrum to ASCE 7

Steel Baseplate Designer to AISC 360

CLT Properties Calculator to ANSI/APA PRG 320

Check out CalcTree's library of structural engineering calculations to North American building and design codes here.

Structural engineering calculations to North American codes and standards

This calculator follows the procedures and guidelines of the American Institute of Steel Construction (AISC) Specification of Structural.

Steel Beam and Column Designer to AISC

This calculator does wind loading analysis for buildings and structures. It is split into five sub-sections depending on application. For each, wind pressure coefficients and parameters are selected or calculated in order to compute the net design wind pressures. 

All calculations are performed in accordance with ASCE 7-10

. An updated revision, ASCE 7-22 exists. Any discrepancies between the two revisions are noted.

Wind Load (Any Height)

Wind Load (Low-Rise)

Wind Load (Wall Components & Cladding)

Wind Load (Roof Components & Cladding)

Wind Load (Open Building)

Buildings and their components must be designed to withstand code-specified wind loads. Wind load is the force exerted on a structure by the wind.

ASCE 7 provides methods for calculating the design wind pressure based on two categories of applications: the main 

 (MWFRS) or components and claddings (C&C).

The process to calculate the wind load involves:

❗The ground elevation factor, Ke is a new factor in ASCE 7-22. It is not considered in this calculator, though ASCE 7-22 permits Ke = 1 for all elevations and so the calculator is still valid. 

ASCE 7-10 provided two methods to calculate the design wind pressures: a simplified procedure and an analytical procedure. ASCE 7-22 has removed the simplified method. This calculator is based on the ASCE 7-10 analytical procedure that is still valid in ASCE 7-22.

ASCE 7-22 provides four separate chapters for determining the design wind pressures, based on application:

Wind loading analysis in all five sub-sections of this 

 involve the following input parameters. 

Program is based on Alex Tomanovich's "ASCE705W" program and modified by David Taylor and William Fultz. Version 2.4 (10/20/2015). Taken from https://www.steeltools.org/load.php.

Optimize Designs with Free-to-Use Wind Loading Calculator to ASCE 7-10. Try our online engineering tool for accurate results and efficient solutions.

Wind Loading Calculator to ASCE 7-10 - CalcTree

Free to Use slab thickness calculator to ACI 360R-10. Design Strong Foundations Easily. Calculate on-ground slab thickness now.

Concrete (RC) Slab-on-grade Calculator to ACI 360R-10

RC Rectangular Beam Calculator to ACI 318-19.

RC Rectangular Beam Calculator (Imperial Units) ACI 318-19

RC Rectangular Beam Calculator (IMP) ACI 318-19

Analyze rectangular spread footings to ACI standards on CalcTree. Free-to-Use engineering calculator. Get results now!

Rectangular Spread Footing Design Calculator

Rectangular Spread Footing Design to ACI

 by the CalcTree engineering team on August 1, 2024

Welcome to CalcTree's Purlin and girt design tool! You will be able to determine the member capacities for purlins and girts according to American Iron and Steel Institute (AISI) S100-16. The purlins are manufactured by AEP. For details on how to design purlins and girts, check out our design guide

All calculations are performed in accordance with AISI S100-16.

Use one of the following pages according to the purlin geometry. 

For details of how to design purlins and girts, check out our design guide

Here is a brief summary to get you up to speed:

Calculate and determine capacities for purlins & girts with on CalcTree. Free-to-use Purlin Size Calculator. Calculate now!

Purlin Size Calculator | Find Purlin and Girt Capacities

 by the CalcTree engineering team on June 27, 2024

This calculator allows the user to assess the structural integrity of simply supported one-way slabs. The calculation will verify the reinforcement needs for concrete slabs ensuring compliance with flexural design criteria. Additionally, it checks the shear capacity of the slabs, employing ultimate limit state design (ULS) methods. 

All calculations are performed in accordance with ACI 318-19.

Slabs are an important structural element in reinforced concrete (RC) structures. They are designed to provide resistance to external loads that cause shear forces and bending moments across their length. 

Concrete exhibits strength in compression but is relatively weak in tension. Therefore, reinforcement is incorporated to withstand the tensile stresses that arise when slabs are subjected to loads. In a simply supported slab, the tensile stresses primarily occur along the bottom of the section. Consequently, in theory, there is no necessity for top reinforcement.

Generally, the limit state checks for RC elements design include the following:

This calculator covers the first two checks - 

. Deflection, stability checks and crack control require a more detailed examination by the engineer.

The flexural (also referred to as 'bending' or 'moment') capacity of a slab cross-section is determined using the Rectangular Stress Block method. The stress distribution in concrete under bending is curved in reality, however, it can be converted to an equivalent rectangular stress block by the use of reduction factors shown in the following image.

Factor ka is not defined explicitly in the standards and must be computed via mechanics solving the equation Cc=T as shown:

The value of Beta is determined using ACI Table 22.2.2.4.3:

The ultimate flexural strength at critical sections should not be less than the minimum required strength in bending and by the minimum flexural reinforcement according to ACI Table 7.6.1.1:

A section will require compression reinforcement when the compressed concrete section is insufficient to balance the external moment. The maximum moment that concrete can balance is achieved when the maximum compression strain in concrete (0.003) is reached, and the minimum tensile strain in steel (0.005 for ductile failure) is maintained. This is deduced from the triangle relationship:

Once the reduction factor ϕ is determined from ACI Table 21.2.2, the reduced moment flexural capacity is thus given as:

The total shear capacity of a section (Vu) is the combination of the shear strength contributed by concrete (Vuc) and shear reinforcement (Vus), limited by Vu.max.:

Since slabs typically lack shear reinforcement, their capacity is assessed solely based on the contribution of concrete.

 In the presence of significant point loads on the slab, such as those from columns, the engineer should verify punching shear.

Contribution to Shear Strength from Concrete (Vuc)

For non-prestressed members, the concrete capacity is determined by ACI Table 22.5.5.1:

In this case, axial tension is neglected. 

The total shear capacity (Vu) is calculated below, with the reduction factor again taken from Table 21.2.1:

This calculation was built in collaboration with 

Free-to-Use RC Beam Design Calculator to AS3600 Standards. Streamline your engineering projects. Get started now for precise calculations!

Concrete Beam Calculator to AS3600

RC one way slab design to ACI318

This calculator performs the analysis and design of a reinforced concrete column. It takes applied axial, shear and moments for several load types and computes design loads for relevant load combinations. It plots these design loads on a P-M Interaction Diagram, to indicate if the design passes ULS requirements. This calculator uses imperial units and currently only accepts columns with a rectangular cross-section. 

Table

matplotImage (1)

matplotImage (2)

The above calculation is according to the following theory:

The concrete is fully fissured when the ultimate axial tensile strength is reached, rendering its contribution null. Therefore, the ultimate strength is attained when the reinforcement reaches its yield stress.

The distribution of strains in a section (a-a) for an immediate failure state assumes that plain sections remain plain and vary linearly with the distance 'c' from the neutral axis.

By ensuring the compatibility of strains, the strains experienced by the reinforcement at any location are identical to those exhibited by the surrounding concrete.

The summation of forces adheres to the internal axial force equilibrium, where 

 represents the ultimate axial strength force.

 Stands for the concrete compression force given by the Whitney equivalent rectangular stress distribution and:

The summation of internal flexural moments and forces originating from the centre of the span must be equal and opposite to the internal force 

In reinforced concrete columns, the concept of "balanced failure in flexo-compression" refers to a condition where the concrete in compression and the tensile reinforcement reach their limit states simultaneously. In this balanced state, the column is designed to maximize the utilization of both materials, ensuring an efficient use of concrete and steel.

Given the above equation, the P-M interaction diagram is crafted by varying the "c" values within the range of (0, h).

The Diagram shows all the possible combinations of P-M valid for the concrete column cross-section. 

Nonprestressed members with ties as transverse reinforcement:

ACI Reinforced Concrete Column P-M Diagram Calculator. Powered by a Python code, it provides P-M diagrams for structural column design.

Reinforced Concrete Columns to ACI318 design tool

ACI Rectangular Column P-M Diagram Calculator [IMP]

 
The spectral response acceleration parameters for earthquakes at short periods, 

, will be determined using the following equations:

To plot the design response spectrum, it is necessary to know the parameters that shape the spectrum using the following expressions:


 is the design spectral response acceleration, and 

 is the fundamental period of the structure.

Explanation and calculators for establishing an earthquake response spectrum to ASCE 7-16 and ASCE 7-22, for use in structural engineering.

Design Response Spectrum Calculation to ASCE 7-16 and ASCE 7-22

Analysis and design of composite slabs on metal decking for both the temporary case (construction loads) and permanent case.

Concrete Metal Deck Composite Slab to ACI 318

This calculator computes the flexural and shear capacity of a fully composite beam, which consists of W-shaped steel members and a concrete slab.

Composite Beam to 360-22 (16th Edition)

This calculator performs capacity checks for a concrete unbraced shear wall, checking axial, shear, in-plane bending and plots the interaction diagram

Concrete Unbraced Shear Wall to ACI 318-19

This steel base plate calculator checks against concrete crushing from a column in compression and provides the minimum required baseplate thickness. There are three types of calculations for different columns types: wide flange, tube and pipe.

All calculations are performed in accordance with:

Summary

Steel base plates are used to distribute the load of a column or other structural member to a concrete foundation and provide a connection for the anchor bolts between the column and concrete foundation. They are typically made of ASTM A36 steel, which is a mild steel with good weldability and formability. Base plates are also available in higher strength steels, such as ASTM A572 Grade 50, for applications where higher loads are expected. 

Generally, a column base plate is made with a plate and a minimum of four anchor rods. 

The column axial force is distributed from the column end to the column base in direct bearing. 

 outlines that in the absence of code regulations the allowable bearing strength for the limit state of concrete crushing can be taken with the safety factor of compression, Ωc = 2.31. The allowable bearing strength, Pp/Ωc is:

are to determine the critical base plate cantilever dimension, 

 which is used to calculate the minimum base plate thickness 

The critical base plate cantilever dimension, 

, determines the critical bending strength of the baseplate. The required strength (column axial force), Pa, is distributed from the column end to the column base plate in direct bearing. The column base plate is then assumed to distribute the column axial force to the concrete or masonry as a uniform bearing pressure by cantilevered bending of the plate. 

 are the minimum required dimensions, for width and depth respectively, for the base plate in order to prevent yielding of the baseplate or buckling of the anchor bolts. 

The minimum required thickness of the base plate, tmin is outlined in 

AISC Steel Construction Manual 14th ed. 14-6

The design variable dimensions are outlined in 

AISC Steel Construction Manual 14th ed 14-5  

[1] American Institute of Steel Construction. (2022). 

Specification for structural steel buildings

[2] American Institute of Steel Construction. (2011). 

This steel baseplate calculator checks against concrete crushing from a column in compression and provides the minimum required baseplate design.

Steel baseplate to AISC 360

This calculator computes geometric and strength properties of CLT panels based on the CLT grade and lay-up selected. Units are in the imperial system. Calculator is for use in the U.S.

All calculations are performed in accordance with

, the American National Standards Institute / American Plywood Association Standard for Performance-Rated Cross-Laminated Timber. 

CLT Grade

tp (2)

Vs,0 (1)

Cross Laminated Timber (CLT) is a prefabricated engineered wood product that consists of at least three layers of solid-sawn lumber. These adjacent layers are cross-oriented and bonded with a structural adhesive to form a solid wood element. It is used in construction for various purposes including structural supports, floors, and walls. 

ANSI/APA PRG 320 refers to out-of-plane bending and shear action as "flatwise", that is the bending and shear produced from transverse (aka perpendicular) loads.

Below, we'll present the equations used to calculate each key property of the CLT panel, as per ANSI/APA PRG 320.

Check out our full library of CalcTree templates 

This calculator computes geometric and strength properties of CLT panels based on the CLT grade and lay-up selected. Units are in the imperial system.

US

Concrete

Steel

Timber

Composite

Analysis