
2D Static's Load Modeler and Calculator Create 2D static's model and solve for reaction forces. 

Engineering, Design a, Manufacturing and Related Excel SpreadSheets Down Loads  Premium Membership Required 

2D Finite Element Analysis Spreadsheet Calculator Premium Membership Required 

Strain Gage Rosette Equations and Calculator applied to a specimen of a linear, isotropic material. 

ThreeElement Delta Rosette Strain Gage Equations and Calculator applied to a specimen of a linear, isotropic material. 

Stress Concentration Factors 

StressStrain Calculator and Plotted Curve Approximation using RambergOsgood Equation 

Vector Mechanics for Engineers, Statics and Dynamics Premium membership required. Mechanics can be defined as that science which describes and predicts
the conditions of rest or motion of bodies under the action of forces. It
is divided into three parts: mechanics of rigid bodies, mechanics of
deformable bodies, and mechanics of fluids. 

Adding Forces by the Parallelogram Resultant of Two Forces Equation and Calculator 

Adding Forces by the Parallelogram Resultant of Two Forces Equation and Calculator
Law of Cosines, "Cosine Rule" for a Parallelogram(nonright angle triangle) to calculate the resultant force vector 
























Cantilevered Pipe Connection Spreadsheet Calculator 

Curved Beam Stress and Deflection Design Spreadsheet Calculator 



Constant Cross Beam Section Shear, Stress Equations and Calculator Structural Beam Deflection, Shear and Stress Equations and calculator for a Beam supported One End Cantilevered with Partial Distributed Load 



Beam Stress, Defection and Slope supported One End Cantilevered with Reversed Tapered Load Structural Beam Deflection, Shear, Slope and Stress Equations and calculator for a Beam supported One End Cantilevered with Tapered Load. 

Deflection, Shear and Stress Equations and Calculator Cantilevered Beam with Limited Tapered Load Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End Cantilevered with Limited Tapered Load 

Cantilevered Beam Deflection, Shear and Stress Equations and Calculator Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End Cantilevered with Limited Tapered Load 

Shear and Stress Equations and calculator for a Beam Triangular Distributed Load Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Triangular Distributed Load 







Beam Stress Deflection Equations / Calculator with Fixed Ends Tapering Loading 




Calculator for a Beam supported One End, Pin Opposite End and Single Moment at End Applied Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Single Moment at End Applied


Beam supported One End, Pin Opposite End and Single Moment at Defined Center Location Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Single Moment at Defined Center Location 

Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load at End Deflection and Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load at End 

Stress Equations and Calculator for a Beam supported One End, , Cantilevered at Defined Location and Distributed Load Between Supports Shear, Deflection and Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Distributed Load Between Supports 

Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load Between Supports Shear, Deflection and Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load Between Supports 

Stress Equations and Calculator for a Beam Supported One End, Cantilevered at Defined Location and Single Moment Applied at End Stress Equations and Calculator for a Beam Supported One End, Cantilevered at Defined Location and Single Moment Applied at End 

Stress Equations and Calculator for a Beam Supported One End, Cantilevered at Defined Location and Uniform loading Applied Stress Equations and Calculator for a Beam Supported One End, Cantilevered at Defined Location and Uniform loading Applied 

Stress Deflection Equations and Calculator Beam Supported Uniform loading Applied on Cantilevered End Stress Deflection Equations and Calculator Beam Supported Uniform loading Applied on Cantilevered End 

Stress Deflection Equations and Calculator Beam Supported Uniform loading Applied Stress Deflection Equations and Calculator Beam Supported Uniform loading Applied 

Stress Deflection and Moment Equations and Calculator Beam Supported Uniform loading Applied Stress Deflection Moment Equations and Calculator Beam Supported Uniform loading Applied 





Beam Stress & Deflection Equations / Calculator Free and Guided on One End Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with bending moment applied 

Beam Stress & Deflection Equations / Calculator Moment Applied at Defined Location Beam Stress & Deflection Equations / Calculator Moment Applied at Defined Location 

Stress Deflection Moment Equations and Calculator Beam Supported Partial Uniform loading Applied Stress Deflection Moment Equations and Calculator Beam Supported Partial Uniform loading Applied 

Stress Deflection Moment Equations and Calculator Beam Supported Partial Distributed Uniform loading Applied Stress Deflection Moment Equations and Calculator Beam Supported Partial Distributed Uniform loading Applied 

Stress Deflection Moment Equations and Calculator Beam Supported Tapering Load Applied Stress Deflection Moment Equations and Calculator Beam Supported Tapering Load Applied 

Stress Deflection Strain Equations and Calculator Beam Supported Tapering Load Applied Stress Deflection Strain Equations and Calculator Beam Supported Tapering Load Applied 

Stress Deflection Moment Equations and Calculator Beam Supported Partial Tapering Load Applied Stress Deflection Moment Equations and Calculator Beam Supported Partial Tapering Load Applied 

Stress Deflection Strain Moment Equations and Calculator Beam Supported Partial Tapering Load Applied Stress Strain Deflection Moment Equations and Calculator Beam Supported Partial Tapering Load Applied 













Beam Stress Deflection Equations / Calculator with Partial Uniform Loading Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Partial Uniform Loading. 

Beam Stress Deflection Equations / Calculator with Partial Tapering Loading Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Partial Tapering Loading. 

Beam Stress Deflection Equations / Calculator with Fixed Ends Tapering Loading Beam Stress Deflection Equations / Calculator with Fixed Ends Tapering Loading 

Beam Stress Deflection Equations / Calculator with Fixed Ends Moment Applied Beam Stress Deflection Equations / Calculator with Fixed Ends Moment Applied 





Area Moment Methods to Calculate Deflection in Beams No Calculator! Calculation of deflections and redundant reactions for beams on two supports can be made by the use of the areamoment method. 

Beam Parabolic Deflection Equation Calculator with Variable Shape Fixed End Single Concentrated Force Applied 

Beam Stress Deflection Equations Calculator Triangular Shape Fixed End Single Concentrated Force Applied 

Beam Cubic Parabola Shape Deflection Equation Calculator with Variable Shape Fixed End Single Concentrated Force Applied 

Flexural Strengthening of Reinforced Concrete Beam with FRP Laminates Spreadsheet Calculator 

Shear Strengthening of Tbeam with FRP Spreadsheet Calculator 

RC Shear Wall Analysis and Design Spreadsheet Calculator 

Base plate with Large Moment to AISC LRFD Spreadsheet Calculator 

Combined Stress Circular Cantilever Beam in Direct Compression and Bending Stress Equations and Calculator Circular Cantilever Beam in Direct Compression. For every calculated normal stress there is a corresponding induced shear stress; the value of the shear stress is equal to half that of the normal stress. 



Beam in Direct Compression and Bending Stress Equations and Calculator Circular Cantilever Beam in Direct Compression and Bending Equations and Calculator 



Combined Loading on Circular Beam or Shaft in Direct Compression and Bending Stress Equation and Calculator Combined Loading on Circular Beam or Shaft in Direct Compression and Bending Equation and Calculator 



















Concentrated Load on the Horizontal Member Elastic Frame Equations and Calculator 

Distributed Load on the Horizontal Member Elastic Frame Deflections Equations and Calculator 

Frame Deflections with Concentrated Moment Applied on Horizontal Member Equations and Calculator 

Frame Deflections with Concentrated Angular Displacement Applied on Horizontal Member Calculator 

Frame Deflections with Concentrated Lateral Displacement Applied on Horizontal Member Equations and Calculator 

Frame Deflections with Concentrated Load Applied to Vertical Member Equations and Calculator 

Frame Deflections with Distributed Load Applied to Left Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Moment Applied to Left Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Angular Displacement Applied to Left Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Lateral Displacement Applied to Left Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Load Applied to Right Vertical Member Equations and Calculator 

Frame Deflections with Distributed Load Applied to Right Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Moment Applied to Right Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Angular Displacement Applied Right Vertical Member Equations and Calculator 

Frame Deflections with Concentrated Lateral Displacement Applied Right Vertical Member Equations and Calculator 

Frame Deflections with Uniform Temperature Rise Equations and Calculator 

Frame Deflections with Uniform Temperature Differential Between Outside and Inside Equations and Calculator 

Frame Deflections with Concentrated Load on the Horizontal Member Equations and Calculator. Left vertical member guided horizontally, right end pinned. 

Distributed Load Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Concentrated Moment on the Horizontal Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Concentrated Angular Displacement on the Horizontal Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Concentrated Lateral Displacement on the Horizontal Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Concentrated load on the Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Distributed Load on the Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator 

Concentrated Moment on the Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator 

Concentrated Angular Displacement on Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator 

Concentrated Lateral Displacement on Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Concentrated Load on Right Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator. 

Reaction and deflection formulas for inplane loading of elastic frame with mounting ends fixed formulas and calculator. Roark's Formulas for Stress and Strain, Seventh Edition, Table 8.2 reference loading number 5a. 





















Reaction and deflection formulas for inplane loading of elastic frame with mounting ends fixed and distributed load on the right vertical member formulas and calculator. Roark's Formulas for Stress and Strain, Seventh Edition, Table 8.2 reference loading number 5L. 





Structural Shapes Moment Connections Design Spreadsheet Calculator 

Stress from Drop Load of Beam Supported on Both Ends and Struck in the Center. 



Stress from Drop Load of Beam Fixed on Both Ends and Struck at Center Equations and Calculator. 

Curved Beam Design Spreadsheet Calculator Excel spreadsheet analysis  premium membership required 

Capacity of Standard Universal Beams According to BS5950 Spreadsheet Calculator  premium membership required 

Aircraft Airframe Structural Design Premium Membership Required to view Document/Book 

Design and Analysis of Leaf Springs using FEA Approach This is a general study the design and analysis of leaf spring. 

Flat spring supported on both ends design equations and calculator 

Flat spring cantilevered design equations and calculator 

Flat spring cantilevered design triangular geometry equations and calculator 

Tapered Flat spring cantilevered design equations and calculator 

Circular Composite Beams and Columns Design Spreadsheet Calculator 

Composite Rectangular Beam and Columns Spreadsheet Calculator 

Cored Laminate Composite Stiffness Calculator Here also are discussed the effects of facing and core stiffness on sandwich bending stiffness so that the degree of approximation implied by simplified formulas neglecting facing and core stiffness is known. 





KSeries Joist Deflection and Stress Analysis Calculator KSeries Joists Specifications
Designations: 8K1 to 30K12
Depths: 8 to 30 in.
Standard Seat Depth (Height): 2.5 in.
Span Range: 8 to 60 ft.
ASD Load Range: 127 to 550 plf
LRFD Load Range: 190 to 825 plf
Maximum Span/Depth Ratio: 24 



Monolithic Corbels and Brackets According To ACI 318  99 Spreadsheet Calculator 

Staircase Analysis and Design Spreadsheet Calculator 

Slab Canopy Design Spreadsheet Calculator 

Lifting Boom, Davits Application and Design Equations
Davits refer to single mechanical arms with a winch for lowering and raising objects. A davit is commonly used system designed to lower an emergency lifeboat from a ship to the embarkation level to be boarded. 

Tension Compression Machine Feature Equation and Calculator 





SingleSpan Beam Deflection for Simple, Propped, Fixed or Cantilever Beams.  Include Shear and Moment Diagram.
NOTE: Large web page that opens in popup window. 
 
 



Flat Plate Deflection & Stress Calculator Assumptions:
The plate is flat, of uniform thickness, and of homogeneous isotropic material;
the thickness is not more than about one quarter of the least transverse dimension, and the maximum deflection
is not more than about onehalf the thickness; 





Honeycomb Beam & Panel Calculations Spreadsheet Calculator 













Eccentric Loads on Bolt Groups for Two Vertical Rows of Bolts Fixed Separation of 8" Based on the Instantaneous Center of Rotation Method and Alternate Method 2 Using Table XII from AISC 9th Ed. Manual (ASD)  page 463 . Vertical Row Bolt Spacing at 8 " 

Eccentric Loads on Bolt Groups for Two Vertical Rows of Bolts Bolt group instantaneous center analysis for three vertical rows spaced at 3 " spacing 

Eccentric Loads on Bolt Groups for Two Vertical Rows of Bolts Bolt group instantaneous center analysis for three vertical rows spaced at 6" spacing 

Structural Eccentric Loading on Bolt Group  For Two Vertical Rows Calculator Fixed Vertical Separation of 51/2 " Based on the Instantaneous Center of Rotation Method and Alternate Method 2 Using Table XII from AISC 9th Ed. Manual (ASD)  page 463 



SingleRiveted LapJoint Formulas for Stress and Strength Design Equations and Calculator. 

DoubleRiveted LapJoint Formulas and Calculator for Stress and Strength Design 

SingleRiveted LapJoint with Inside Cover Plate Formulas and Calculator for Stress and Strength Design 

DoubleRiveted LapJoint with Inside Cover Plate Formulas and Calculator for Stress and Strength Design. 

DoubleRiveted Butt Joint Plate Formulas and Calculator for Stress and Strength Design 

TripleRiveted Butt Joint Plate Formulas and Calculator for Stress and Strength Design 

Collar Bolt Flange Pressure Vessel Spreadsheet Calculator 

Ideal Pinned Column Buckling Calculator When a column buckles, it maintains its deflected shape after the application of the critical load. In most applications, the critical load is usually regarded as the maximum load sustainable by the column. 

Column Loading and Elastic Stability Formulae and Calculator Stepped straight bar under end load P and intermediate load P_{2}; upper end free, lower end fixed. 

Column Loading and Elastic Stability Formulae and Calculator Case 1b Stepped straight bar under end load P_{1} and intermediate load P_{2}; both ends pinned 











Column Loading and Elastic Stability Formulae and Calculator Case 2c Stepped straight bar under tensile end load P1 and intermediate load P2; upper end guided, lower end fixed. 

Column Loading and Elastic Stability Formulae and Calculator Case 2d Stepped straight bar under tensile end load P1 and intermediate load P2; upper end pinned, lower end fixed. 

Column Loading and Elastic Stability Formulae and Calculator Case 2e. Stepped straight bar under tensile end load P1 and intermediate load P2; both ends fixed 

Column Loading and Elastic Stability Formulae and Calculator Case 3a1 Uniform straight bar under end load P and a uniformly distributed load p over a lower portion of the length; several end conditions. Upper end free, lower end fixed. 







Column Loading and Elastic Stability Formulae and Calculator Case 3B1. Uniform straight bar under end load P and a uniformly distributed load p over an upper portion of the length; several end conditions Upper end free, lower end fixed. 





Column Loading and Elastic Stability Formulae and Calculator Case 3B4. Uniform straight bar under end load P and a uniformly distributed load p over an upper portion of the length; both ends fixed. 



Column Loading and Elastic Stability Formulae and Calculator Case 3C2. Stepped straight bar under end load P and a distributed load of maximum value p at the bottom linearly decreasing to zero at a distance a from the bottom Both ends pinned. 







Torsional Deformation and Stress Solid Circular Section Equations and Calculator 

Torsional Deformation and Stress Solid Elliptical Section Equations and Calculator 

Solid Square Section Torsional Deformation and Stress Calculator and Equations 

Torsional Deformation and Stress Solid Rectangular Section Equations and Calculator 

Torsion Deformation and Stress Hollow Rectangle Thin Wall Tube Section Equations and Calculator 

Torsional Deformation and Stress Solid Triangular Section Equations and Calculator 

Torsional Deformation and Stress Solid Isosceles Triangle Section Equations and Calculator 

Torsional Deformation and Stress Solid Circular Segmental Section Equations and Calculator 

Torsional Deformation and Stress Circular Segmental Section Equations and Calculator 

Torsional Deformation and Stress Circular shaft with opposite sides flattened Equations and Calculator. 

Torsional Deformation and Stress Concentric Circular Section Equations and Calculator. Torsional deflection and stress of a pipe. 

Torsional Deformation and Stress Eccentric Hollow Circular Section Equations and Calculator 

Torsional Deformation and Stress Hollow Elliptical Section Equations and Calculator 

Torsional Deformation and Stress Elliptical Hollow thinwalled section of uniform thickness Equations and Calculator 

Torsional Deformation and Stress Thin Circular Open Tube of Uniform Thickness Section Equations and Calculator 

Torsional Deformation and Stress Any Thin Open Tube of Uniform Thickness Calculator 

Torsion Applied Deformation and Stress of any elongated section with axis of symmetry OX; Equations and Calculator 

Torque Applied Deformation and Stress of a Trapezoid Equations and Calculator 

Torque Applied Deformation and Stress of a TSection Equations and Calculator 

Torque Applied Deformation and Stress of a LSection Equations and Calculator 

Torque Applied Deformation and Stress of a I Beam Section Equations and Calculator 

Torque Applied Deformation and Stress of a C Beam Section Calculator 

Torque Applied Deformation and Stress of a Shaft with Keyway Equations and Calculator 

Torque Applied Deformation and Stress of a Shaft with Two Keyways Equations and Calculator 

Torque Applied Deformation and Stress of a Shaft with Four Keyways Equations and Calculator 

Torque Applied Deformation and Stress of a Shaft with One Spline Equations and Calculator 

Torque Applied Deformation and Stress of a Shaft with Two Splines Equations and Calculator 

Torque Applied Deformation and Stress of a Shaft with Four Splines Equations and Calculator 

Torque Applied Deformation and Stress of a Pinned Shaft Equations and Calculator 

Torque Applied Deformation and Stress of a Two Grooved Pinned Shaft Equations and Calculator 

Torque Applied Deformation and Stress of a Four Grooved Pinned Shaft Equations and Calculator 

Torsional Deformation and Stress of a Cross Shaft Equations and Calculator 



Pipe Stress due to Clamping Force Spreadsheet Calculator
This spreadsheet calculates the a variety of resultant engineering requirements per. Roark's Formulas for Stress and Strain, 7th edition, Table 9.2 Case 1, Pressure Vessel Design Manual, 3rd Edition, ASME B31.12006 

Thin Wall Pressure Vessel Hoop Stress Hoop stress is twice that of the longitudinal stress for a thin wall pressure vessel. Therefore, the Hoop stress should be the driving design stress. 



Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator.
Loading W applied at 180° through center of circular section 



Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #3.
Loading moment applied M_{o }at θ relative to x angle. Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #3.
Formulas for moments, loads, and deformations and some selected numerical values. 



Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #5.
Loading W at θ relative to AC Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #5. 



Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #7. Ring under any number of equal radial forces equally spaced. Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #7.
Formulas for moments, loads, and deformations and some selected numerical values. 





Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #10 Per. Roark's Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #10.
Formulas for moments, loads, and deformations and some selected numerical values.


Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #11. Per. Roark's Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #11. Formulas for moments, loads, and deformations and some selected numerical values. 





Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #14. Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms #14. Formulas for moments, loads, and deformations and some selected numerical values. 

Circular Ring Analysis No 15 Roarks Formulas for Stress and Strain Equations and Calculator Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms Formulas for moments, loads, and deformations and some selected numerical values. 

Circular Ring Analysis No 16 Roarks Formulas for Stress and Strain Equations and Calculator. Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms.
Formulas for moments, loads, and deformations and some selected numerical values.
Unit axial segment of pipe filled with liquid of weight per unit volume ρ and supported at the base. 

Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #17. Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms. Formulas for moments, loads, and deformations and some selected numerical values. Unit axial segment of pipe partly filled with liquid of weight per unit volume ρ and supported at the base. 

Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #18 Per. Roark's Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms. Formulas for moments, loads, and deformations and some selected numerical values. 



Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #20. Per. Roark's Formulas for Stress and Strain Formulas Section 9, Reference, loading, and load terms #20. Bulkhead or supporting ring in pipe, supported at bottom and carrying total load W transferred by tangential shear v distributed as shown. 

Circular Ring Moment, Hoop Load, and Radial Shear Equations and Calculator #21 Per. Roarks Formulas for Stress and Strain Formulas for Circular Rings Section 9, Reference, loading, and load terms. Formulas for moments, loads, and deformations and some selected numerical values. Ring rotating at angular rate ω rad/s about an axis perpendicular to the plane of the ring. Note the requirement of symmetry of the cross section. 



Punching Shear/Conductor Modification Analysis 



The Shaft Design Book (Design Charts and Calculations for Torsional Properties of NonCircular Shafts) Premium Membership Required 



Dowel Pin Design Length Shear Stress and Contact Pressure Check Equations and Calculator 





Bolt Elongation Equation and Calculator while under Axial Stress 

Method and Equations of Analysis BS449: Part 2 

Bearing Strength of a Pin in a Drilled Hole Spreadsheet Calculator 

Analysis of Stress and Deformation,
George W. Housner,
Thad Vreeland, Jr.,
Division of Engineering and Applied Science, California Institute
447 Pages Premium Membership Required 

Stress Concentration Factors for Flat Plates and Cylinders: In a structure or machine part having a notch or any abrupt change in cross section, the maximum stress will occur at this location and will be greater than the stress calculated by elementary formulas based upon simplified assumptions as to the stress distribution. 

Channel Section with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #1a.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

CSection with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #2 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 



Twin Channel With Flanges Inward Section with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #4 of 1a Loading. Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

Twin Channel With Flanges Outward Section with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #5 of 1a Loading. Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

Wide Flange with Equal Flanges Section with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #6 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. 

Wide Flange Beam with Unequal Flanges Section with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #7 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

ZSection Flange Beam with Concentrated Intermediate Torsional Loading Applied Deflection and Stress Equations and Calculator #8 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

Segment of a Circular Tube Beam with Concentrated Intermediate Torsional Loading Applied Deflection and Stress Equations and Calculator #9 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2, Row 9. 

Missing Segment Rectangular Tube Section with Concentrated Intermediate Torsional Loading Applied Deflection and Stress Equations and Calculator #10 of 1a Loading. Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2, Row 10. 

Double Y Section with Concentrated Intermediate Torsional Loading Applied Deflection and Stress Equations and Calculator #11 of 1a Loading.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roark's Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2, Row 11. 

Channel Section with Left end free to twist and warp right end fixed (no twist or warp) Deflection and Stress Equations and Calculator.
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading. Per. Roark's Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2, Loading Configuration 1b. 

CSection with Concentrated Intermediate Torque applied Deflection and Stress Equations and Calculator #2 of 1b Loading .
Formulas for the elastic deformations of uniform thinwalled open members under torsional loading.
Per. Roarks Formulas for Stress and Strain  Formulas for torsional properties and stresses in thinwalled open cross sections, Table 10.2. 

Stress Analysis Manual Premium Membership Required 

Beam Deflection and Stress Excel Spreadsheet Calculator  Premium (annual) membership required 

Double Integration Method for Beam Deflections Overview
The Double Integration Method, also known as Macaulay’s Method is a powerful tool in solving deflection and slope of a beam at any point 

Double Integration Method Example 1 Simply Supported Beam with Concentrated Load at Mid Span 

Double Integration Method Example 3 Proof Cantilevered Beam of Length L with Variable Increasing Load to ω_{o} at free end. 





Deflection and Stresses in Uniformly Loaded, Simply Supported, Rectangular Sandwich plate  Premium membership required 

Bending of a Circular Sandwich Plate by Load Applied Through an Insert  Premium membership required 

Metal Fatigue Engineering Analysis Excel Spreadsheet Calculator Note: Accessing this resource requires an active Premium Annual Membership with Engineers Edge 