Joist Analysis Spreadsheet

 

Joist Analysis is a spreadsheet program written in MS-Excel for the purpose of analysis of steel joists considered as
simple-span beams subjected to virtually any type of loading configuration.  Specifically, beam end reactions as well
as the maximum moments and deflections are calculated.

Plots of both the shear and moment diagrams are produced, as well as a tabulation of the shear, moment, slope, and deflection for the joist span.

There are two worksheets for selecting K-series and LH-series joists, and 2 worksheets which are the SJI Standard Load Tables.

Program Assumptions and Limitations:
1.   For the “General Joist Analysis” worksheet, the following reference was used in the development of this program: “Modern Formulas for Statics and Dynamics, A Stress-and-Strain Approach” by Walter D. Pilkey and Pin Yu Chang, McGraw-Hill Book Company (1978), pages 11 to 21.
2.   The “General Joist Analysis” worksheet on the joist span will handle a full length uniform load and up to eight (8) partial uniform, triangular, or trapezoidal loads, up to fifteen (15) point loads, and up to four (4) applied moments.
3.   The “General Joist Analysis” worksheet will calculate the joist end vertical reactions, the maximum positive moment and negative moment (if applicable), and the maximum negative deflection and positive deflection (if applicable).  The calculated values for the end reactions and maximum moments and deflections are determined from dividing the joist into fifty (50) equal segments with fifty-one (51) points, and including all of the point load and applied moment locations as well.  (Note: the actual point of maximum moment occurs where the shear = 0, or passes through zero, while the actual point of maximum deflection is where the slope = 0.)
4.   In the “General Joist Analysis” worksheet the user is given the ability to input two (2) specific locations from the left end of the joist to calculate the shear, moment, slope, deflection, as well as the stress ratios for shear and moment.  This should be utilized when the maximum moment does not occur at the start or end of a segment.
5.   In the “General Joist Analysis” worksheet, the plots of the shear and moment diagrams as well as the displayed tabulation of shear, moment, slope, and deflection are based on the joist span being divided up into fifty (50) equal segments with-one (51) points.
6.   The “General Joist Analysis” worksheet will enable the user to either analyze an existing joist for new loads or determine the required total equivalent uniform load to be used to size a new joist.
7.   The “General Joist Analysis” worksheet only analyzes the joist “as a whole” and does not perform checks on the individual components.
8.   In the “General Joist Analysis” worksheet,  the deflections calculated include a 15% increase above the values calculated using traditional “simple-beam” flexure to more closely match actual test results obtained by SJI.
9.   For the “K-Joist Analysis” and “LH-Joist Analysis” worksheets, the Steel Joist Institute (SJI) Standard Load Table as well the “Recommended Code of Standard Practice for Steel Joists and Joist Girders” are used.  The Standard Load Tables are built into each of these two analysis worksheets.  The two worksheets will evaluate a user selected joist size, as well as display up to a maximum of 15 of the lightest joist sizes that are satisfactory for the loading and deflection criteria specified by the user.  The bridging requirements are also determined.
10.  This program contains numerous “comment boxes” which contain a wide variety of information including explanations of input or output items, equations used, data tables, etc.  (Note:  presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell.  Merely move the mouse pointer to the desired cell to view the contents of that particular “comment box”.)

Calculation Reference
AISC

Download Link

 

Light-weight Composite Beam Design Spreadsheet

 

Purpose of calculation: 
Consider a cantilever beam with a load applied at the free end. The applied load creates a bending moment which is a maximum at the fixed end, and a shear force along the length of the beam. In a sandwich panel these forces create tension in the upper skin and compression in the lower skin. The core spaces the facing skins and transfers shear between them to make the composite panel work as a homogeneous structure.
Calculation Reference
HexWeb SANDWICH DESIGN MANUAL

Calculation Validation
Reproduced result published in manual.

Calculation Procedure

The following face materials can be selected using a drop down combo box (you could also add your own).

• Epoxy UD CARBON tape (0°) 60% volume fraction
• Epoxy UD GLASS tape (0°) 55% volume fraction
• Epoxy WOVEN CARBON (G793-5HS) 55% volume fraction
• Epoxy WOVEN ARAMID (285K-4HS) 60% volume fraction
• Epoxy WOVEN GLASS (7781-8HS) 50% volume fraction
• Phenolic WOVEN GLASS (7781-8HS) 55% volume fraction
• ALUMINIUM Alloy 2024 T3
• ALUMINIUM Alloy 5251 H24
• ALUMINIUM Alloy 6061 T6
• STEEL carbon 1006
• STEEL carbon 1017
• Exterior PLYWOOD Fir
• Tempered HARDWOOD Teak

The following core materials can be selected using a drop down combo box (you could also add your own).

• 3003 Aluminium  29kg/m³
• 3003 Aluminium  37kg/m³
• 3003 Aluminium  42kg/m³
• 3003 Aluminium  54kg/m³
• 3003 Aluminium  59kg/m³
• 3003 Aluminium  83kg/m³
• 5052 Aluminium  37kg/m³
• 5052 Aluminium  50kg/m³
• 5052 Aluminium  54kg/m³
• 5052 Aluminium  72kg/m³
• 5052 Aluminium  83kg/m³
• 5052 Aluminium  127kg/m³
• 5052 Aluminium  130kg/m³
• 5056 Aluminium  37kg/m³
• 5056 Aluminium  50kg/m³
• 5056 Aluminium  50kg/m³
• 5056 Aluminium  72kg/m³
• HRH10 Nomex (Aramid) 29kg/m³
• HRH10 Nomex (Aramid) 32kg/m³
• HRH10 Nomex (Aramid) 32kg/m³
• HRH10 Nomex (Aramid) 48kg/m³
• HRH10 Nomex (Aramid) 48kg/m³
• HRH10 Nomex (Aramid) 64kg/m³
• HRH10 Nomex (Aramid) 64kg/m³
• HRH10 Nomex (Aramid) 80kg/m³
• HRH10 Nomex (Aramid) 96kg/m³
• HRH10 Nomex (Aramid) 123kg/m³
• HRH10 Nomex (Aramid) 144kg/m³

1) Determine Panel Properties

• Thickness of face material and core
• Young’s modulus of face and core
• Shear modulus of core
• Core allowable shear stress
• Core Cell size
• Poisson’s ratio of face
• Limiting stress in face
• Safety Factor
• Poisson’s ratio term
• Distance between face centres
• Critical intracell buckling stress
• Critical face wrinkling stress
• Allowable Tensile Stress on Face
• Panel stiffness coefficient

2) Beam Loading Assessment. The following beam loading conditions can be selected using a drop down combo box:

L1) Simple Support with Uniform Load Distribution
L2) Both Ends Fixed with Uniform Load Distribution
L3) Simple Support with Central Load
L4) Both Ends Fixed with Central Load
L5) Cantilever with Uniform Load Distribution
L6) Cantilever with Load at End
L7) Cantilever with Triangular Load Distribution

• Dimensions of panel
• max shear coefficient
• max bending moment coefficient
• bending deflection coefficient
• shear deflection coefficient
• Total load on beam
• Max bending moment
• Max face stress
• Max shear force
• Core shear stress
• Bending deflection
• Shear deflection
• Total deflection

3) Equivalent plate properties for use with finite element software
It is possible to use the following equivalent plate element properties to match stress and deflection with standard plate elements using finite element analysis software. This should only be done if you can assure that the following conditions are true:
Shear deflections are negligible compared to bending deflections.
Strength of core material is independently checked.

• Equivalent plate thickness for plate element.
• Equivalent Young’s modulus
• Check deflection (note that only deflection due to bending is calculated)

Calculation Reference
Composites Design

Download Link

Moving Loads Spreadsheet

 

Moving Loads Spreadsheet is an excel calculation to determine the loads in a span as a vehicle passes over it. The vehicle can have up to 10 axel loads making it suitable for the assessment of trains as well as wheeled vehicles.

The end supports of the span may be fixed, free, pinned or on rollers making this a very flexible tool for designers. The calculation produces a shear force, bending moment slope and deflection diagrams. Each diagram includes a summary table showing the maximum shear force, bending moment slope and deflection and the positions where they occur.

Using a scrollbar the vehicle can be dragged over the span and the diagrams instantaneously update. This interactive feature of the spreadsheet makes it very easy to understand the calculation. A second scrollbar can be used to interrogate the shear force, bending moment slope and deflection at any point along the span.

Calculation Reference
Structural Analysis

 

Download Link

 

Beam design including torsion spreadsheet

 

• Reinforced Concrete Design Analysis and Design for Torsion
• Torsional effects in reinforced concrete
• Torsion in plain concrete members
• Torsion in reinforced concrete members
• Combined shear and torsion

Download Link