Beam Stability Program

v1.0	1/4/10
- program first released
v1.01	1/27/10
- changed Strength I Load Factor for Construction Load (finishing machine) to 1.5 from 1.25 .
v1.02   11/8/11
- added note to summarize program's intent  
v1.03	1/18/12
- deleted unit weight of concrete for deck pour
- revised recommended finishing machine weights
- added offset to application of live load
- added setting tolerance
- revised bearing pad rotational stiffness
- revised bracing coefficients and allowable number of braces and beams
- revised construction moments
- revised roll stability checks for braced beam
- revised overturning force equations
v2	7/1/13
- revised bearing pad stiffness calculation and failure angle based on bearing pad rollover
- revised girder pressure coefficients
- added worker platform loads and width and weight of overhang forms
- revised end bracing coefficient
- revised construction load equations
- added equations for maximum wind load and required bracing stiffness
- removed wind load from Strength I limit state calculations
- added Modulus of Elasticity correction factor
v2.1	12/2/13
- removed required brace stiffness section
v2.2	8/14/15
- added Excel data table input file with examples
- changed required Safety Factor against Wind to 4.0
- changed value of C in UF equation from 1.5 to 1.0 and factored wind pressure by 1.5
- changed equation for sweep to PCI recommendations times a user defined factor (1.4 typ.) 
- simplified the lateral beam bending coefficients for beams with interior bracing
- defined 3 specific beam stability stages
- incorporated tables from linked Excel files into Mathcad
- added vector variables instead of single values to present graphical results
- renamed variables, rearranged equations, and reformatted sections for clarity
 v2.3	11/18/16
- renamed load variables in Stage 3 and added a load graph for Stage 3.
- Changed Active Construction Wind Speed to 30 mph and reduced Safety Factor against Wind to 2.0 (changes offset each other)
- Removed Stage 2 wind speed as a variable, use 90 mph for all of Florida
- removed the user defined thermal factors for sweep and added a thermal sweep equation based on UF research.
- revised the equation for Co to account for thermal sweep (see UF Research Report BDV31-977-46).
v2.4	11/7/18
- corrected stage 3 moment of deck overhang DC load
- corrected the boundry conditions on the figures for determinining bracing loads. 
v3.0	11/01/23
- Added graphs for Factor of Safety against Rollover and Stability
- Added bridge skew as a new variable
- Updated Kz formula per AASHTO (Kz=1.0 for Service I) and included Wind Exposure Category D
- Updated the Strength III load factor for wind loads during construction from 1.25 to 1.0[SDG 2.4.3]. 
- Converted from Mathcad 15 to Prime 9.
v3.1	11/21/23
- Corrected an error in v3.0 only (K2 matrix for calculation of Stage 2 Strength III brace horizontal load) 