buddyd16
commented
6 years ago Made an attempt to implement the switch to Simpson rule integration and calculation time increased exponentially. Test case was for an 8 span beam with patterned live loads and calc time was +/- 3.5 mins. vs. +/- 1 min. for current cum. trap. method. for a real world beam the accuracy gains are not worth the increased computation time. My take away from this is I really need to spend some time and do the real derivations for slope and deflection for point moments and start/end span moments. I would think getting into these derivations would also solve bug #1 .If anyone out there wants to weigh in with solutions please do....as on my end real world work is going to take priority over this personal project :(
Upon testing for short weak beams with extreme loads (1000 kips/ft, 1 ft long, E = 1 psi, I = 1 in^4) and extremely long weak beams (1000 ft, 1 kip/ft, , E = 1 psi, I = 1 in^4) the error from the cumulative trapezoidal integration utilized for the slope and deflection values becomes unacceptable. Initial testing indicates shifting to Simpson rule integration will lead to an acceptable level of error.
Cum Trap - Deflection @ right support - Value should be: 0 : Error,short/weak = -0.288 in (500 calculation stations) Error,long/weak = -500000.675 in (12000 calculation stations, 1 station per inch) Error,long/weak as steel = -0.01724 in (12000 calculation stations, 1 station per inch, E= 29000000 psi, I=1 in^4) Error,long/weak Concrete - 150 pcf, F'c = 2500 psi = -0.16495 in (12000 calculation stations, 1 station per inch, E= 3031243.56 psi, I=1 in^4)
Simpson - Deflection @ right support - Value should be: 0 : Error,short/weak = -0.001 in (500 calculation stations) Error,long/weak = -55.57 in (12000 calculation stations, 1 station per inch) Error,long/weak as steel = -0.000001916 in (12000 calculation stations, 1 station per inch, E= 29000000 psi, I=1 in^4) Error,long/weak Concrete - 150 pcf, F'c = 2500 psi = -0.00001833 in (12000 calculation stations, 1 station per inch, E= 3031243.56 psi, I=1 in^4)
Further implementing a method to identify point load application points and insert them as additional calculation stations will reduce error at those locations of abrupt diagram changes, should allow for the implementation of point moments which currently introduce unacceptable error into the slope and deflection values.
No eta on this implementation but it is being studied
Alternatively I can stop being a wimp and go thru the derivation of the real slope and deflection values for the general cases of pin-pin beam with moments at both ends with point load anywhere, variable partial UDL, and point moment and apply the principle of super position.