R/SDM3FF.R

In sivarajahm/CEngineering: Tools/Functions for Civil and Water Resources Engineering

#' @title 3-Span Slope Deflection Method(Fixed-Fixed)
#'
#' @description This function computes the moments and the rotations using slope deflection method(SDM).
#'
#' @param LengthAB The length of span AB
#' @param LengthBC The length of span BC
#' @param LengthCD The length of span CD
#' @param Typeof1 The type of load(i.e., UDL/PL/TDLS/TDLE) on span AB
#' @param Typeof2 The type of load(i.e., UDL/PL/TDLS/TDLE) on span BC
#' @param Typeof3 The type of load(i.e., UDL/PL/TDLS/TDLE) on span CD
#' @param Magnitude1 The magnitude of the load on span AB
#' @param Magnitude2 The magnitude of the load on span BC
#' @param Magnitude3 The magnitude of the load on span CD
#' @param Pointof1 The point at  which the load is applied on span AB
#' @param Pointof2 The point at  which the load is applied on span BC
#' @param Pointof3 The point at  which the load is applied on span CD
#' @param EAB Young's Modulus(E) of span AB
#' @param EBC Young's Modulus(E) of span BC
#' @param ECD Young's Modulus(E) of span CD
#' @param IAB Inertia(second moment of area, I) of span AB
#' @param IBC Inertia(second moment of area, I) of span BC
#' @param ICD Inertia(second moment of area, I) of span CD
#'
#' @export
#' @details Given the span length, magnitude of load, type of load, point of action, Young's Modulus, and interia, the function computes the moments and the rotations using SDM.
#'
#' @note
#' The possible values for Typeof1, Typeof2, and Typeof3 are UDL/PL/TDLS/TDLE.\cr
#' UDL:Uniformly Distributed Load \cr
#' PL:Point Load\cr
#' TDLS:Triangular Distributed Load(the maximum value is at the start, see http://www.abzwater.com/sdm)\cr
#' TDLE:Triangular Distributed Load(the maximum value is at the end, see http://www.abzwater.com/sdm )\cr
#'
#' @return  Moments and Rotations
#'
#' @author \strong{Sivarajah Mylevaganam}
#'
#' @examples
#' Single load on a span (http://www.abzwater.com/sdm)
#' SDM3FF(8,4,8,"PL","UDL","PL",40,24,20,4,1,4,1,1,1,1,1,1)
#' SDM3FF(2,2,2,"UDL","UDL","UDL",40,40,40,1,1,1,1,1,1,1,1,1)
#' SDM3FF(2,2,2,"UDL","UDL","UDL",40,80,40,1,1,1,1,1,1,1,1,1)
#'
#'
#' Multiple load on a span(http://www.abzwater.com/sdm)
#' SDM3FF(5,10,5,"PL","PL","PL",0,40,0,1,3,1,1,1,1,1,1,1) + SDM3FF(5,10,5,"PL","PL","PL",0,40,0,1,7,1,1,1,1,1,1,1)
#'
#' Framed  Structure(http://www.abzwater.com/sdm)
#' SDM3FF(5,10,5,"PL","UDL","PL",0,5,0,1,1,1,1,1,1,1,1,1)
#'
#'
#'
#' @keywords Slope
#' @keywords Deflection
#' @keywords Structural
#' @keywords Civil
#' @keywords Engineering
#' @keywords Indeterminate
#'
#' @references (1) Wikipedia contributors. (2018, February 19). Slope deflection method. In Wikipedia, The Free Encyclopedia. Retrieved 09:17, March 26, 2018, from https://en.wikipedia.org/w/index.php?title=Slope_deflection_method&oldid=826540985
#' \cr
#' \cr
#' (2) Norris, Charles Head; John Benson Wilbur; Senol Utku (1976). Elementary Structural Analysis (3rd ed.). McGraw-Hill. pp. 313–326. ISBN 0-07-047256-4.
#' \cr
#' \cr
#' (3) McCormac, Jack C.; Nelson, James K. Jr. (1997). Structural Analysis: A Classical and Matrix Approach (2nd ed.). Addison-Wesley. pp. 430–451. ISBN 0-673-99753-7.
#' \cr
#' \cr
#'
#' @seealso
#' \link{SDM2FS}
#' \link{SDM2FSC}
#' \link{SDM2FF}
#'

SDM3FF=function(LengthAB,
                LengthBC,
                LengthCD,
                Typeof1,
                Typeof2,
                Typeof3,
                Magnitude1,
                Magnitude2,
                Magnitude3,
                Pointof1,
                Pointof2,
                Pointof3,
                EAB,EBC,ECD,IAB,IBC,ICD
) {
  FEMAB=0
  FEMBA=0
  FEMBC=0
  FEMCB=0
  FEMCD=0
  FEMDC=0

  ThetaA=0
  ThetaB=0
  ThetaC=0
  ThetaD=0

  if(Typeof1=="UDL")
  {
    FEMAB=-1*Magnitude1*(LengthAB^2)/12
    FEMBA=1*Magnitude1*(LengthAB^2)/12
  }else if(Typeof1=="PL"){
    FEMAB=-1*Magnitude1*Pointof1*((LengthAB-Pointof1)^2)/(LengthAB^2)
    FEMBA=1*Magnitude1*(LengthAB-Pointof1)*(Pointof1^2)/(LengthAB^2)
  }else if(Typeof1=="TDLS")
  {
    FEMAB=-1*Magnitude1*(LengthAB^2)/20
    FEMBA=1*Magnitude1*(LengthAB^2)/30
  }else if(Typeof1=="TDLE")
  {
    FEMAB=-1*Magnitude1*(LengthAB^2)/30
    FEMBA=1*Magnitude1*(LengthAB^2)/20
  }


  if(Typeof2=="UDL")
  {
    FEMBC=-1*Magnitude2*(LengthBC^2)/12
    FEMCB=1*Magnitude2*(LengthBC^2)/12
  }else if(Typeof2=="PL"){
    FEMBC=-1*Magnitude2*Pointof2*((LengthBC-Pointof2)^2)/(LengthBC^2)
    FEMCB=1*Magnitude2*(LengthBC-Pointof2)*(Pointof2^2)/(LengthBC^2)

  }else if(Typeof2=="TDLS")
  {
    FEMBC=-1*Magnitude2*(LengthBC^2)/20
    FEMCB=1*Magnitude2*(LengthBC^2)/30
  }else if(Typeof2=="TDLE")
  {
    FEMBC=-1*Magnitude2*(LengthBC^2)/30
    FEMCB=1*Magnitude2*(LengthBC^2)/20
  }


  if(Typeof3=="UDL")
  {
    FEMCD=-1*Magnitude3*(LengthCD^2)/12
    FEMDC=1*Magnitude3*(LengthCD^2)/12
  }else if(Typeof3=="PL"){
    FEMCD=-1*Magnitude3*Pointof3*((LengthCD-Pointof3)^2)/(LengthCD^2)
    FEMDC=1*Magnitude3*(LengthCD-Pointof3)*(Pointof3^2)/(LengthCD^2)

  }else if(Typeof3=="TDLS")
  {
    FEMCD=-1*Magnitude3*(LengthCD^2)/20
    FEMDC=1*Magnitude3*(LengthCD^2)/30
  }else if(Typeof3=="TDLE")
  {
    FEMCD=-1*Magnitude3*(LengthCD^2)/30
    FEMDC=1*Magnitude3*(LengthCD^2)/20
  }

  matrix1=matrix(c(4*EAB*IAB/LengthAB+4*EBC*IBC/LengthBC,
                   2*EBC*IBC/LengthBC,
                   2*EBC*IBC/LengthBC,
                   4*EBC*IBC/LengthBC+4*ECD*ICD/LengthCD),
                 nrow=2, byrow=TRUE)
  matrix1
  matrix2=matrix(c(-FEMBA-FEMBC,-FEMCB-FEMCD), nrow=2, byrow=TRUE)
  matrix2
  result=solve(matrix1,matrix2)
  result

  ThetaB=result[1]
  ThetaC=result[2]


  MAB=2*EAB*IAB/LengthAB*(2*ThetaA+ThetaB)+FEMAB
  MBA=2*EAB*IAB/LengthAB*(2*ThetaB+ThetaA)+FEMBA
  MBC=2*EBC*IBC/LengthBC*(2*ThetaB+ThetaC)+FEMBC
  MCB=2*EBC*IBC/LengthBC*(2*ThetaC+ThetaB)+FEMCB
  MCD=2*ECD*ICD/LengthCD*(2*ThetaC+ThetaD)+FEMCD
  MDC=2*ECD*ICD/LengthCD*(2*ThetaD+ThetaC)+FEMDC

  print(c("Fixed End Moment AB",FEMAB))
  print(c("Fixed End Moment BA",FEMBA))
  print(c("Fixed End Moment BC",FEMBC))
  print(c("Fixed End Moment CB",FEMCB))

  print(c("Fixed End Moment CD",FEMCD))
  print(c("Fixed End Moment DC",FEMDC))

  print(c("Moment AB",MAB))
  print(c("Moment BA",MBA))
  print(c("Moment BC",MBC))
  print(c("Moment CB",MCB))
  print(c("Moment CD",MCD))
  print(c("Moment DC",MDC))
  print(c("Theta B",ThetaB))
  print(c("Theta C",ThetaC))
}