//first find deformations due to end rotation and translation 

			var ldxSt = dxSt * c + dySt * s; //start and end displacements in local coordinates
			var ldySt = -dxSt * s + dySt * c;
			var ldxEnd = dxEnd * c + dyEnd * s;
			var ldyEnd = -dxEnd * s + dyEnd * c;

			//FOR HINGED MEMBERS, MUST ADJUST END ROTATIONS!!!
			if (this.hingeSt>0){rotSt=0} //adjust rotation for hinges!
			else(rotSt=drSt);
			if (this.hingeEnd>0){rotEnd=0}
			else(rotEnd=drEnd);
			
			var defl=new Array();
			
			var x=0;
				// - use shape function: http://www.eng.fsu.edu/~chandra/courses/eml4536/
			for (var i = 0; i <= lens.length-1; i++){ 		
				x=lens[i];
				defl[i]=(1-3*x*x/l/l+2*x*x*x/l/l/l)*ldySt+(x-2*x*x/l+x*x*x/l/l)*rotSt+(3*x*x/l/l-2*x*x*x/l/l/l)*ldyEnd+((-1)*x*x/l+x*x*x/l/l)*rotEnd;
				};
			//console.log("defl1: ", defl);
		//end deformations due to end rotation and translation	
		
		
		//secondly find deformations due to internal forces - integrate member bending moments
			if (this.hingeSt!=0 ){
				if (lens.length>6){mzSt=(-1)*this.getFEMs(lc)[0];}
				else {mzSt=0;};
				}; //adjust start/end moments for hinges!
			if (this.hingeEnd!=0){
				if(lens.length>6){mzEnd=this.getFEMs(lc)[1];}
				else{mzEnd=0};
				};
			
			

			var mei = new Array(); var defl2 = new Array(); defl2[0]=0;
			//console.log("mzSt: ", mzSt," mzEnd: ",mzEnd);
			for (var i = 0; i<=lens.length-1; i++){ //find M/EI values
				if (this.orientation==0){
					mei[i] = (-mzSt*(1-lens[i]/l)+mzEnd*(lens[i]/l)-moments[i])/this.Ex/this.Ix;} // M/EI
				else{mei[i] = (-mzSt*(1-lens[i]/l)+mzEnd*(lens[i]/l)-moments[i])/this.Ex/this.Iy;};
				//n.b. use fixed end moments to form M/EI values for a fixed end beam
				};
			//console.log("mei: ",mei);
				
			var leverArm=0; var area=0
			for (var i = 1; i<=lens.length-1; i++){ //apply moment-area theorem to find deflections due to member moments
				// http://books.google.rs/books?id=_IOw1aiAxVAC&pg=PA35&lpg=PA35&dq=moment-area+theorem+fixed+beam&source=bl&ots=QWzSEjHinJ&sig=2xCYCcNBLdrVTvfaKaGlCUomq38&hl=en&sa=X&ei=IzdhUYS6JsTf4QTd_YHYBA&redir_esc=y#v=onepage&q=moment-area%20theorem%20fixed%20beam&f=false
				// book Graphical Methods in Structural Analysis By D.S. Prakash and
				// youtube lecture: http://www.youtube.com/watch?v=BFisP060YFQ
				
				defl2[i]=0;
				for (var j = 1; j<=i; j++){
					area=(mei[j]+mei[j-1])/2*(lens[j]-lens[j-1]); //slope = integral of M/EI = area under the M/EI diagram for a segment
					leverArm=lens[i]-lens[j]+(lens[j]-lens[j-1])/2; //lever arm = distance from a point along the beam to the c/l of the segment
					//console.log("liverArm: ",Math.round(leverArm*10)/10,"area: ",area);
					defl2[i]=defl2[i] + area * leverArm; //and finally deflection equals integral of slope = second integral of M/EI = area of the segment x lever arm
				};
			};				
		//end deformations due to internal forces

		
		
		//REPEAT FOR OUT-OF-PLANE DEFORMATIONS!
		//first find deformations due to end rotation and translation 

			//n.b. no rotation of end deflections required because beam lies in x-y plane!
			if (this.hingeSt>0){rotSt=0} //adjust rotation for hinges!
			else{rotSt=-drzSt};
			if (this.hingeEnd>0){rotEnd=0} //will need to be tackled further!
			else{rotEnd=-drzEnd};
			
			//rotSt=-drzSt;rotEnd=-drzEnd;
			
			var deflY=new Array();
			//dzSt=-dzSt;
			//dzEnd=-dzEnd;
			//console.log("rotZst:",rotSt, "ZdeflSt:", dzSt, "rotZEnd:",rotEnd, "ZdeflEnd:", dzEnd);	
			var x=0;
			// - use shape function: http://www.eng.fsu.edu/~chandra/courses/eml4536/
			for (var i = 0; i <= lens.length-1; i++){ 		
				x=lens[i];
				deflY[i]=(1-3*x*x/l/l+2*x*x*x/l/l/l)*dzSt+(x-2*x*x/l+x*x*x/l/l)*rotSt+(3*x*x/l/l-2*x*x*x/l/l/l)*dzEnd+((-1)*x*x/l+x*x*x/l/l)*rotEnd;
				};
			//console.log("deflY:", deflY);		
		//end deformations due to end rotation and translation	
		
		
		//secondly find deformations due to internal forces - integrate member bending moments FOR OUT OF PLANE MOMENTS

			//console.log(this.getFEMs(lc)[1]);
			if (this.hingeSt!=0 ){
				if (lens.length>6){mySt=(-1)*this.getFEMs(lc)[2];}
				else {mySt=0;};
				}; //adjust start/end moments for hinges!
			if (this.hingeEnd!=0){
				if(lens.length>6){myEnd=this.getFEMs(lc)[3];}
				else{myEnd=0};
				};

				var mei = new Array(); var deflY2 = new Array(); deflY2[0]=0;
			//console.log("mzSt: ", mySt," mzEnd: ",myEnd);
			//console.log("momentsY",momentsY);
			for (var i = 0; i<=lens.length-1; i++){ //find M/EI values
				if (this.orientation==0){
				mei[i] = (-mySt*(1-lens[i]/l)+myEnd*(lens[i]/l)-momentsY[i])/this.Ex/this.Iy;} // M/EI
				else{mei[i] = (-mySt*(1-lens[i]/l)+myEnd*(lens[i]/l)-momentsY[i])/this.Ex/this.Ix;};
				//n.b. use fixed end moments to form M/EI values for a fixed end beam
				};
			//console.log("mei: ",mei);
				
			var leverArm=0; var area=0
			for (var i = 1; i<=lens.length-1; i++){ //apply moment-area theorem to find deflections due to member moments
				// http://books.google.rs/books?id=_IOw1aiAxVAC&pg=PA35&lpg=PA35&dq=moment-area+theorem+fixed+beam&source=bl&ots=QWzSEjHinJ&sig=2xCYCcNBLdrVTvfaKaGlCUomq38&hl=en&sa=X&ei=IzdhUYS6JsTf4QTd_YHYBA&redir_esc=y#v=onepage&q=moment-area%20theorem%20fixed%20beam&f=false
				// book Graphical Methods in Structural Analysis By D.S. Prakash and
				// youtube lecture: http://www.youtube.com/watch?v=BFisP060YFQ
				
				deflY2[i]=0;
				for (var j = 1; j<=i; j++){
					area=(mei[j]+mei[j-1])/2*(lens[j]-lens[j-1]); //slope = integral of M/EI = area under the M/EI diagram for a segment
					leverArm=lens[i]-lens[j]+(lens[j]-lens[j-1])/2; //lever arm = distance from a point along the beam to the c/l of the segment
					//console.log("liverArm: ",Math.round(leverArm*10)/10,"area: ",area);
					deflY2[i]=deflY2[i] + area * leverArm; //and finally deflection equals integral of slope = second integral of M/EI = area of the segment x lever arm
				};
			};				
		//end deformations due to internal forces