STRESSES IN BEAMS. 



537 



38.5JMPLE Be AH- CONCENTRATED LOAD AT THC 



End Reactions; tfj~R?* 

 Shear at any point: 



.*,( ! J 



~~j&~;~~ 

 * 





ri 



4* 



Diagram 



Moment 

 Diagram 



Curve 



Max- Shear, V-%. 

 Moment at any point * 



Between />/ &P;M X R,x - -* 



Befwetn P& &; M x ~X#-P(Xr&(l-xJ 



Max- Moment,- M=^Pl, occurs atx-. 

 f/ash'c Curve and Deflections 



Sefween R, P>y*&f (4x 3 -3l*x) - 

 Set ween P & R f ; symmetrical abouf center. 

 Max- Deflection; A=4 ** % = i . 

 48 ET' 2 



39 -SJMPLE BEAM - CONCENTRATED LOAD AT ANY Poittr- 





Beam 



, 



\ I 



"I 



End Reactions: R/ - 



Shear at any po/'nf: 



Between R,&P, K 



Between PR 2 , Y x *R k 



Max- 5fiear; fora^,^, V= 

 Moment at any point 



Between R, P; M x =R,x = 



Between PR 2 ; M x =R,x-P(xra)= 



MdxMcment,~M=R,a= ^^a; occurs at X" a- 

 Elastic Curve and Deflections: 



BehveenP,&P;y='. 



Between P$;y, = 



*' 





t 

 ^ 



-A- 





t* 



40-5JMPLC BEAM -Two OUAL CoMCEMTRATeo LCA>S,SYMMETK/CALLY PLACED- 



End Reactions ; R, =R Z =P- 



Shear at any point: 



Between R, andleftP; V X =P- 

 Between L oads; y x = 0- 

 Between right P and Rf, l/x~P' 

 Max- Shear, Y^P- 



Momenf at anypo/nf: 



Between R, andleftP; M x *Px 

 Between Loads; M x =R,x-P(x-a) "Pa- 

 Max- Momenf; M= Pa 



Elastic Curve 0e flections : 



Diagram 

 Moment 



8efweenJ?,&/eft P; y- & (3Za-3a f -x*)- 

 pfj 



Between Loads ;y f **-. (3lx-3x f -a*) 



vCl 



Between right P& Re ; symmetrical with kftlodd&R, 

 Max- Deflection; A "zjpr (3 



