STRESSES IN BEAMS. 



45.BfAM 

 w per unit / not ft 



Shear 

 Diagram* 



Moment 

 Diagram 



Elastic 

 Curve 



SUPPORT - UffiFORM LOAD- 



Reactions RI -jwZ-jiwmffijjRi 



Shear at any point f 



Between R, R f ; V x - R, - \ 

 Between Rt and End; V x " 



Mo men t dt any point: 



Between P./ &P f ;M x -fix, - i 



Between R f Fnd;M x s ^(^ .. . v 



Max- Positive Moment; M* /%; occurs when x* 



Elasftc Curvff and Def/ecfions : 

 Between fy&fay 



4 6- BE AM OvER-HAHG/ftff Offf 5UPPORT -C0ffCeHTRATf> L0AD AT Affy_ 



Reactions; R/* 



Beam 



Shear 

 Diagram 



Moment 

 Diagram 



Elastic Curve 



Shear at any point: 

 Be f ween f, &P, : y x =k 

 Between R? &%; Y x 



Moment at any point : 

 Between P.,P,; M x 

 Between P,P.?; M x 

 Between Rt 



i J 



? -f} (3 +x z -l) 



47 -BEAM OVER- 



tv per unit length 

 -^ 



UA4*-Mi 

 IA|;^| >to- 



xrT^+TTv ' 



-w 



BOTH SUPPORTS - UM/FORM LOAD 



Reactions: Ri-fflfm+l) -nyj R? = 2iU n 

 Beam Shear at any point : 



Between /eft end & P,i / P x = wfm -xj 

 Between RI& fa ;Vx s P./ -wfrn+Xt) 

 Shear Between Rz right end; f* = w(n-Xs. 



Diagram Max -Shear; P" wm, or /-wrri' 



Moment at any point: 



Moment *Jen K,* f sM x -t 



Diagram Between R z & right end, 



Max- Positive Moment; M*R, f~, -m), occurs af*t 

 Elastic Max- Negative Moments;M=j wm'atRi; ff' s ? 



Curve Points oFConfraf/exufVfXo =fi.-nr)2:1/f&)*+ Zfr 



* * Iff * ft tt/J ' -m- 



= j: 





 ~ 



48- BE AM 

 P,] L _Rr, 



BOTH SUPPORTS -Two EXTERIOR CowCftfTKATte LOADS 



Beam ^actions. R,= 



Shear at any point: 



Shear 

 Diagram 



Moment 

 Diagram 



Elastic 

 Curve 



Moment at any point: 



Between fiKR,; M x **P,fm-xJ 

 Between R, & K t ; M x = P,m +fa- 

 Between R f P f ; M* = Pz(/7-x 3 



Moment at Ri;M=P,m; at R f> 



