STRESSES IN BEAMS. 



Ml 



52. BEAM FIXED AT &OTH FNDS - UNJFOKM LOAD- 

 End Reactions: Ri a #e"wl 

 Shear at any point: Y* ** j>wl- tvx 



Max- Shear; Ywl, occurs at supports 

 Moment at any point: M* " ^fal'+lx-x*) 



Max- Positive Moment; M a fiwl* occurs ar center- 

 Max- Negative Moment; M'^fe wl* occurs at supports- 

 Points of Contra flexure; x,-0-?!15 1; xi= 0-7887 1- 



Elastic Curve and Deflections : 



53 -BEAM F/x0 AT BOTH EMDS - COMCNTKATD LOAD AT 



Seam 



Shear 

 Diagram 



Moment 

 Diagram 



Elastic 

 Curve 



End Reactions: R I =R Z '=-^P- 



Shear at any point: Y* = jP- Max- 5hear, Y= jP' 



Moment at any point: 

 Between R, & P; M x =i 

 Between P&R^', M x =P(%Z-x)- 

 Max- Positive Moment; M= Pl, occurs at center- 

 Max-Hegafive Moment ;M -jrPl ; occurs at supports 

 Points of Contra f/exure; x =^-j Xg^^Z' 



Elastic Curve and De flections : 

 Between Rj P; y- JfJ^x-f-g'l)' 

 Between P&R?; Symmetrical- 



/ D7& 7 



Js ^7v''- Z ' a 'F' 



54'BAM FIXED AT BOTH ENDS- ConcenTRATeo LOAD. AT ANY POJHT^-, 



End Reactions :Rj= t 



z 



Shear at any point: Between Rj <&P; Vjc* 



Max- Shear; V=Rj rora<b; ?=& for <=?> b 

 Moment df any point: 3 ^ jtf, 



Negative Moments at Supports; M,--P "py Mg="P ~J*' 

 Between R,&P; M x =R,x+M,' T Hote that M, carries 

 Between Pt*;Mx=RtXi+M,-P(xj-d) / a minus s/ffn- 

 MaxPosifiveMomenf:M=R l a+M,; occurs under load- 

 Max-ffegafive Moments occur at supports: See^bove- 

 Points of Contra f/exirre;Xff - J^TA > Xo^Z* 

 Elastic Curve and Pef/ecfions : 



Between R,&P; 



r^ji"-p,f nsfx-a^~* i 7 



Between P and R*; y,~~^tl J rr^f-' l '^dt~^dXroxJ- 





Beam 



Shear 

 Diagram 



Moment 

 Diagram 



Hsx-Def/ ;when a(b', A-- 



Xj 



IF P Is A Moviffs LOAD: 



Absolute Max- 5hf3rs;5*P, occurs atRi tvhena0;afRi when a* I 

 Elastic Mto/ufe rfax-f/egative Moment; ft, = zjPl; occurs when a*j Z- 

 Curve AksoIofvM3xt/g9fivsMomenfjMz='jjPl} occurs when a "f- 1 



Abso/uff Max- Positive Mfment;M s ^-Pl;gccurs whsn 



occurs at Z 



Absolute Max- Def fection; A s j5rPJi } occurs when 3" 



