STRUCTURAL MECHANICS. 



CHAP. XVI. 



FIXED AT ONE END AND SUPPORTED AT &TJIER- CONCENTRATED LOAD_AT ANY POINT- 



End Reactions : -j 



Pa 

 R 



Beam 



5hear 



Shear at any pofnt:BetHeenRj& %,(=?.,; between P &, i 



, 



Max- Positive Moment :M=f?, a, occurs under had- 

 Max- Negative Moment: M=fi l-P(l-a), occurs at fixed end- 

 Point if Contra flexure: Xf- 



Elastic Curve & Deflections : 



.. . 

 z 



Between PXR^y^ 



D/aaram i*nwr&;y-& / LKVi-*i*m~* n < f ~*V 



RZ fora=HJ4l;Max-Deff- A*M09fffcfcwn under bad- 



JF P Js A MOVING LOAD: 



Absolute End Reactions: 



RrP, occurs when a- 0;&=P, occurs when 3-1- 

 Absolute Maximum Shears: 



Moment" 



Elastic 

 Curve 



Absolute Maximum Moments: 



Max- Moment !s Negative and is M= 0-1925 PI; occurs 



g f fixed end when 3= 0-5774- 1- 

 Absolute Maximum DeFlecfiffn : 



A =0-009#L 3 ,occurs underload when 



50 -BEAM FIXED AT ONE END AND SUPPORTED AT OTHER - UNIFORM LOAD 



w per unif Jengfh 



Beam 



M> 



tfi-t^m %f ar 

 Jimifei^SsH Di3 * ram 



-M \ 



Moment 



Diagram 



Elasficforve 



End Reactions : P, =-gwl; fo~-g\ 



Shear at any point : V*=w (f-2 ~ x) 



Max- Shear; y=jrtvl, occurs #f Tight support. 



Moment at any point: M x =wxfg'l~x) 



Max- Positive Momenf;M=}2g wlf occurs sfx=-Z 

 Max-NegafiveMemenf; M~ # 'wl; incurs ai '"right 'support- 

 Point of 'Contra 'flexure ; X =jj: I 



Elastic Curve and Deflections: 



= 0-0054 -, X= 



S/'BEAM FIXED AT ONE END SUPPORTED 



-CwcENrxATED LOAD AT CENTER- 



-J 

 I 



\^-M 



y-i 



Seam 



Shear 

 Diagram 



Moment 

 Diagram 



Elastic 

 Curve 



End Reactions: Rj=^P; 

 Shear at any point: 



Between fij&P; **?; 



Max- Shear; V=%P, occurs at 2 

 Moment at any point : 



Between P., P;Mx=%P;etwffnPJ?z ;M X ^Pl-fePx 



Max- Positive Moment: M=jj> PZ, occurs under Joad- 



Max-Hegafivf Moment: M'-fcPZ, occurs at fixed end- 

 Elastic Curve Pffffect/'ens ' 



Between P.,P; y=jjj (5x?-3Z*)- 



Between PSX 



