538 



STRUCTURAL MECHANICS. 



CHAP. XVI. 



yper unit length-. 



4f. SIMPLE BEAM- UNIFORM LOAD- 



Beam 



Shear 

 Diagram 



Moment 

 Diagram 

 Elastic 

 Curve 



End Reactions RI =R Z - *^r 

 Shear at any point: V* - ^5- - wx 



Max- Shear ; V- *~ ; occurs <3tesch support 



Moment at any point M* = ^TX - j wx f 

 Max- Moment; M=-wl 2 , occurs at center- 



Elastic Curve and Deflections : 



Max- De Fleet ion; A *j rf; T= 



42. SIMPLE BEAM- TRIAN&ULAR LOAD WITH MAX/MUM AT THE CEHTFR 



R, 



M- 



Beam 



Shear 

 wl Diagram 



Moment 

 Diagram 



Elastic 

 Curve 



Total Load = 



End Reactions: R, *R? = -^ 



5hear at any point: 



between R, Center; V x = *{$- 

 Between Center ft; l/ x = tvfj-l*- 

 Max Shear; /- ^ wl^ occurs af supports- 



Moment at any point : 



Between $ and Center; MX "meff- *- 



Between Center f??; M x = 

 Max- Moment; M = jJ4 wl 3 ; occurs 3t center- 

 Elastic Curve and Deflections: 



Between/?, & 'Center: y= ^ r f&- &- i 

 ' ?4EIL 2 J6J 



Between Center & R?', Symmetrical- 

 Max-DeFtecffon; A 



Beam 



43- SIMPLE BEAM- TRIANGULAR LOAD WITH MAXIMUM AT RIGHT EMD- 



Total Load = ^ 



End Reactions :j = (-wl 2 ; Rz ~jwl z - 

 Shear at any point: P* ~ %jff-jf ~x*J 



Max- Shear / V=jwZ?ocarrs af righf svpporf- 

 Moment at any point: M x = -g'fZ^-x*}- 



Max-Moment; M=0-064tvl 3 , occurs at 2=0-5774 1- 

 Elastic Curve and Deflections : 



'1=0-5774 1 \ 



> 



5hear 

 Diagram 



, Moment 

 ~M Dfagram 



Efo'sticCurve 



Max- Deflection; A = 



44-S/MPLe 



y-^> 



Beam 



Shear 

 Diagram 



Moment 

 Diagram 



Elastic Curve- 



LOAD W/TH MAXIMUM AT KfffHT END - 

 Total Load = w,l -i- ^- 

 End React ions =8,=jfa + 

 Shear at any point: V x ~ w, 



Max- Shear - f V" jrfa/ +JWZ l)> occurs atrighf support- 

 Moment at any porn f; M x ** ^(ix-X^+^Clx -x z ) 



Max- Momenf; M=(w f ll- l*)- (Approx-) 

 Elastic Curve and DefJecf/osis : t 



~" J0~30 



