WORK OF RESILIENCE. 



585 



30. 5TRC5Sf5lfirLATPLATf5 -(JfilFORflLOAD. 



Gircu/ar Plate; 



Circumference fixed, 



' 64 t z ' 



Circumference supported, 

 c. IJ7wr' 



' 



Rectangular Plate, 

 Circumference fixed, 

 c. 

 " 



Circumference supported, 

 Unit stress is about j 

 that for circumference fixed. 

 Square Plates, 



Circumference fixed, 

 f- wa*. 



~ > 1-9 > 



Circumference supported, 

 (/nit stress is about j that 

 for circumference fixed. 



See Chapter VIII, p. W and fable 115. 



BARS. 



Work done in stressing a bar below elastic 

 limit. From Otoftor Otof, 



From P,toP z or fjto , 

 K-iPA-l/Wi-ltFA-WAl; It,) 



BEAMS. 



Deflection under one loaof 



Deflection at any point, 

 y,ft 



(d) 



where M* = moment at any point due to 

 given loadincj and M = momentat any 

 point due to a unit load placed at the 

 point at which the deflection is rey- 

 uired. 



Y 



r 



V r 



y y 

 i * 



CEHTROID (CEVTER OF GRAVITY). 

 General formulas; 



%*?< 

 SA UJL I ).&.&, < b > 



35. flOMEnTOFlriERTIA AfID PRODUCT OF IflERTIA. 



'i 



.A^; ' /6A A 



*.j..+ Fig I. Structural sections canbe 

 Y divided into finite elements 



? . . . . -chepropert/es of which are 

 known. The n(a) and ft>) become 



A 

 Static moment about given axis 



Y 

 V 



d,ory 

 1 



8A General Formulas, 



AreaA -Jf 



Trans formation Formulas, 

 centroid- X 



beordinates of their centroids. 



O by symmetry. 

 y- 



entroidoftrapesoid 



f * / / *// 



rig 4. Centro/dofjnytwarejs. 



Axes are designated by subscripts . 



