1-LKXl KAL STKKSSKS. 



Fiber stress due toa given moment in 



flomenttocwseagivenfiberstressihagivenbeam, 

 ff'^f (b) 



Section modulus for given moment and fiber stress, 



liomentofinerta forgiven moment, fiberstress 

 and distance to extreme fiber, 



I = JT (d) 



Id. 



Differentialeqvdtfort from *hich equation of elastic 

 ******* &%,-#* <*) 



Jbdetermbeelasticcwve^AenTa/K/ fare const- 

 ant, integrate twice determining constants of 

 integration by substituting known ra/ues of slope 

 anddef/ection and corresponding values ofa . 



Theequation of curve change sdt every concen- 

 trated had but is same throughout/or uniform 

 load or for uniform// varying had. 



20. 



Average unitshearing stress, 



c V 



r v = (a) 



A 



*T'j , '. f l/nithorizonfalshearing stress, 

 rteutralAx,s- (/ 0fJ gitudinahLr) 



Fy ==r "fa, t fb) 



Oi\ centroidof , 



shaded area fastac/cmomentofarea, 



at>OYesecti'onconsidered,aboot 

 neucrafaxis. fbrhorizonta/sfyearatm-m, 9n = 

 area of shaded portionmv/tip/iecfbyz, the 

 distance toits centroi'cf. Themax. un)6 horiz- 

 ontal shear w iff occur st the neutral axis. 



The max. unithorizonfat 'shear for a rectang- 

 ular beam -^ average unit shear, for circv/ar 

 section^dndforanl-beammaybeasmuch 

 as E ^ times average unit shear. 



For rolled or bvi/t I-beams tne max. unit 

 horizontal shear very nearly eguals Me fotaf 

 vertica I shear divided bf area of web. 



Straight Line Formula, 



'**-0Z 



A r 

 For constants oc and 13 see Tab/elXpaqeSO. 



f?<3nt<ine's(Gordons)Formu/a, 



. ' ' & 



A 



For constants CCandftseeTabteJXpageSO. 

 Euler's Formula, 



(c) 

 A r* 



According to Merriman cc "has the 

 following values; 

 Both ends hinged, tz"=rr z 

 On e end fixed and one hinged, cc "- ?jff * 

 Both ends fixed, oc tt =4rr? 



In Eu/er 's Formula P= ultimate strength. 



El. TORSIOH OF 5HAFTS. 



Solid round shafts, 



H 



P 



= horse power. 

 : rev. per minute. 



(a) 

 (b) 



(0 



5 olid sguare shafts, 

 Pe=d 3 f (approx.) (d) 



(f) 



IfiFl 



22: STRESSES Itt HOOKS: Approximate Solution. 

 E: | | Maximum tension, 



**A*I <3) 



where A = area of sect ion 

 m-m, e - distance from line 

 of action ofloadtfto cent- 

 roidofmm, c* distance 

 from centroid to extreme 

 fiber on tension sicfe > r= 

 moment of inertia of sec- 

 tion m-m about axis thr- 

 ough cenlroiof. M 

 For exact solution see 'SlocumandHancoc^pldl. 



^ / 



