534 



STRUCTURAL MECHANICS. 



CHAP. XVI. 



/2 ///f OiRDERS: See also Chapter XVII 

 f I) flomenl all carried by Flanges, 



M=A' F Fh (<a) 



(ZjOne-eiqhtharea oFweb a variable as Mange 

 ares. M-(A',*&A)Fh (t>) 



(3) Moment ofi'nertia oFnet sect/on, 



M*g' (0 



(4)t1omenkoFinerl/a oF gross section. 



= netareaofonefJange anc/gross area 

 of web, I and I = moment ofinerlia oFqross 

 and ofnet section, h -disf. $tci oF Flanges. 



24UrtSrnmTI?IC4LLOAD50ri6fAH5Jpproxim<}te5olution. 

 Fl-max moment For vertical loads. 



I*- moment oFinertid,axis2-2 

 . .flax compressive Fiber stress, 



25. ECCEfiTRICLOAD50flPRI5r15:5eealsoChapt. V. 

 ' + e \.P 



kiily 



Z6.FL EXURE/MD DIRECT 5TRE5S. 



Flexure and compression, F--J- 

 A 



Flexure and tension, , .^ ^ frfp^fef 



k- /OForbothendshinged, 24 For one end hinged 

 and one Fixed, 5? For both ends Fixed> 



Approximate Formula, F-jJ: -~; (c, 



For direct stress either tension orcompression. 

 M may be due to weight oFmemberorto external load. 



27. TRUE 5TRE55. 



Stressatm, p.P.Mc .Stressatm' )F .P Me . 

 f ' ' 



I n = moment 'oF inertia oFsectionm-maboutdxisn-n. 



A =area oF section m-m'. 



Line oF action oFre suit ant, x=firP ; 



IF there is tension at m'and section tvillnotMeitJht 



stress at m '=0 anal 3tm=^P(j-/) For rectanq. sect. 



-* 



F n F z ,& Fj- apparent unit stresses 

 ttStt ^true unit stresses. 



(b) 



/f any stress is tension chan- 

 ge its sign in above Formulas. 

 /y=j For steel and wrought iron. 

 A --jForcdstiron. 



\ =Poiss on's Ratio. A ^r For concrete . 



28. CYLINDRICAL ROLLERS. 



Unit Stress Forgiven load ^JSIV^l} (3) 

 and roller, ~L6 3 L z Du , 



Length Forgiven load,diam. 3W f7f 

 and.unit stress, L= ZFDLlFJJ f> 



Total load For given roller ... 2/nffZfJz/r 



i i i rr 5"' ft I -= I (t-j 



and unit stress. 5 L CJ' t 



L oad per unit length For w=-DFfl^ IH) 



given roller and unit stress. 5 LEJ 

 D=diam. oF roller. L= length oF roller, 

 E= modulus oF elasticity. 



29. THICK PIPES AttD CYllHDERS-.lntemal Pressure. 

 Maximum unit tension, 



Maximum unit compression, 

 f c *w (b) 



Thickness For given pressure, 

 unit tension and internal radius. 



w= unit internal pressure. 



