A.1 Trigonometric functions. A.2 Hyperbolic functions. x sinh. cosh. x 2. tan. cos. sin. Appendix A Mathematical formulae (1/5)

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1 PPENDX MTHEMTCL FORMULE Vrion.. Jn rt qtion f trpzim inrti. Vrion.. My rt qtion f trpzim inrti.. Trigonomtri fntion ppni Mthmtil fml (/5) in in tn i i i in o B ± o in B tn ± tn B tn tn B in + in B in o o + o B o o in in B in o B in [ o in [ in in [ o( B) o( + B) [ in( + B) + in( B) o o i i + o o B in in B o in o o B in in o o B o o [ o( + B) + o( B) [ + o [ o + o in in B. Hyprboli fntion + i o inh i iin inh inh inh ( ± y) y ± inh inh ( ± y) inh y ± inh ( ± iy) o y ± iinh in y ( ± iy) inh o y ± i in y y y inh o i in i i inh THS DOCUMENT S COPYRGHT ND S PUBLSHED FOR DSTRBUTON ONLY WTHN THE OVE RUP PRTNERSHP. T S NOT NTENDED FOR ND SHOULD NOT BE RELED UPON BY NY THRD PRTY. Vr. / My 000

2 ppni Mthmtil fml (/5). Stnr infinit intgrl ntgrn ntgrl ntgrn ntgrl in -o inh o in inh tn -ln (o ) tnh ln ( ) o ln(tn / ) oh ln (tnh / ) ln (tn + ) h tn - ( ) ot ln (in ) oth ln (inh ) tn h tnh tn tnh h -h ot o -o oth oh -oh + + in inh tn o ln ln ( + + ) ( + ). Stnr btittion f intgrtion f th intgrn i fntion of : Sbtitt: ( ) inθ oθ ( + ) + tnθ inhθ ( ) θ θ of th fm: {( + b) p + q} p + q {( + b) p + q + r } + b rtionl fntion of: in n / o t whn in + t t o + t t tn t + t THS DOCUMENT S COPYRGHT ND S PUBLSHED FOR DSTRBUTON ONLY WTHN THE OVE RUP PRTNERSHP. T S NOT NTENDED FOR ND SHOULD NOT BE RELED UPON BY NY THRD PRTY. Vr. / My 000

3 ppni Mthmtil fml (/5).5 Gomtri proprti of pln tion tion r Poition of ntroi Momnt of inrti Stion Moli Tringl bh h bh bh bh hb / 6 / 8 / / b bh p bh bh / / / Rtngl b h b b b / / / b b / 6 / 6 Rtngl b b b + b 6 + ( b ) b + 6 b Rtngl b binθ + oθ b + ( b in θ o θ ) b in θ + b o θ 6 ( binθ + oθ ) Sqr / / / 6 6 Trpzim ( + b) ( + b) ( + b) ( + b + b ) 6( + b) ( + b + b + b ) 8 ( two l) b Dimon b b 8 b 8 b b Hgon THS DOCUMENT S COPYRGHT ND S PUBLSHED FOR DSTRBUTON ONLY WTHN THE OVE RUP PRTNERSHP. T S NOT NTENDED FOR ND SHOULD NOT BE RELED UPON BY NY THRD PRTY. Vr. / My 000

4 Gomtri proprti of pln tion (ont.) ppni Mthmtil fml (/5) Stion r Poition of ntroi Momnt of inrti Stion Moli Otgon Polygon n otθ nr tnθ n R in θ r R pning on th i n l of n ( 6R ) ( r + ) 8 Cirl π r r π r π 0.785r Smi-Cirl.5708r 0. r 0.098r 0.97r b 0.587r rown 0.907r 0.97r Qrnt St Sgmnt π θ inθ 80 r θ π r 60 π r 0 θ 0 r o r r 0.r 0.6r 0.707r r π θ in θ r ( oθ ) π θ 80 inθ π θ r 0 8 8inθ + in θ 60 θ r o in θ π 9 r π θ inθ 8 80 r π θ 0 + inθ r 0.07r 0.08r 0.059r b rown b ntr / rown r 0.06r MinimmVl 0.009r 0.095r Complmnt 0.6r 0.777r.098r 0.707r 0.6r σ 0.9r b 0.0r 0.00r r MinimmVl 0.07r r r THS DOCUMENT S COPYRGHT ND S PUBLSHED FOR DSTRBUTON ONLY WTHN THE OVE RUP PRTNERSHP. T S NOT NTENDED FOR ND SHOULD NOT BE RELED UPON BY NY THRD PRTY. Vr. / My 000

5 ppni Mthmtil fml (5/5).6 Conrion Ft mpril : Mtri onrion ft M kg tonn Lngth mm m m r mm m m Volm mm m m Dnity kg/m tonn/m F N N kn.05 lb 0.98 ton in.8 ft.09 y in 0.76 ft.96 y in 5. ft.08 y 0.06 lb/ft 0.75 ton/y 0.0 kgf 0.8 lbf 0.00 tonf lb ton in ft y in ft y in ft y lb/ft ton/y kgf lbf tonf 0.56 kg.06 tonn 5.0 mm 0.08 m 0.9 m 65. mm m 0.86 m 690 mm 0.08 m m 6.0 kg/m.9 tonn/m N.8 N 9.96 kn Str N/mm N/m kgf/m N/m kn/m N/mm 5.0 lbf/in 0.0 kgf/m 0.08 lbf/ft lbf/ft tonf/ft tonf/in Strip Loing N/m kgf/m kn/m kn/m Momnt 0.0 kgf/m lbf/ft 68.5 lbf/ft tonf/ft Nm kgf.m Nm Nm knm 0.0 kgf.m lbf.in 8.85 lbf.in lbf.ft.95 tonf.in Mol of Eltiity N/mm 5.00 lbf/in Stion Mol mm in Son Momnt of r mm in lbf/in kgf/m lbf/ft lbf/ft tonf/ft tonf/in kgf/m lbf/ft lbf/ft tonf/ft kgf.m lbf.in lbf.in lbf.in tonf.in lbf/in in in N/mm N/m.88 kgf/m 7.88 N/m 07. kn/m 5. N/mm N/m.88 kgf/m 0.06 kn/m.69 kn/m Nm 0.05 kgf.m 0.0 Nm.56 Nm 0.5 knm N/mm 690 mm 600 mm THS DOCUMENT S COPYRGHT ND S PUBLSHED FOR DSTRBUTON ONLY WTHN THE OVE RUP PRTNERSHP. T S NOT NTENDED FOR ND SHOULD NOT BE RELED UPON BY NY THRD PRTY. Vr. / My 000

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