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r . (-----: <br /> CI -42 <br /> V r~ .-1... c .. <br /> �I/•, s i•p 1 <br /> N -;+ <br /> r, ‘0' <br /> ri j' ' tl 0 <br /> (I <br /> `� ` ll ., W u I I <br /> C <br /> .... <br /> a 3 s' ' ! ' o ) <br /> n ., �r = <br /> rE 1 c a L .. 1 <br /> L. ...t l'.' la I'3,..". <br /> AAd qr <br /> i 't <br /> ":,,,,:.,s.'wi,,,,, Tr...ta <br /> N ,.._i, <br /> a 11 ('i U r"1 I 'l f. S$ <br /> \ <br /> ,--,, c- <br /> �' 2 C4 <br /> •---13� -,\ N <br /> Csi <br /> � i <br /> r: r FI <br /> 7 Z +.v <br /> q. I` f• <br /> • w r1 1 <br /> PI <br /> rt �� c ( 3' v. i z-, cti� .° <br /> t , C Li a1 <br /> rs -� v ,h jl 0.* <br /> • Irt( sa = r4�� Z t� �(� r .�C p •t ‘••• I )1 M <br /> , <br /> IA �. ♦ J <br /> ij <br /> ( <br /> • <br /> r <br /> 2.198 i <br /> ' <br /> BEAM DIAGRAMS ANS 2.199 <br /> RMULAS BEAM DIAGRAMS AND FORMULAS <br /> For various static loading conditions For various static loading conditions <br /> Equivalent Tabular Load is the unifomly distributed load given in beam tables,pages 2-28 to 2-81. <br /> For meaning of symbols,see page 2.196. For meaning of symbols,see page 2.196. <br /> 1. SIMPLE E EAM—UNIFORMLY DISTRIBUTED LOAD <br /> 4. SIMPLE BEAM—UNIFORM LOAD PARTIALLY DISTRIBUTED <br /> 1 Equivalent Tabular Load . . . = wl <br /> x. { _ RI=VI (max.when a<c) =27 (2c+b) <br /> 1IIIII�IIIIIIII� R v = 21 <br /> R R l 11111 Ra=Va (max.when a>o) =21 (2a+b) <br /> Vx w(2-x/ R2 • <br /> I ( t 1 R, <br /> 2 2 _ � Vx (when x>a and<(a+b)) . = Ri-w(x-a) <br /> !! M max.(at center) � gull <br /> S ' 111'I,ke shear M max.(at x=a+ F:--7-:-) = Ra(a i--12-11-: <br /> R2) <br /> Shear -"Illiiii <br /> V Mx =2(l-x) nig 2 M (whenx<a) 2w <br /> Rix <br /> 14 <br /> Amax. (at center) 5"- <br /> M w ��'I�', = 384 E1wx <br /> I Mx (::::: <br /> >a and<(a+b)) . = :: i!, <br /> x- (x-a)a <br /> 2 - M�/�Imoma ( ( t )) . . . . = <br /> x i ► Ax (12-21x2•}-x2) . Mx > a b <br /> Moment N1on5,ynt <br /> r <br /> 2. SIMPLE BEAM—LOAD INCREASING UNIFORMLY TO ONE END 5. SIMPLE BEAM—UNIFORM LOAD PARTIALLY DISTRIBUTED AT ONE END <br /> ) <br /> Equivalent Tabular Load 9 =1.0264W RI Vi max tea <br /> (21-a <br /> x 1 wr Rt=Vi = 3 111111 Ra=Va 2a <br /> 1 <br /> ,a.ui1•IIIIt11 2W; R' R2 Vx x<a <br /> RI R2 Ra=Va Max = (when ) = Ri-wX <br /> 3 <br /> 1 W Wx2 Mmax.(at x= Ri) Ria <br /> ,o77�ji1 Vx =3 l2 '1 u' / _ 2w <br /> Ih . <br /> V1 /it U as t ' M max.(at x= !-=4.57741) 2W!-;17 1283 W1 =wrrms=rr 2 M5 (whenx<a) = Rix-w22 <br /> Shear �, x 3 s 9 � Mx (when x>a) = Ra(t-x) <br /> um <br /> \ tpl Ax when <a =24E111(a2(21-a)=-2axa(2t-a)�-Ixa‘ <br /> Mm Amax.1 (atx�l�I- =,5193!ia .01304 Ela j1ii'11111111� Ax (when x>a� wa2(1-x) i101111111iL <br /> TTT / V--1X- <br /> Moment ent ( 24E11 (4x1-2x=-aa) <br /> Moment <br /> Ax 'Wx (3x4-1012x2-}•714) <br /> = TabEI 12 <br /> 6. SIMPLE BEAM—UNIFORM LOAD PARTIALLY DISTRIBUTED AT EACH END <br /> 3. SIMPLE! BEAM—LOAD INCREASING UNIFORMLY TO CENTER <br /> Ra=Vi = tuaa(2t-a) }wsc2 <br /> 1 Equivalent Tabular Load = 4W t R2=VS = toaa(2t Zc)+wiaa <br /> '3 .-- <br /> 21 <br /> R'".r'�il�i R = W `"a w e Vx (when x<a) Ri-wix <br /> R=V Y IIIIII ■!!1 <br /> R1 R2 Vx x>a and<(ab <br /> l ,V 1 Vx (when x<12-) . . . . =2 21x1 (12-4x2) (when + )1 = RI-w2a <br /> \,............,---.....) ' 4 Vx (when x>(a+b)) . . /. . = Ra-wa(1-x) <br /> "1102. M max. ( at center ) . . . . = W1t <br /> : v. Shegr '111111111 1 —r. 1�>..1-5-0;;74441 V2 M max.(at x=El when R3<wta) -RAZ- <br /> it'"/ 2zo <br /> .' Mx (when x<4-) . . . . = Wx(-1.-- -.;11) M max.(at x= 1-R2 when R <Mac)= Rii <br /> ,0',•t) wa 2 <br /> 2w: <br /> Masai/�Il��l�lhl�►. Amax. at center 1 =W-12 M :::: <br /> x:: nd <br /> ••\ ! EIM llhIIIII Mx (x ( x <(ab <br /> Moment Ax (whenx < 2) _ 1 ('51'2-4x2)2 Moment + ) • = Rix-i(2x-a) <br />