Sol HW6 - PTOblem 4-47 4.47 The reinforced concrete beam...

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Unformatted text preview: PTOblem 4-47 4.47 The reinforced concrete beam shown is subjected to a positive bending moment of 175 kN ‘ m. knowing that the modulus of elasticity is 25 GPa for the concrete and 200 GPa for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete. 22-mm diameter E 200 6%. : J : ‘ %mm ‘n E¢ 256m 8 O —T A5 = LI‘ 1&1 = (HEM) = 1 sza§xzo mt fl ’Loca‘le ‘Hne HW‘I'V‘CLE axfs is A $09 250 x—g‘: — (12.I64X/03)<Lt00—x3 : o “A5 __._l |25X1+ [2.Ié‘hl103x —- 4,2657 Xlo‘ : o — £2,165} x103 + magma}? 4 (u)(:25)(e.8e57>gloé “_WW X = 154,55 mm ) ‘450- X = 2'45; 45mm Solvinfl ‘FcV‘ X X = I = @3250 x3 + (Izgthlosflqoo—fl‘ :- é (250)(’5¥-55)3+02. [6'1 x103)(7_t}5’.q.5 )1 = LO‘tolfx/o" W.“ = Lo‘tolelo‘s m" 6—: -‘flflj I (on Stcefl: \y = — 245.45 mm = —o.245~5‘m _ (2-0)(z7sxlo‘)(—o.2454s) : . 33040" 194, = 330 MPcL d [-0704 x [0-3 G: (by Concrde.‘ 3y:- IS‘LSS wuw. = 0-!54§§m (1.0](175X103)(0./§455‘l 6:- Leela? x10“ = ~Zé.0 xzo‘ P4 = »26.0 MPa, e PrOblem 4-50 4.50 Knowing that the bending moment in the reinforced concrete beam is +150 kip - fl and that the modulus of elasticity is 3,75 X 106 psi for the concrete and 30 X 106 psi for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete. T " r/ 30 in. ——#>1 5 i“ _ E; - 30xlo‘ : O 24in. n _ Ea — 3-7Sx506' 8’ As : aid?- = [Li = 3.!‘HéfnL nAs= 25.13 M Loco/49. Hie nadir»? axis (303(530 + 2.5) +, 12 x 21$ ‘ «(25.133X16.5 — x3 = o ; [50x + 375 + 6x1; HILLQ? +2583 x =0 ex"+ 175;ng 49.07 = 0 ~ 175433 + 4075.133}; +(H)(e)(3‘t.e°l) . : . 2 n. (mg) 0 2 5 t [6.5- X '-' [6.275 in. I. : fihkfl Adi" r fi(3°K5)3 + (3>0)(5)(2.725)z = “42$ .3 in" 3 Iz=élozx3=~é02¥a2253 = 509% 4:0.» x x :- I3= nAsoi: = (25133304175? = $4.57.} in" I. 1“ I,+ I2 +123 : I‘m.l 1‘ ‘w where M1 ISO 1459 ‘-' 1300 kip'iw I (a) 5+eefl n=8.o 3 3,: 416.275,». ~_ (g,ol(lzoo>(—Ic.27§) _ . 4 6 * ‘_“8““0_“““""““'_—‘83.5 - $7.0 [(51 (b) Congre+e n = LO) j = 5.225 m V 6” (1.0)(420b\(5.2253 : w HQ?) kg“ 4 8083-5 Problem 4. 1 03 4.103 The vertical portion of the press shown consists of a rectangular tube of wall thickness 1 = 10 mm. Knowing that the press has been tightened on wooden planks being glued together until P = 20 kN, determine the stress at (a) point A, (b) point B. RCCA’QMfiUJ/xf cu+oo+ {5 GOme ‘i‘D em... ZEN“ A = {803 (G5) ’ (GOXWA T 2.4)!)(93 mmz': 2.1-)” 0—3 m1 ALsommAB = fiéco><zo’:3 — wawf = 1.24120“ Wt -4 ‘ '+ :: X [D M Section a-a 200 mm 80 mm c: = #0 MMT’O_OH*O'm a: ZOOM-t0! 2qu: 0.240 W. M = P6 = (zoxlogvcoxqol = shin/0‘ NW». P M: Roxlos <.Q.8>1105 Max:415) ,r 4 :~——+-—————:—-———-———- ——————-—-—————-——-=r.7l/O Pa. (a) G; A I 2.le to“ + I34 x to“ m . 62 = “2.87 MPa. 4 3 g 1 ~ ” E _ Mc ROY/O __ (&.8>llo X00401 T H L (m 6'3 f A I 2H Yb" [1.3414 10-“ , 'qe'QHO P“ ‘ 6; =7 —- 776. d. MPQ. 4 Problem 4 120 4.120 The C~shaped steel bar is used as adynamometer to determine the magnitude ' P of the forces shown. Knowing that the cross section of the bar is a square of side 1.6 in. and the strain on the inner edge was measured and found to be 450p, determine the magnitude P of the forces. Use E = 29 x 10‘ psi. 1" _ ' “*9; * P ‘ l X i a ‘HIE. 5% V‘Gvfh gocajj'l“om 3.2111. > g: V 6 : E8 = (xenowcm we“; ' I 13.05Xl03 Pst~ 1.6m. I z A = (texts) —- 254; :n I : imam/4;? = 0.54.413 in‘ 2‘ 3.1+ 0.3 '5 4.0134. 6 C =’ 0.8 in, e P fig _. .1: Pee. _ S _ K 4' I ' A + I " _ __l__ ii (LLDi(O«8) . -7. K ' A + I 2.55 J" 0.54613 815 m P = 76;: = 131M? - 2,088 x/og 1/9. P = 2.0:; ksPsq 5.25 ...
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Sol HW6 - PTOblem 4-47 4.47 The reinforced concrete beam...

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