Question

The beam ABC is supported at A with a guided support (fixed with roller) and hinge at B has rectangular cross section and supports concentrated loads P both ends A and C as shown in the figure. The span length from A to Bis L, and the length of the overhang is 1/2. Point D is located midway between the supports at a distance d from the top face of the beam Knowing that the maximum tensile stress (principal stress) at point Dis = 37 MPa. determine the magnitude of the load P. (Show your calculations with Mohr's circle) Given: L = 1.9 m, b = 50 mm, h - 250 mm, and d = 38 mm TO Answer: Ра KN

Answer 1

Р EV =0 7 P-PARE SO <%=0 - ( 1 8 A Ro=0 + 0.95m 6.95m 1 0.95m 3 SO 50X dio 38 " Shear fence at D, V=P Bending moment at D, M = 1.9 p = 65.104x20 mort from , sechoorI = Bending stres, o = q (me) = 1.32x37 - 957koʻp TD= 2.539x10p (Tensile) Sheas stres at D! B N 87 LA QV てこ Ib Q = (50x38)(87** 201400 mm mm3 2 201400 XP => 767 (65.104 xilhoso = 1.1474x104p : Principal stresss 0,2 = Site +62)*+2? =) 57,2 = 2.571ko'p 0.529 koʻp) +(1.3492104p)? => 61,2 = 1.16 xo'p, -1.135x154 p (-ve, compressive) Z Tomax - 36.60mm 40 30 BO 37 26 max. Tensile stren at 0,010 = 1,168104p 1.16X10"p P = 370/mm² P - 318920 N 1.168104 --) |P= 318.92 km -49-30-40 -10 mas comprom Shen, 08.0= -1.125xió"x 318.72x10° 30 =-37 N/rom 2 10 + 30 40 50 A coa Toe A(0.8.-3658) LA To Malin's circle of To = 2.589x10 x 21912103 D = 0,84/mm2 To = 1.147864 x 38.92X103 20 36.58N/mm2 Тр

= temsile normal strus at point D > 6m = mxy 1.9P x 87 bha 12 » 6n = 1.9 p/krv) X IWON x 87 Jun 50x2503 where pis in un - 60 = 20539x10-3p mpa & Shear stress at fouint D 2 Exy=t0 = 6 V bha they?) 6x PXIV 2502 (2502 – 872) = 61187810-2p MPa 50x2503 62.87'. X10-3 mpa to a ☺ To = at mohr's cincle :- 2 TD far/200) = bxe-by = 20 p = tan tant (p.529x109 2X 62.87810 2.539x103 88.820 2:539x10-3 5) 20P = &, contre at on 7(1.26 162695310-30) 2 7

TD Simeop Со = ) = 61.88X100mpa 8 = Sim20p (onito TED Marionum principle Strees = 60 + 8 e E dor! H 3 -) 63 61.88X10-3 P + 2.539x107 2 16m 2 =) 69 = 63•1526x103 p mpa Tg Hence - 3 p = = 37 63.1526X10 7 / p = 585.88 km

Answer 2

D = 37 mpa Given That Principal stress at Length Of Beams (-) = 1.99 Breadth of Beam (1) - 50 mm Height (H) = 2500 and also Given that, D = 380 Р WP АВ ,فيلم A 42 42 니그 els, using principal stress at D, MA -PL+pX5 PL Now, -PL MD - PL pX5 No shear face at D. ND =P of Pneulia (I we know that moment I- bh3 12 5072503 6.51 X10 many vi I: 6:51x10 noy

calculate Centroid in the beam els bod 87mon aso -38 2 Y-87 corso calculate shear stress syco) wa shean folce Qa first moment Inectia moment of Breedia sy Ib ba breadth w.kot, Q = ba (22 - 2) = 50x38 ( 220-382 2.014 X10 Sayo 3 values in ees axy substitue all wap mm3 2.014/105xp Tary: ***) G.sixox@50 26.1874710 X 106 100m2 osmona Tay -1.87up Noma 61.8tup N/m2 (14

we know that, 3 Stress comenty 7xd-- -(-PL)xy 고 + CPxLx27 x16 mm2 6.518107 mmuz yom 2539.140 W/m2 Two gol que Ox= 2539217p Non 2 org calculate principal stress, we know that Extory+ szory ſtray? Dia

a=2539.17P t J62539/1973+ (61.844p2 ☺ 2 By solving 2.547103 p. 2540.67 P aa substitue 2589087 37 mpa oi, stress Q (0) - Nom² = 106 N/m2 2.54M03 p 37 377106 -14566.92 N Р Qosunio 3 2140566 KN magnitude of the Hood (p2 = 14.566kŅ

Answer 3

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Р EV =0 7 P-PARE SO <%=0 - ( 1 8 A Ro=0 + 0.95m 6.95m 1 0.95m 3 SO 50X dio 38 " Shear fence at D, V=P Bending moment at D, M = 1.9 p = 65.104x20 mort from , sechoorI = Bending stres, o = q (me) = 1.32x37 - 957koʻp TD= 2.539x10p (Tensile) Sheas stres at D! B N 87 LA QV てこ Ib Q = (50x38)(87** 201400 mm mm3 2 201400 XP => 767 (65.104 xilhoso = 1.1474x104p : Principal stresss 0,2 = Site +62)*+2? =) 57,2 = 2.571ko'p 0.529 koʻp) +(1.3492104p)? => 61,2 = 1.16 xo'p, -1.135x154 p (-ve, compressive) Z Tomax - 36.60mm 40 30 BO 37 26 max. Tensile stren at 0,010 = 1,168104p 1.16X10"p P = 370/mm² P - 318920 N 1.168104 --) |P= 318.92 km -49-30-40 -10 mas comprom Shen, 08.0= -1.125xió"x 318.72x10° 30 =-37 N/rom 2 10 + 30 40 50 A coa Toe A(0.8.-3658) LA To Malin's circle of To = 2.589x10 x 21912103 D = 0,84/mm2 To = 1.147864 x 38.92X103 20 36.58N/mm2 Тр