Question

p = 2600 Kgm3, L2 = 4.1m, t = 8.3 mm Q3 CLO3 An open channel ABCD is used to contain a liquid of mass density p, as shown in Figure 4. It is made of steel and simply supported at B and C. It has a cross section shape and axis direction as shown in Figure 5. The cross section is symmetrical about z axis. The beam has dimensions AB = 2.5 m and BC-L2 and CD 3 m. Under normal conditions, it is always full of liquid. The cross-section dimension is given in Figure 5 and the value oft in data sheet. C4|a) Determine maximum tensile and compressive bending stresses, (5 marks) zar mar Piensile and compressive at C4b) Evaluate the maximum value of transverse shear stress at C, Tear. [5 marks)

Answer 1

Given that density of the liavid f= 2600 kg / m3 فیہ ہے mam mo A B u.lm 3m k 2.5m.se RB = 125.84 ek Ro= 160.80 Cls Area rake of loading w z (e) (g) CAo) A-(1- 260.0063) ][12- 0.0083] N of the charme Az 117 m2 W = (600) (9.81) C1:173)/1000 W=29.86 kN/m forom the eauiibrium Condition ERB=0 L= 4.142.5+3 9.6 (Rc) (u. 1) = (w) (7.12 (W) (2.52 2

(Rc) Cu-1)= 29. 1686) ((.))² Q.5) 2) Rc 160.80 kn Efyzo Rc + R8 - 29.86) (a.c) Ro= 125.84 kN) Bending moment W = 29.86 kN lm 2.5m Te Uolm 3m RB=125.89 Re = 160.80 4.2lum Main> -93.31 - yq.uz KNM KNM -134.74 INM

MA=0 me = = 29.86) (2.52% A -93.31 kNm. moz - (29.86 (3) ²/2 E Bu 37 kN.m Sfa SER 125.84- 29.86CX) at 2.5m 13 16 ma= 125.84 (a-2.5- 125.84 29.86 (n-oje 2 at Srizo - B.m- maximum / minimum. 29.86 CM) 20 = 125.84- x= 4.214 m from enda Mnan = 125.84 (4:214-215) - 29086 (4.21432 Mmin= -19. ug KNM manimum Bending moment is raman= -1B4• 37 kN/m at point c.

"The Given als is k LI E-83mm t=83mm → 0.4885 k Oilm ool ma Ľ. LS у Y 0.983um 0.7115 k a) Centsioid +A535 az & A333 + Audy (1 Aigit Az Ast Art AztAUTAS A, = A5 = (0.1) (0.0083) O. 00083 m2 312 25 - 1.2 - 0.00 83 10083)2 1.195 m. 2 &(3 =) A2 = Az = (1.2) (0.0083) = 0.000 996 32 233.5 1.2/2 = 0.6m. m2 ♡ --> Aus (1-2)(0.0083)) (0.0089) 0.000816 m²

3 Iy-y = 3.2152 x 10 my. Since the beam is subjected to Eve) Bending moment at c. opper layen Eensile stress bottom layer - Compre ssive stress Thensice = (man) (1.2-y) INA Skensile = (134-37x103) (1.2-0.745) 3-2182 410-3. Stensile = 20.402x106. Pa Stensu = 20.00 mpa - Upper laye, Comp = (mman) (5) INA 17 -( 134-37X103) Cotus) 3-2152 (03 Comp= 29.735x6106 & Comp 29.735 mpa

manimum shear stoness induces at Neotral aris TNA = (Sfman) CQNA) (INA) (b) SFc (29.26) (3) -229.86 KN fe 3m sted 89.58 kN. Sfc= 89.58 160.80 -71.22 kN. SFC =89.58 KN b=(2) C0.0083 0.0166 m Ay+ Azg & Azyz + Ag95 QNA E 1 =20.00053) (0.4885-0-0083 )( + 6.4895) (2) C0.0083). C0.1885/2) 2 QNA - 2.78 4x103 m 3. ENA = man = (89.58*103) (2.784 X103) (3.2152x60-3-) (0.0166) eman - 4673782.53 Pa Eman = 9.673. impas at Neutral anis.