Question

Calculate the second moment of area around axis z-z in m^4 and the maximum first moment of area Q in m^3

Find the maximum load if the maximum bending stress is not to exceed 110 MPa and the maximum shear stress is not to exceed 55 MPa

Find the resulting bending and shear stresses at a point located at x=0 and y = +0.25 mm

Find σ1and σ2 at that point and the beam deflection at x = 2.5m

у P х 2.5 m 100 mm 7 7 150 mm

E = 200 GPa

Answer 1

Bending stress at О, 25 mm Я? | 6, 5 x 10^x 0. 3S 12500 1 x 8 = І. 1503x100 12 0.36666 н Pa дог Also, we can calculate by О тох Это да 1. О о 025 8 7s mg x o 2 О. 3666 MPa, 25 Transurse sheas stress VO 16. 5x 10° x 450 - о. 23) за- 25). 1Sox) ооу ТОО Іь ј 2 0.06 5 4 4 MP4 - 25 О. О. 366 , 7 * o.o659 9 О, о, а t B)** + 7.5* :/ed)" 0,366 + 0.06ѕ992 О. 183 + O, 1945 02 — О. ОТ 5 меа Ота О. 3 7 2 5 3 м/ra

2.5m Deflection at a. va 16.5X103 x 25003 23 X 200 x103 x 1503X100 ALL P23 3 El 12 - 1 5.277 mm

MOMENT OF FIRST AREA IJA Saaxy ty 150mm - ¿ N ( 100 x dyxy [!] 75 100 mm 100 -75 SECOND MO MENT AREA OF 100 off"1" 100 x dy x y? → -75 100x 1503 100x (750 +753) 12 2 81 25000 mm 4 M 110 Max shear stress Maximum bending stress = 11OMPA =55MPa Jo= Ily p'. 55x100x150 Px 2500 p' 825 KN i 50°x100 6 P = 16.5kN So, the maximum load we can apply is 16.5KN.