Question

the steel lever shown in figure is loaded by a vertical force f=2000 N. A stress element is located on the upper side of the lever at A (on the smaller diameter) as shown .Draw the stress element at A showing the magnitude and directions of the stresses acting on it and find the principal stresses and directions.

Problem 3 The steel lever shown in figure is loaded by a vertical force F = 2000 N A stress element is located on the upper side of the lever at A (on the smaller diameter) as shown. Draw the stress element at A showing the magnitude and directions of the stresses acting on it and find the principal stresses and directions. 50 mm A 300 mn 35 mm D 50 mm 25 n D. nan 400 m 35 D. Bl

Answer 1

Dur to occuYs abrut the moment doYCe F:2000 counter clockwise divechon (ve Toveue) in x-axis NYI M T 2000 x400 800000 N.mm moment (bend.ng) hovce F= 2000N & due to the Same clockwise divection OCcuYs about Z-axis n N.mm M, = FX 350 7 PoindA M,2000 x350 7 350 7 M,700 0o0 N.m m mym Now, the cvoy section is A 2000N M,CCw) N.A 400Mm 25 mm stvers( bending) due to M, NOYmal it is locate at A is n tensionSince 1Heve top MiS Peint Clockwise in sNEM is given by bending thet we Know y=distance to point A ydP2.5 mm rom Neutial-axs 700000x12.5 Ox N/mm I(25)H 4 T= 1 25 mm 64 64 Cx=456.33 MPa to due It is given 4 toYgue, 7,- she ar strems C distance ron centve to A C= d 5 mm N/ TXC Try Tay 800000x12.5 J-J 25 32 mm" X254 32 260.76 Ma

Sthess etement at Ai て =260-76M Lax 456.33 MPa Txy= 260.76 MPa Prinaple shemer Ox+Oy ox-oy 2 O,2 we know that 2 2. 50-0 2. 456.33 +56-33 +260.762 2 O,228.165 346,49 O 574.655 MPa O=228.165-34649 = -118.325 MPa Cmas =346.49 MI Pa divections: 2txy Ox-04 tan tan 20P 20s Ox-Oy 2 Txy - Piinciple Plamne angle -456.33 2260.76 angle 20 tan plane Sheay es 2*260.76 Os-20.593 20p 456-33 24.41 σ5 =19.325M 0,574.655MP Plane Phinciple ep.