Question

For the joint and loading shown, determine the stress states at points A and B on section-aa, and the principle stresses at point A. The free-body diagram including section-aa is given below for your convenience. Section-aa has a rectangular cross-section area of thickness 12 mm (shown) and width 18 mm. a) Sketch each stress state using a square stress element. b) Determine the principle stresses at point A (no need to sketch the stress element).

Problem 1: (25%) For the joint and loading shown, determine the stress states at points A and B on section-aa, and the principle stresses at point A. The free-body diagram including section-aa is given below for your convenience. Section-aa has a rectangular cross-section area of thickness 12 mm (shown) and width 18 mm. 12 mm 0.75 kN a) Sketch each stress state using a square stress element. b) Determine the principle stresses at point A (no need to sketch the stress element). 32 mm 1 kN FBD: 1 KN 5.5 kN.mm 0.75 KN 50 mm 0.75 KN 32 mm I KN li hii 1,

Answer 1

arven Goss-sechon G-ą 5.5 KN-mm -at inato- BLI KWT 1 o. 75 KM 18 mm 12mm A) for state of stress at A. YA 1000 5a Due to aniol Normal stress Due to axial load of 1 kN -6 - [isa Rice] ED12x18 1 Ga = 4.629 MPa Shear stres de to, Egypte= (3-4) (242) Sif = 0.75 KM Тачь 12x 18 x 3 526] Caa Grz ing = 0.45X10Ⓡ 12818 x 3 Tex 18x123 x 18 CT2 V Cam speroune mon 10.416 MPa direchty araxis 2-face CS Scanned with. CamScanner

= 66 M Normal spons due to bending moment My = 5.5 land-mm at point A Tobool (as yoo (on NA)] NetNormal force = o- Gat 62 = 4.629 +0 o=4.629 Mial Net sheas fora - T24877 = 10.416 MPa. PPP IP IPPPPPP stress element at A. OA 57:5 = 4.629 MPa. Tanz = 10:416 MPa For state of stress at B. Normal smens due axia) - Gat lood I lear loro (2x18 Scanned with CamScanner 5a = 4.629 mipal

e Tx7 Sheas sten due to S-F = 0.75 KN. (S«fo) AJC91) Тань Typ : 0 as alea abone] point B is zuio Normal show due to e 02 Bending momenta Bing 5.5 kW-om EN * +5.5 * 403x(-6) Tax 18x12% 67 -12.7314 MPa. - Net Normal Shens = = Go to = 4.629 -12-7314 6 = -8.1024 Net Sheas stress - Taz = 0 Stres element at B. 6758.1024 MPa Scanned with CamScanner

b) principle pros at point A. 612 - 62 - 6x2 *w = 695): 10299 +689347 Tiia - (9.1 / (4-629*+ 60.40652 535 572 = 2.314 I 10.67 6 = 12.98.4 MParl Jary 62 = -8.356 MPa CS Scanned with CamScanner

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