Question

Aroadway sign that weighs Py = 12 kN is supported by a structural pipe with an outside diameter of 300 mm and a wall thickness of 12.5 mm. Wind pressure on the sign creates a resultant force of P, - 18 kN, acting as shown. Using length dimensions of a = 4.5 m and b = 6.1 m, determine (a) the normal and shear stresses at point H. (b) the normal and shear stresses at point K. P. H K Answers (a) Point H: 0x i MPa Oy MPa Txy i MPa (b) Point Koy MPa 0 MPa Та MPa

Answer 1

solutions do = 3oo him tz 12.5mm Py = 12kN P2 = 18kN a = 4S m b=6.1m Inside diameten, diz do-ata 300- 2 x 12.5 275 mm the pipez As? (dor-di) X Area of ((3001?-(273)") 4 = 11 290.098 mm? Popo Polau moment g Invitia J. 2 (do - di" 32 Д ((300;" 127514) 233.74 x 100 mm 4 Moment Inertia cross section about x and you ins: I= I (do_di) 116.87 x 106 mm 4 0 of 4 - 64 3 cross sectional area = 0 03 I cdo -d) Transverse 12 516 927.084 m2y3 Now, Fy = - Py -12 EN 1 Normal al point force elements Ez = -P2 = -181N H and to bending woment al H and K k , Max Mx=-Pyra =-18000 x us oo mu = -81x100 Naim My - P₂ xb = 109.88106 N.mm 18000 x 6100 =

M2 = Py xb 12000 x 6loomem 6. 73.2 x 10 N mm at point point for 12000 Oy - -1.063 MPa wala A 1 1290.098 ما Myz -81x100x 300 - 103.9619 Pa I 116.87 x 106 + og 1.063 -103.96 105.025 MPa og 109.8x106x300 194c 70.46 MPa 2 2 Txy E Myc J 233. 74 x 106 at Point Ko- 1.063 Mpa @ P - 12000 il A 1 1 29o.o98 FzQ 18000 x 5 26.927.084 Tyz I ldo-dil 116.87 x 100 (25mm) 3. 185 MPa

Туг shwa - To9 - х 10 6 x 15 о т 2 3 3 . ux (o6 - 10, Ч6 A P4 Now 42 с 1 х г: St. os | x 90 x ° I 991 x ta - 9TTE - - 3.95 MP4 — 93 - 95-1.0D 63 “Я " = 95-64 MP4 о; г до: Ч6 - 31PG "у? — — 1 3. бЧs MPa

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