Question

Problem 5 The cross-section shown below is subject to a positive internal bending moment M = 60 kNm applied about the local z-axis of the section. Determine the maximum tensile and compressive normal stresses in this section due to this internal moment. 200 mm - 25 mm 25 mm 150 mm comp = -79.8 MPa O ten = 118.3 MPa 25 mm 100 mm

Answer 1

Note: Figure Not scale Moment - bokn-in Drawn to x zoomm 2.Swim D smm 180 56 mm Isomn -- - - 25 mm --* - center'dal Ayus 119.44mm 25mm I Toomm 17.5 min solution : Calculating the Distence from centroid of section and bottom of the section [ý]. Let A = Area of Top gange = 200x25 = 5000 mm" Az = Avea of web= 25x150 = 3750mm² A3= Avea of Bolton jonge = 100x 25= 2500 mm Let yi= Distence of controid of top flenge from bottom 2 yı= 25+ 150+2 → yo = 189 Ye = Distence of contrond of web from bottom Y2 = 25+ 150 = 25+ 75 = loomma y3 = Distence of centurid of Bottom flange from Botton 73 = 29 = 1205 mm. As we know ý - Algi + Az Y 2 + A343 . Ai e As f Az

* [Fsơ x 1815]t [350 x so] + [2500 x1251 5000 +-3750 +2500 s ģ= 119.44 mm fence from of Centroid bottom: section is at Distance of 119°44mm Now calculating moment of Inertion of section about centuridal Axis in calculating moment of Ireetion of Top flonge about centre of Gravity [I ] I, = In + Area of longe x [Distence] Parallel Axis Theory I1 - 200x25° + Sooo x [1975-19.00]" Note we knows Iq=bd3 12 12 » Il = 23421234,67 umy in calenlating moment of Fuentia of web about contue of Guarity (I.) Iz = 25x1503 Iz=7031250mm"

IT) Calculating Merment of Inertia of Bolton flange . about centre of Gravity (Is) - Iz = In + Area of Boltorn flange + [Distree]² 9 Iz = 100x 25° + 2500x 5119.44-1205]" 12 → Iz = 20720617.33 mmy Hence Total Moment of Ivertia of the section about centuridal of Neutral Axis will be as Is It Is t I3 =23421234.67 +7031250 + 28720617:33 ~ l I - 59173102 mma ! and Tensile stresses Calculation of compressive is Compressive Stress We know £ = Moment [Euler Founda] Inuti

Neys fere f = compressive strees - Yc = Distence of Top Jobie from conturital oxis ► yo- 80156 mm Given Moment = 60x10°-N-mm Неми + box No 6 - 80.56 59173102 f = 80 N/mm2 = 80 MPa. corupucisive shees + Negative conventuri & compressive stices =-80 Mpal Answer moxinuem in Tensile stress we know I = moment Y Ivectia Here - Yt= Distence of Bottom fibve grona centendal Axis = 119.44 mm f = Tensile strees Answer £ . a boxloo SANAT - f = 119 mpa 119.44 59173102 | Tensile + Tensile stuus = 119 MPa Maxel mun