Question

Q1. A 2 m long T-beam is built-in at one end and has a force of 7 kN applied at its free end. The dimensions of the cross-section of the beam are shown in Fig. Q1 and the force acts at 10° to the vertical though the centroid of the section. 7 KN 1 -10° 251 -y 100 1 44 32 44 all dimensions in mm Fig. Q1 - Cross-sectional Dimensions of T-beam (a) Find the position of the centroid of the section and its second moments of areal, and le [6 marks] (b) Determine the orientation of the neutral axis and sketch the distribution of stress across the section [6 marks] (c) Locate the points of highest tensile and compressive stresses in the section. Is the largest magnitude of stress tensile or compressive? [7 marks] contd. nas

Answer 1

Som Gives T- section! pZ K 120 mpos 25 mm two mm oy (al K44- Centroid: AZ line N(K) G (Centroid) -Reference Clearly, Gy=0) { Symmeroic about ze asis) Z (160x32x59) +(25X120)% (100 +12:5) (1WX32 + 120x25) Z 5 80-24 mas frem reference tine centroid (0, 80.24 m). ماه لي Iz = 25X1203 + 12x323 38730661667 mm 12 12 12 12 24-1123 Ip = .3241 10? + 100232 *(80.24-50)?+ 120%2534 broxx) (80-2 = 2666666.67 2926264.32 + 156250 + 322212208 Iy = 88713 03.72 mmt [b] Orientation of natural aris: the neupal asis is oriented at ž= 80.24 mm fooon better reference line for verscal components force nerile g=0 for horizontal component of force. CS

Stress-distribution: vertical component of fooce = 760010" = 6.89 ka Horizontal component of force = 751010 2 = 1.21556 bone Bending Shear stress Stress 17Sinzo Obman z fig. 2 Berding Shear Shen (toen the Element shown by 0 has morumum tensile stress While element has mascerurss compressive shesse clearly, yo bomar I mora A T Stress permit vength clearly from figure Y, KY 2 Ebeltool Clagnitude of tensile stress is lesser than magnetide of compressive (6.890% 64.26 - 34076 Megln [cne w perspical compo 8871301.22 net of force tenile 6.89 x 80.24 62.22 m2 (compressive) 8871,303.312 Eb1 = I Eb2 l CSC

due to horizontal component of force fy= 1.2155 kn b= 1: 2155 * (U4+16) = 1883 Mpalon 3873066.667 1.2155 X 16 G62 I 5.02:12 Miplom 387 3066.662 or total tensile stress = 53.59 on P.)m. total compress, vespress = 6703721989) om (6232 +503413) Clearly, Compressive smess is the largest value (al ween force is vertical: resile stress = im Iy loxe Jonan x &4.26 887130.22 = 50. Uslorian Compressive stress = lox ex 80.24 8871303.72 = 90.440MPS i % chaye in teasile = 20653:59-50.45 9.45) Xw a 5.81 53.55 chage in Compressive a sones g0.64 – 67132) XIw= 34,4% 67.32 CS
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