The beam AB shown below in Figure 3 has the cross section as shown. The beam has been fabricated by welding a 150 x 50 x 5.0 RHS (Rectangular Hollow Section) to two sections of flat plate; 150 mm x 10 mm and 120 mm x 24 mm as shown in Figure 3. The geometric properties for the 150 x 50 x 5.0 RHS are shown tabulated in Figure 4.  

(a) Ignoring the self weight of the beam, show that the internal actions in the beam immediately to the right of Point A are: Axial Force P = -34.64 kN, Shear Force V = +20.0 kN and Bending Moment M = - 50.0 kNm. 

(b) Locate the centroidal axis (find   y bar   ) and show that Iz = 42.83 x 106 mm4 

(c) Sketch the distribution of normal stresses due to axial force and bending moment over the beam cross section at A. Show keys values.

(d) Determine the shear stress in the beam at A, at section y-y (immediately above the junction of the web and the bottom flange). Hence determine the maximum and minimum principal normal stresses also at this location.

40 kN B 30 2.5 m Rectangular hollow section: 150 x 50 x 5.0 RHS 25mm Z, - -eid ----- 25mm 150 mm 10mm 24 mm 120 mm Section 1-1 (cross section of beam) TABLE 1.2-15(A) DIMENSIONS AND PROPERTIES RECTANGULAR HOLLOW SECTIONS : GRADE C350 DIMENSIONS AND RATIOS PROPERTIES Designation About x-axis About y-axis Jorsion Conatant per m Tonion S. Area 10mm 10'mm 243 10mm 10'mm 10mm mm 10mm 10mm 250 x 150 x 9.0RHS 53.7 327 24 324 60 KORH 3810 150 200 x 100 x 9.0RHS 228 153 11 26.2 22.1 14.7 180 142 121 6.OHHS 16.7 167 144 192 983 41.8 14.4 91. 98 150 x 100 x 6.0RHS 5.ORHS 4ORHS 180 280 109 134 951 6.64 2.30 182 2310 707 78.2 63.0 150 x 50 x 5 ORHS 59.2 49.8 78.9 30.6 35.7 1480 374 es 4 50 2 0.65 26.1 29 21.0 125 x 75 x 5.0euS 116 168 293 3.05 139 75.3 1480 37.0 311 316 3ORHS 100 x 50 x 6.0RHS 33.4 0.56 14.7 1.53 1,35 1.13 0.886 0.754 0.593 0.259 1.71 15 409 36 342 45.3 10.3 8.0 30. 398 27. 24. 34.1 0.11 20.4 19.7 20.2 1.31 20.6 31.2 3.5AHS 3.ORHS 213 35.6 0.36 1.06 75 x 50 x 4.0RHS 3.0RHS 65 x 35 x 3.0RHS 6.92 10.5 0.630 22.7 16.8 21.1 26.7 275 228 0.335 0278 13.4 160 19.5 200 14.0 4.25 367 197 541 0.281 8.65 110 106 6.04 71 10.4 N 1-