Question

A WT305 × 41 standard steel shape is used to support the loads shown on the beam. The dimensions from the top and bottom of the shape to the centroidal axis are shown in the sketch of the cross section. Assume L_AB = 3 m, L_BC = 3 m, L_CD = 3 m, P_A = 17 kN, w_BC = 11 kN/m. Consider the entire 9-m length of the beam and determine:
(a) the maximum tension bending stress σT at any location along the beam, and
(b) the maximum compression bending stress σC at any location along the beam.

Answer 1

PA WBC mm sis ste TO А 3 Ro RB PA =) 14kn EFX=0 RB + PD - WBC (BC) - PA = 6 RB + Rp = WCBC) + PA -> (11x 3)+17 z) 33+17 SO-> EMB=0 - Pb (BC+ CD) + WAL (BO) (B4) - PA (AB) = 0 W (Bc)? - PALAB) ROCBC4CD) RB + Rp ) es 2 R(6 دح 11x3? -1.5 = 1703) 49.5-51 = Rp (6) Ro (6) Ro= -0.25 kn PB=50-(-0.25) RB = 50+ 0.25 50.25 ka RB

we Draw BMO (Bending moment diagram) Bl at Do C -0.25% (3) 7) – 0-75 kwa B= -0.2516) -.. "() B -1.5 - 49.5 =) -51 kom Ato 17 mmmm 10.25 50125 - 0075 y=x2 - 51 Masamem bending moment =) Sikam Iz for W 730374) 2) 48.78 105 mmy from Properties of (WT 30541) ( Bending equation) 4 0 y I R 6 ty => 1.0472 y o= SIX16 4807x106 Maxium tensile strey =) 1.0472x 88.9 (upper layer ly=88.a) z) z) 193.996N/mm2 Max Compressive stres) y=211.1mm on 1.0472x 211.8mm (lower player) 221.063 N/mm