Question

QI A cantilever steel beam of length L 7.5 m carries both a uniformly distributed load w of 20 kN/m throughout its length and a point load P of 10 kN at its free end, as shown in Figure QI (a). The beam is made from a rectangular hollow box section with a width of 300 mm and a depth of 450 mm (refer to Figure Q1 (b)). The wall thickness of the box section is constant throughout which is 20 mm. Self-weight of the beam is neglected. 300 mm P = 10 KN W= 20 kN/m 450 mm 7.5 m 20 mm Figure Q1 (a) Figure Q1 (b) (a) Determine the maximum bending moment of the beam. [5] (b) Calculate the maximum bending stress of the beam and draw the corresp ding bending stress distribution across the section. [10] (c) If the beam is subject to an additional axial tensile load of 500 kN at its free end, calculate the maximum longitudinal stresses and draw the resulting stress distribution across the section. [10]

Answer 1

sol Ma 1972 = 20 kolm Paloka Centre 75am B va {fyzo y Vaz to + 20x7.5 -1600 KN €79120 >>) - Ma + 20x7.5x7.5 10x7.520 Ma = 637.5kNim. (s) Maximum Bending moment of the beam is Maz 637.5 kNm. k Boomm 182.761 Hension Tar 5mm 225mm ANA 166.51 som pasti 4lomm 166.515 450mm to comprension Pro 182.515 k A 260 fArea of cool -section) Az 300x450 - (300–2x20) * (450-2420) 28400 mm INA 300x4503 260x4103 -784836666.7mmy 12 12 mx y 637.5x 106 x 225 182.768 N/mman Oman INIA 784836666.7 6 637,5x10x205 - 166.515N/mm2 mina mx Y, INA 7848366667

arial tensile load of 500 kn at the free end. additional (c) If the beam is subject to Longitisairal omal & Maximum stresses p = 5ooko -PM DY A on that & INA 500 xlooo - + 182:761 man 28400 = 2001367 N/mm (Tension Stol 200 2367 AD E ( T ) 184.121 ENA G 148.960 H: 65-155 stress distribution 2001367 N/mm² (Tension), of man P f MY, INA = A soonloo -+166-515 28400 2184.121N/mm Sooxloo 4_1827612-1651155 28400 (com Pi MY INA A pronion) Imm? of = МЧ, INA 500 xloo $166.5152 A 28100 (comprenion) =-148.91014mm