Question

Please hel me solve this problem

1n 035 n Fepure 4: Signheard Fieure S: Cross section 3) Th·botal slear and iwrmal streses at point Λ ef the trees wrtín af the cehama. The b) maximum ณ.rmal star" snd the sh sol." mashaumshest stre" at the ssme Paint Problem 3 :30 points) Wind laadw 1 m 05m 2 m 25 0.75 m Figure 4: Signhoard Figure 5: Cross section Figure 4 shows a sign board used to indicate some directions on the street. The signboarod supports a wind load W 1.5 kPa. Moreover, the signboard has a volumetric mass p 2700 kg/ m2 and a thickness of 5 mm. Neglecting the weight of the column supporting the signboard and using the gravity's acceleration g = 9.81 m/s, find: a) The total shear and normal stresses at point A of the cross section of the cohumn. The column has a c me ular cross section of radius R-20:nm b) The maximum normal stress and the ah solute maximum shear stress at the same point A. The Debate Club Page 9 of 17

Answer 1

Draw the free body diagram of the sign board. Wind loadw 05 m 25 0.75 m Calculate the bending moment at section M,-Wx(2.5-0.75) -(2700> (2x1)(0005)x981)-(25-075) 463.52 Nm

Calculate the stress due to bending at point A (463.52) (0.020) rx (0.020) 7.377×107 Pa 73.77 MPa Calculate the axial compressive stress due to weight of the sign board TTR (2700x(2x1)(0.005)x 9.81) π(0.020) -2.108 x105 Pa -0.211 MPa Calculate the torque developed at free end due to wind load (1.5x10x(1x2))(1.5) - 4500 N-m Calculate the shear stress due to developed torque

TR (4500) (0.020) π(0.020 )4 -3.581x10* Pa - 35.81MPa Calculate the maximum normal stress at same point A. 73.774(-0.211). 73.77-(-0211) +(35.81) 73.77(-0273.77-(-0.211) +(35.81) -88.264 MPa 73.774(-0211)-r73.77-(-0.211)). (358 σ -14.705 MPa

Calculate the maximum shear stress at same point A. 73.77-(-0.211) 4(35.81)2 51.485 MPa