a) Calculate under linear elastic conditions the angle of twist at mid-span, axial stresses at positions...

  

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a) Calculate under linear elastic conditions the angle of twist at mid-span, axial stresses at positions 1 to 7 for a cross-section located at mid-span and shear stresses at 1 to 7 for a cross-section located at the left support. The beam is subjected to a uniformly distributed load qa = 40,0kN/m. The beam is simply supported having end-forked conditions, i.e. no restraints against bending and warping but fully restrained against twisting. All cross-sectional parts have equal material properties with E210000 MPa and G= 81 000 MPa. NOTE that the profile is cut open with a thin slot at positions 3 and 4, which extends along the whole beam. The profile is, therefore, an open C-section. b) Carry out the analysis one more time, but now under the assumption that the slot is closed, i.e. no slot exists so that the section is a closed box-section. The section is made of flat steel plates that have been welded together at the corners. The welds are not shown in the figure. All dimensions are: Flange width b = 68mm Plate thickness t = 4,0mm Beam depth h = 108mm Length of span L = 1200mm Note that b and h are measured from the centre line of each plate. AH 4z, Ed A a) Calculate under linear elastic conditions the angle of twist at mid-span, axial stresses at positions 1 to 7 for a cross-section located at mid-span and shear stresses at 1 to 7 for a cross-section located at the left support. The beam is subjected to a uniformly distributed load qa = 40,0kN/m. The beam is simply supported having end-forked conditions, i.e. no restraints against bending and warping but fully restrained against twisting. All cross-sectional parts have equal material properties with E210000 MPa and G= 81 000 MPa. NOTE that the profile is cut open with a thin slot at positions 3 and 4, which extends along the whole beam. The profile is, therefore, an open C-section. b) Carry out the analysis one more time, but now under the assumption that the slot is closed, i.e. no slot exists so that the section is a closed box-section. The section is made of flat steel plates that have been welded together at the corners. The welds are not shown in the figure. All dimensions are: Flange width b = 68mm Plate thickness t = 4,0mm Beam depth h = 108mm Length of span L = 1200mm Note that b and h are measured from the centre line of each plate. AH 4z, Ed A

Answer rating: 100% (QA)

Solutions Step 1 Given data b68mm t4mm h108mm L1200mm12m qziED40KN m E210GPa G81GPa now Drawing FBD ... View the full answer