See sketch in attachment
The sketch overleaf shows part of the structure of a timber portal-truss building whose timber floor is supported on double Gluelam timber cross-beams which span between posts on lines 2 and 4 then continue at each end for 1.4 m as cantilevers to lines 1 and 5. The beams are spaced at “E” metres where E is given by:
E = 0.6(5000+(e + f)*50)/1000 (e and f are the fifth & sixth integers of your student number)
All roof and wall load paths go through the lower columns leaving the cross-beams to support floor loads only. Assume the dead load G, over the floor area (timber structure and linings) is 0.5 kN/m2 overall. The applicable live load, Q is 3 kN/m2 overall. In this case, factors for strength limit state design are W*=1.25G +1.5Q and those for serviceability (deflection) are Ws=1.0G +0.5Q.
The central span "L" (metres), between lines 2 and 4 is given by: L = (6000+(f + g)*50)/1000 (f and g are the last two integers of your student number). Both cantilever spans (N) are 1.4 m.
a) Considering gravity loads only, assess the region of the floor contributing to the line load on a typical double cross-beam (say Line D) which spans "L" metres between lines 2 and 4 and cantilevers 1.4 m at each end to lines 1 and 5. Use the calculated load-width (equal to the cross-beam spacing) with the data and factors given to quantify the design line loads (kN/m) for strength, W* and for serviceability, Ws (ignore the beam's self weight and consider floor loads only).
b) Use the expressions overleaf to quantify the maximum positive design bending moment, M* (kN.m) caused by W* (kN/m).
c) From the available double Gluelam GL18 timber beam sections shown in the table below, choose a beam (call it Section 1) that would have just sufficient bending moment capacity to support the floor on line D. i.e. a beam whose moment capacity (M) is just greater than the design ultimate bending moment, M* (note: M = f’bZx ). , the capacity reduction factor = 0.85. The characteristic bending strength of GL18 timber, f’b is 50 MPa. The Modulus of Elasticity, E of GL18 Gluelam timber is 18000 MPa. (Note that 1MPa = 1N/mm^2, 1 kPa=1kN/m^2)
d) Using the expression overleaf with the cross-section and material properties of the Section 1 double beam selected above, calculate the long-term central deflection using a creep factor, J of 1.5. Compare the deflection with the allowable limit of Span/240. If the cross-beam deflects more than the limit, up-size it so the deflection criteria is met (call this “Section 2”). Please enter your answers in the Structures Assignment Results Table available on Moodle and upload your completed table to the submission folder for your tutorial group. Retain neat calculations to support your answers.
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