Q5. Now you wish to identify a steel option for the portal frame. As such, considering the same load, W, what is the lightest universal beam (UB) steel section size that you would require in order to limit the lateral drift of the building to H/500? Note that you can again assume that the same steel UB section will be used for both the columns and beams (i.e. I_b = I_c). Also note that steel will not be affected by the load duration and that section tables provided at the back of the course reader provide section properties for different-sized steel sections. Report the section size, e.g. 360UB44.7.

Q4. Now you wish to investigate whether the timber glulam portal frame option sized in assignment 4 would be stiff enough. As such, use the equation above to check whether a 765mm x 120mm wide glulam beam section would be stiff enough to limit the lateral drift of the building (lateral displacement at top of columns divided by the column height) to H/500 for an SLS lateral wind load of W = 15kN (per portal frame)? Assume that the glulam section will be made with GL12 timber and you can assume that the same glulam section will be used for both the columns and beams (i.e. I_b = I_c).  Note that glulam material properties from AS NZS1720.1 are shown below. Note also, if required, that the load duration deformation modification factors (j₂ and j₃) for glulam are the same as those for sawn timber (reported in Table 2.3 of reader). Report the ratio of the displacement demand to the displacement limit in %.

Q2. In previous assignments it was noted that the initial proposal to use two timber sections for the main timber beams, to span the 3.6m between the columns on gridlines A and B1, was inadequate (and hence, four sections were trialed as an alternative). Now check if instead, a single steel 300PFC beam section would have adequate strength to resist a maximum moment demand, due to 1.2G+1.5Q, of M*= 57kNm. For this check, note that the beam is working in its major axis and that the floor joists provide lateral restraint of the beam. Consequently, you can assume here that no flexural-torsional buckling check is required and therefore, the nominal flexural strength of the beam can be taken as M_n = k_f∙Z∙fy (where k_f and Z can be obtained from tables – see the back of the course reader). Also note that the steel yield strength should be taken as f_y = 300MPa. Report the ratio of the moment demand to the factored moment resistance (M*/ϕM_n) in %.

Q3. Noting that a single steel 300PFC beam section appears to have adequate strength, now check if it would have adequate stiffness to limit the sag to L/300 over the 3.6m span when subject to a uniformly distributed SLS line load (for the mezzanine storage level), w, for G+Ψ_lQ, of w = 14.9kN/m. Analyse the beam as though it is simply supported over the 3.6m length (this is a conservative assumption) and assume that steel is not affected by creep. Report the ratio of the displacement demand to the displacement limit in %.

Q1. Do calculations to check whether the SG8 300mm x 50mm (i.e. 280 x 45mm) floor joists at the mezzanine level, spaced 300mm apart, have adequate stiffness to limit the sag to L/300, due to a uniformly distributed line load (for the mezzanine storage level), w, for G+Ψ_lQ, of w = 1.5kN/m. Treat the floor joists as though they are simply supported with a length of 3.0m (and moisture content is 15%). In addition, assume that the plywood sheeting means that the floor joists displace together (and so you can use average modulus of elasticity, E’). Report the ratio of the displacement demand to the displacement limit in %.

PART 2: BEAM MEMBER BENDING STRENGTH CHECK

Q4)b What is the ratio of demand to capacity; M_x*/ϕM_d,x? [%]

PART 3: TIMBER STUD COMBINED BENDING & COMPRESSION CHECK 

Q6. Do calculations to check whether the SG8 timber studs on gridline A, illustrated in Figure 10, with nominal section size 150mm x 50mm (these are rough sawn dimensions and once dried, assume section size is 140mm x 45mm) are able to sustain ULS loads due to 1.2G+Wu+ycQ of N*= 10kN in compression and M* = 1.3kNm. Report the critical ratio of demand (due to combined actions) to capacity (see Equations 3.27 & 3.28 in reader). For the column end restraint conditions, treat as “studs in light framing” (refer Table 3.1 of reader).  Report the answer on a scale of  0  to 1.

PART 2: BEAM MEMBER BENDING STRENGTH CHECK

Q5) Further to question 4, now check whether the beam size you identified in Question 4 can also resist the bending moment demand at the ends of the beam, where M* = -90kNm. Report the bending moment demand to capacity ratio (as a %).

What is the ratio of demand to capacity; M_x*/ϕM_d,x? [%]

PART 2: BEAM MEMBER BENDING STRENGTH CHECK

Q4) Now, for the portal frame, you wish to investigate whether a timber glulam portal frame could be used instead of the steel system shown in the sketches. The beam should be able to resist the bending moment demands shown in Figure 6 due to the load case of 1.4G. As such, do calculations to find the glulam portal section depth required to ensure the beam has sufficient flexural strength (be sure to check the member strength considering the possibility of flexural-torsional buckling). Assume that the glulam section will be 120mm wide, will use GL12 timber, and that you will need to specify the required section depth of the glulam considering 45mm laminations (see Figure 9). Glulam material properties from AS NZS1720.1 are provided. Size the beam section for the maximum bending moment acting at the mid-span of the beam, shown in Figure 6, of M* = 120kNm (and assume this value accounts for the self-weight of the beam). Report the bending moment demand to capacity ratio (as a %).

Q4)a What is the slenderness coefficient, S1?

PART 1: COLUMN MEMBER COMPRESSION CHECKS

Q2. In assignment 3 we checked the section strength of the SG8 timber studs in the wall along gridline A, with nominal section size 100mm x 50mm (these are rough sawn dimensions and once dried, assume section size is 90mm x 45mm) for a ULS compression load due to 1.2G+1.5Q of N*= 21kN. Now member buckling needs to be checked (i.e. do the checks as per Chapter 3 of reader) noting that the stud height is 3m and blocking is provided at 1m centers, as shown in Figure 8. Report the critical (maximum) ratio of axial force demand to capacity. For the buckling in the out-of-plane wall direction, treat as “studs in light framing” (refer Table 3.1 of reader) whereas for other direction, assume that buckling is not a problem as the wall lining would laterally restrain the post buckling in the line of the wall.

Report the ratio of the axial force demand to capacity (as a %).