McGILL UNIVERSITY Department of Civil Engineering and Applied ...
CIVE 318 STRUCTURAL ENGINEERING II
2010
McGILL UNIVERSITY Department of Civil Engineering and Applied Mechanics CIVE 318 STRUCTURAL ENGINEERING II ASSIGNMENT 1
Due Tuesday January 19
1. Select appropriate values for the Specified Strengths, fb, fv, fc (parallel to grain), and ft (parallel to grain), as well as the Modulus of Elasticity, E and E05, for the following cases: a) b) c) d) e)
DFir-L, No. 2 grade, 6 x 8 Eastern white pine, SS grade, 89 x 184 mm Balsam fir, No. 1grade, 191 x 241 mm Hem-Fir, No. 1 grade, 191 x 292 mm, load on wide face S-P-F, grade M-12, 2 x 6 (see Cl. 5.5.6.2.4 pg W73 for E05 definition)
2. Consider the layout of the floor system illustrated on pg. W31 of the course notes. Verify whether a 2 x 6 Hem-Fir No. 1 joist would be adequate to support a billiards room. The specified dead load is 0.80 kPa including the self-weight of the joists. Do not use live load reduction factors. The joist spacing is 300 mm o/c instead of 400 mm. The expected humidity and temperature in the building will be maintained at 70% and 20oC over a typical year. No treatment has been applied. A gypsum ceiling is to be screwed directly to the underside of the joists. Comment on what would need to be changed if the joists were not adequate. Show your calculations. 3. Determine the specified live load, wl (kN/m), that can be applied based on the bending moment and shear resistance of a simply supported fully braced (laterally) 38 x 235 mm western larch No. 2 beam. The beam is 6.0 m long, is not part of a system, has standard loading, is in a wet location and is incised and treated with a preservative. The specified dead load is 0.1 kN/m + the beam self-weight. For the same beam, where lateral support is only provided at its ends, determine wl and compare this value with that of the fully braced beam. Use a load combination of 1.25D + 1.5L. The density of western larch is 490 kg/m3. Show your calculations.
CIVE 318 STRUCTURAL ENGINEERING II
2010
4. Design the roof beam for the loading shown in Figure 1. Cedar sawn timber sections are to be used. The roof structure is composed of simply supported beams that span 5.0 m, and are spaced at 1.1 m on centre (o/c). Wood decking, which will be nailed to the top of the beams, is to act as the roof. No preservative is to be applied. The building is to house a swimming pool. The beams will be left exposed on their underside. The beams are supported on 75 mm long joist hangers. The specified dead load of the roof has been calculated as 0.6 kPa, although the self-weight of the beam has not yet been included in this value. The density of Cedar is 350 kg/m3. Use the beam selection tables in your course notes to help with the initial choice of a beam size in No. 1 grade wood. Using this initial selection, show all of your calculations required to prove that the beam is of adequate size. Consider ULS failure modes with the 1.25D + 1.5S + 0.5 L load combination. Consider deflection limits with the 1.0D + 1.0S + 0.5 L load combination. Show all calculations. 2.2 m
wS = 4.2 kPa
wS = 1.9 kPa wL = 1.0 kPa Roof deck (typ.)
wD = 0.6 kPa
Beam 5.2 m
Figure 1 The deflection can be estimated by superimposing the values obtained from the equations shown in Figure 2. Note: W for the triangular load is the total load on the beam (kN). 0.42L
W (kN) w (kN/m)
4
= 5wL 384EI
L
Figure 2
3 =7.81 WL EI
L
CIVE 318 STRUCTURAL ENGINEERING II
2010
McGILL UNIVERSITY Department of Civil Engineering and Applied Mechanics CIVE 318 STRUCTURAL ENGINEERING II ASSIGNMENT 2
Due Thursday January 28
1. A system of trusses spaced at 2.1 m o/c is used to support a viewing platform at the base of the Montmorency Falls as illustrated in Figure 1. Steel plates with 3/4” diameter bolts are used to connect all members. Note: the bolt holes are oversized by 1/16”. Hemlock 6 x 8 (No. 1) sections are used throughout unless noted otherwise. Decking will be placed on the top chords; assume that it does not provide lateral support. All members are incised and treated with a preservative. The trusses are subjected to dead (1.1 kPa (includes self-weight)), live (2.4 kPa), and snow (3.1 kPa) uniformly distributed loads. In addition, four temporary lifting attachments (12 kN each) have been placed along the bottom chord of the truss. Consider the load case in which all of the loads occur simultaneously. Use the 2005 NBCC ULS load case 1.25D + 1.5L + 0.5S. Note: member ‘E’ intersects member ‘B’ at 90o. a) Draw diagrams showing the forces found in all truss members given the load case above. b) Does member ‘B’ have adequate ultimate resistance to carry the loads shown? c) Does member ‘K’ have adequate ultimate resistance to carry the loads shown? d) Does member ‘A’ have adequate ultimate resistance to carry the loads shown? e) Does member ‘D’ have adequate ultimate resistance to carry the loads shown? Member D is 8 x 10 in size. Ignore deflection limits and bearing design. The direct moment amplification method may be used if needed. Use the centre-line dimensions shown for calculations.
Show all calculations.
CIVE 318 STRUCTURAL ENGINEERING II
wD wL
2010 Connection Info.
wS
‘F’ Member 'E’
Section ‘A’
Deck
2000
Member 'A’ ‘K’
Member 'G’ ‘L’
‘M’
‘O’
‘N’
‘P’
Member 'C’
Member 'B’
600 600 PL PL Member 'D’
1628
2200
1345
Member 'H’
Member 'I’
2200
600 600 PL PL Member 'J’
2200
2200
Elevation Section ‘A’
2100
2100
Cross-bracing (lat. support) (typ)
2200
2200
2200
2200
Plan Roof deck Top chord
Steel plate
Bolt
Truss
Truss
Truss
2000
Diagonal
Bottom chord
Connections 2100
2100
Section ‘A’
Figure 1 Schematics of typical truss in wood structure (dimensions in mm)
2010
McGILL UNIVERSITY Department of Civil Engineering and Applied Mechanics CIVE 318 STRUCTURAL ENGINEERING II ASSIGNMENT 1
Due Tuesday January 19
1. Select appropriate values for the Specified Strengths, fb, fv, fc (parallel to grain), and ft (parallel to grain), as well as the Modulus of Elasticity, E and E05, for the following cases: a) b) c) d) e)
DFir-L, No. 2 grade, 6 x 8 Eastern white pine, SS grade, 89 x 184 mm Balsam fir, No. 1grade, 191 x 241 mm Hem-Fir, No. 1 grade, 191 x 292 mm, load on wide face S-P-F, grade M-12, 2 x 6 (see Cl. 5.5.6.2.4 pg W73 for E05 definition)
2. Consider the layout of the floor system illustrated on pg. W31 of the course notes. Verify whether a 2 x 6 Hem-Fir No. 1 joist would be adequate to support a billiards room. The specified dead load is 0.80 kPa including the self-weight of the joists. Do not use live load reduction factors. The joist spacing is 300 mm o/c instead of 400 mm. The expected humidity and temperature in the building will be maintained at 70% and 20oC over a typical year. No treatment has been applied. A gypsum ceiling is to be screwed directly to the underside of the joists. Comment on what would need to be changed if the joists were not adequate. Show your calculations. 3. Determine the specified live load, wl (kN/m), that can be applied based on the bending moment and shear resistance of a simply supported fully braced (laterally) 38 x 235 mm western larch No. 2 beam. The beam is 6.0 m long, is not part of a system, has standard loading, is in a wet location and is incised and treated with a preservative. The specified dead load is 0.1 kN/m + the beam self-weight. For the same beam, where lateral support is only provided at its ends, determine wl and compare this value with that of the fully braced beam. Use a load combination of 1.25D + 1.5L. The density of western larch is 490 kg/m3. Show your calculations.
CIVE 318 STRUCTURAL ENGINEERING II
2010
4. Design the roof beam for the loading shown in Figure 1. Cedar sawn timber sections are to be used. The roof structure is composed of simply supported beams that span 5.0 m, and are spaced at 1.1 m on centre (o/c). Wood decking, which will be nailed to the top of the beams, is to act as the roof. No preservative is to be applied. The building is to house a swimming pool. The beams will be left exposed on their underside. The beams are supported on 75 mm long joist hangers. The specified dead load of the roof has been calculated as 0.6 kPa, although the self-weight of the beam has not yet been included in this value. The density of Cedar is 350 kg/m3. Use the beam selection tables in your course notes to help with the initial choice of a beam size in No. 1 grade wood. Using this initial selection, show all of your calculations required to prove that the beam is of adequate size. Consider ULS failure modes with the 1.25D + 1.5S + 0.5 L load combination. Consider deflection limits with the 1.0D + 1.0S + 0.5 L load combination. Show all calculations. 2.2 m
wS = 4.2 kPa
wS = 1.9 kPa wL = 1.0 kPa Roof deck (typ.)
wD = 0.6 kPa
Beam 5.2 m
Figure 1 The deflection can be estimated by superimposing the values obtained from the equations shown in Figure 2. Note: W for the triangular load is the total load on the beam (kN). 0.42L
W (kN) w (kN/m)
4
= 5wL 384EI
L
Figure 2
3 =7.81 WL EI
L
CIVE 318 STRUCTURAL ENGINEERING II
2010
McGILL UNIVERSITY Department of Civil Engineering and Applied Mechanics CIVE 318 STRUCTURAL ENGINEERING II ASSIGNMENT 2
Due Thursday January 28
1. A system of trusses spaced at 2.1 m o/c is used to support a viewing platform at the base of the Montmorency Falls as illustrated in Figure 1. Steel plates with 3/4” diameter bolts are used to connect all members. Note: the bolt holes are oversized by 1/16”. Hemlock 6 x 8 (No. 1) sections are used throughout unless noted otherwise. Decking will be placed on the top chords; assume that it does not provide lateral support. All members are incised and treated with a preservative. The trusses are subjected to dead (1.1 kPa (includes self-weight)), live (2.4 kPa), and snow (3.1 kPa) uniformly distributed loads. In addition, four temporary lifting attachments (12 kN each) have been placed along the bottom chord of the truss. Consider the load case in which all of the loads occur simultaneously. Use the 2005 NBCC ULS load case 1.25D + 1.5L + 0.5S. Note: member ‘E’ intersects member ‘B’ at 90o. a) Draw diagrams showing the forces found in all truss members given the load case above. b) Does member ‘B’ have adequate ultimate resistance to carry the loads shown? c) Does member ‘K’ have adequate ultimate resistance to carry the loads shown? d) Does member ‘A’ have adequate ultimate resistance to carry the loads shown? e) Does member ‘D’ have adequate ultimate resistance to carry the loads shown? Member D is 8 x 10 in size. Ignore deflection limits and bearing design. The direct moment amplification method may be used if needed. Use the centre-line dimensions shown for calculations.
Show all calculations.
CIVE 318 STRUCTURAL ENGINEERING II
wD wL
2010 Connection Info.
wS
‘F’ Member 'E’
Section ‘A’
Deck
2000
Member 'A’ ‘K’
Member 'G’ ‘L’
‘M’
‘O’
‘N’
‘P’
Member 'C’
Member 'B’
600 600 PL PL Member 'D’
1628
2200
1345
Member 'H’
Member 'I’
2200
600 600 PL PL Member 'J’
2200
2200
Elevation Section ‘A’
2100
2100
Cross-bracing (lat. support) (typ)
2200
2200
2200
2200
Plan Roof deck Top chord
Steel plate
Bolt
Truss
Truss
Truss
2000
Diagonal
Bottom chord
Connections 2100
2100
Section ‘A’
Figure 1 Schematics of typical truss in wood structure (dimensions in mm)
