Lateral Forces and Frames (Advanced Structures)

Quiz 2: Lateral Forces and Frames

Elementary School

Los Angeles, California

High Seismic Zone

Project Summary

Building Type: Elementary School

Location: Los Angeles, California, 90012

Primary Structural System: Mass Timber

Our team was tasked with option A: the high seismic zone of Los Angeles California. Because of this, mass timber was selected as the structural system. A timber based structural system as several benefits when combating seismic forces. Timber is somewhat ductile and able to dissipate energy. It also allows the flexibility to move, enhanced when using eccentric bracing. The grid of the system was planned to best fit the given architectural plans for the elementary school. 15’ by 22’-6” bays fit nicely into the plan, limiting the encroachment of columns: most columns end up in walls. These dimensions also work well for the span of glulam beams. Mass timber also has an aesthetic appeal if left exposed. Glulam-steel trusses are used span the gym roof due to the lower self-weight and higher strength. Eccentric bracing is utilized at the corner bays at every level of the building.

https://www.naturallywood.com/project/university-of-british-columbiaearth-sciences-building/

Quiz 2

Matthew Malski

Kaung Kyaw

Elementary School

High Seismic Zone

Los Angeles, California

Beams

Glulam beams were used for the typical horizontal member. They were sized utilizing the table from The Architect's Studio Companion. The beams run in the major span of 22’-6”. With this span, beam depth was estimated to be 15”.

Decking

Mass timber decking was utilized for the decking. While this would most likely take the form of dowel laminated timber panels, the wood decking chart in The Architect's Studio Companion was used for preliminary sizing. The decking runs in the minor span of 15’. Using this span, decking depth was estimated at 6” for floor decking. 4” could be utilized for roof decking due to lighter loads.

Matthew Malski

Kaung Kyaw Elementary School

Typ. Columns

Glulam columns were utilized for the typical vertical member. Because no glulam column sizing table exists in The Architect's Studio Companion, the wood column table was used. Glulam was considered the strong woods category. The total tributary area was estimated at 1518.75’ for all levels supported by the typical column (including the mezzanine). Using this number, a 10” x 10” column would suffice. Rectangular sections appear more commonly for glulam columns, so a 10” x 12” section was used.

Roof Columns

Due to the extra load of columns carrying the roof trusses, a double column section was used. This section is connected at various intervals by wood chocks, which allow the beams to connect to the column, while restraining it from buckling. Because this column spans all floors of the building, it was considered as a tall column. It was sized using the tall wood column table from The Architect's Studio Companion. The tallest unbraced height of the column is 15’ and the total tributary area (including the roof) is estimated at 1350 SF. A 14” x 14” column fits this requirement, giving a cross-sectional area of 196 square inches. This was split between two 8.75” x 12” columns (210 square inches).

Roof Trusses

The trusses that support the roof over the gym are glulam-steel composite trusses. A glulam beam forms the top chord, taking most of the compressive forces. Steel rods form the bottom chord, taking most of the tension forces. HSS tubes form the vertical webs, due to the possible compressive forces present. HSS tubes are also used at the rends of the bottom chord to allow for a rigid connection to the double columns. A Pratt format was used for the diagonals since, in this configuration, the diagonals would be in tension. Steel rods then can be used for the diagonals.

The composite construction of the truss was chosen to reduce the dead weight of the truss and decrease its depth. Both the heavy timber truss table and the steel truss table from The Architect's Studio Companion were used for estimated sizing. The span is 90’ for the roof. Both charts for the parallel chord truss suggested a 8’ deep truss. This posed a problem for head clearance on the balcony, however, so 7’ was used for the depth. To make up for this loss in depth, a deeper glulam top chord was used, with larger steel sections.

Fall 2023

Matthew Malski

Kaung Kyaw Elementary School

Los Angeles, California High Seismic Zone

Member Sizing

The Kendeda Building is an example utilizing glulam-steel trusses

8.75” x 12”

Glulam Beams for Stair & Elevator Framing

10.75” x 12”

Glulam Column Typ.

Glulam Column for Roof Trusses

Matthew Malski

8.75” x 15”

Glulam Beams Typ.

6” Mass Timber Decking Typ.

8.75” x 12”

Glulam Eccentric Cross Bracing

Glulam Column Typ. 8.75” x 12”

Glulam Beams for Stair & Elevator Framing

Glulam Beams Typ.

6” Mass Timber Decking Typ.

8.75” x 12”

Glulam Eccentric Cross Bracing

Glulam Beams for Stair & Elevator Framing

Glulam Beams Typ.

6” Mass Timber Decking Typ.

8.75” x 12”

Glulam Eccentric Cross Bracing

8.75” x 12”

Glulam Beams for Stair & Elevator

Framing

10.75” x 12”

Glulam Column

Typ.

Double 8.75” x 12”

Glulam Column for Roof Trusses

Fall 2023

Quiz 2

8.75” x 15”

Glulam Beams Typ.

Matthew Malski

Kaung Kyaw

Elementary School

Los Angeles, California

8.75” x 12”

Glulam Mezzanine Bracing

6” Mass Timber Decking Typ.

High Seismic Zone

8.75” x 12”

Glulam Eccentric Cross Bracing

Mezzanine

Structural

Glulam-Steel Composite Truss:

8.75” x 24” Glulam Top Chord, HSS Round Tubes for vertical members, Steel Rods for Diagonals and Bottom Chord

Quiz 2

Double 8.75” x 12”

Glulam Column for Roof Trusses

8.75” x 15”

Glulam Beams Typ.

6” Mass Timber Decking Typ.

Matthew Malski

Kaung Kyaw

Elementary School

Los Angeles, California

High Seismic Zone

Roof Structural Fall 2023

8.75” x 15”

Glulam Beams Typ.

8.75” x 12”

Glulam Eccentric Cross Bracing

Glulam-Steel Composite Truss:

8.75” x 24” Glulam Top Chord, HSS Round Tubes for vertical members, Steel Rods for Diagonals and Bottom Chord

Double 8.75” x 12”

Glulam Column for Roof Trusses 10.75” x 12”

Glulam Column Typ. 6” Mass Timber Decking Typ.

8.75” x 15”

Glulam Beams Typ.

Glulam-Steel

Composite Truss:

8.75” x 24”

Glulam

Top Chord, HSS Round Tubes for vertical members, Steel Rods for Diagonals and Bottom Chord

Double 8.75” x 12”

Glulam Column for Roof Trusses

8.75” x 12”

Glulam Mezzanine Bracing

6” Mass Timber Decking Typ.

10.75” x 12”

Glulam Column Typ.

8.75” x 15”

Glulam Beams Typ.

8.75” x 12”

Glulam Eccentric Cross Bracing

Matthew Malski

Kaung Kyaw

Double 8.75” x 12”

Glulam Column for Roof Trusses

10.75” x 12”

Glulam Column

Typ. 6” Mass Timber Decking Typ.

Elementary School

Los Angeles, California High Seismic Zone

Size of Member and Dimensions

Lateral Load Resistance

R = 1.5 (table

Ss value = 0.625

FA = ?

Ss=0.50 is Fa=1.2 and Ss=0.75 is Fa=1.1 so the average of the two for Ss=0.625 is Fa=1.15

Soil Class = C I = 1.25 (risk category III)

S1 = 0.45

S1= 0.4 is Fv= 1.4 and S1=0.5 is Fv=1.3 therefore, when S1=0.45, Fv=1.35.

Fv

V = Cs x W

Cs = SDSR/Ie

SDS = 2/3 SMS

Matthew

SMS = Fa(Ss)

SMS = 1.15(0.625)

SMS = 0.71875

SDS = ⅔ SMS

SDS = ⅔ (0.71875)

SDS = 0.474375 (Larger than SD1)

SM1 = Fv(S1)

SM1 = 1.35(0.45)

SM1 = 0.6075

SD1 = ⅔ SM1

SD1 = ⅔ (0.6075)

SD1 = 0.40095

Building Period:

Ta = Ct(hn)x

Ct = 0.02

X = 0.75

h = 57 ft (building height)

T = 0.02(57)0.75

T = 0.41489 sec

Cs = ������ /����

Cs = 0.474375

1.5/1.25

Cs = 0.3953

But not exceed the following:

Cs (max) = ���� ��������

Cs (max) = 0.40095

0.41489(1.5/1.25)

Cs (max) = 0.80533

Cs min lower limit:

Cs (min) = 0.044(SDS)(Ie)

Cs (min) = 0.044(0.474375)(1.25)

Cs (min) = 0.026091

Cs (min) < Cs Base Value < Cs (max)

0.026091 < 0.3953 < 0.80533 OK

Use Cs = 0.3953

Loads:

Area of floors and roof: 90x120 =10800 SF

Area of mezzanine: Total hole: 10800 (78.75 x 105) = 2531.25 SF

Floors 2,3,4 Dead Load: 50 psf x 10800 SF = 540000 # or540 kips

Mezzanine Dead Load: 50 psf x 2531.25 SF = 126562.5 # or 126.56 kips

Roof Dead Load: 30 psf x 10800 SF = 324000 # or 324 kips

Total Dead load: 540 + 540 + 540 + 126.56 + 324 = 2070.56 kips

Base Shear

V = Cs*W

V = 0.3953(2070.56)

V = 818.49

Base Shear Distribution:

*For base shear distribution, mezzanine loading and shear transferred to level 4

Vx is diaphragm shear distribution

Distribution of Base Shear Section

259.87 kips

300.22 kips

Drift Calculations

Mass Timber decking is rigid diaphragm.

Diaphragm loads transferred to bracing:

P (bracing) = P (diaphragm)/Number of braces:

Roof: 259.87/4 = 64.97 kips

4: 560.09/4 = 140.02 kips

3: 727.31/4 = 181.83 kips

2: 818.49/4 = 204.62 kips

(2 braces per side at 2 sides)

E = 1410 ksi (Douglas Fir)

h= 15 ft L= 22.5 ft

Use ft for wood instead of fb

ft = 1300 psi or 1.3 ksi

Tan (θ) = h/L = tan-1(15/22.5) = 33.69 degrees

Cos (θ) = 0.83’

Cos^2 (θ) = 9/13 = 0.69’

Δ = ft L/[E cos2(θ)] = (1 3)(22 5′ �� ) 1410 (9/13 ) = 0.36”

Seismic drift max 2.5% of total building height 0.025 x 57’ = 1.425’ or 17.1”

Δallowable = 17.1” > 1.472” OK

Check P/A

Try 8.75” x 12”

A = 8.75” x 12” = 105 in2

Roof: P/A = 64.97/105 = 0.62 ksi < 1.3 ksi OK

4: P/A = 140.02/105 = 1.33 > 1.3 ksi NOT OK

3: P/A = 181.83/105 = 1.73 > 1.3 ksi NOT OK

Need larger section areas:

4: Area needed = 140.02/1.3 = 107.71 in2

Use 10.75” x 10.5” Area provided: 112.88 in2

P/A = 140.02/112.88 = 1.24 ksi < 1.3 ksi OK

3: Area needed = 181.83/1.3 = 139.87 in2

Use 10.75” x 13.5” Area provided: 145.125 in2

P/A = 181.83/145.125 = 1.25 ksi < 1.3 ksi OK

2: Area needed = 204.62/1.3 = 157.4 in2

Use 10.75” x 15” Area provided: 161.25 in2 P/A = 204.62/161.25 = 1.27 ksi < 1.3 ksi OK

2006 Table 1613.5.3(2), page 304 Maximum Spectral Response Accelerations for Short and 1-Second Periods:

= 0.719

= Fa*SS, IBC 2006 Eqn. 16-37, page 303

Design Category:

2006 Table 1613.5.3(1), page 304

2006 Table 1613.5.3(2), page 304

Maximum Spectral Response Accelerations for Short and 1-Second Periods:

= 0.719

Design Spectral Response Accelerations for Short and 1-Second Periods :

= 0.405

= Fa*SS, IBC 2006 Eqn. 16-37, page 303

= Fv*S1, IBC 2006 Eqn. 16-38, page 303

= 2*SMS/3, IBC 2006 Eqn. 16-39, page 304

= 2*SM1/3, IBC 2006 Eqn. 16-40, page 304

Seismic Design Category: Category(for SDS) = C IBC 2006 Table 1613.5.6(1), page 306

Category(for SD1) = D IBC 2006 Table 1613.5.6(2), page 306

Use Category = D Most critical of either category case above controls