PPD - Math Questions Flashcards

(16 cards)

1
Q

Refer to the exhibit.

A developer wants to build a new riverfront apartment building on Lot B and the architect needs to calculate the maximum building footprint. Site details follow:

The street frontage is 175 feet and the lot depth is 150 feet.
The AHJ requires a FAR of 2.5 and setbacks of 10 feet at the rear, front, and side.
The north boundary is a community walkway along Brooke River.
Brooke River’s ordinary high water mark (OHWM) is 75 feet from the plot boundary.
The AHJ does not permit buildings within 100 feet of a waterway’s OHWM.

What is the maximum building footprint allowed on this site?

a. 6,200 square feet

b. 17,825 square feet

c. 20,150 square feet

d. 65,625 square feet

A

17,825 square feet

CALCULATIONS

  1. Maximum footprint width: The side setbacks are 10 feet each, 175 feet (street frontage) - 10 feet (right side setback) - 10 feet (left side setback) = 155 feet
  2. Maximum footprint depth: 150 feet (lot depth) - 10 feet (front setback) - 25 feet (rear setback, 100 feet from the OHWM) = 115 feet
  3. Maximum footprint: 115 feet x 155 feet = 17,825 square feet

Topic: Codes & Regulations

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2
Q

An architect is designing a new 1,200-square-foot house with eight-foot ceilings. The initial design calls for five 3’ x 4’ windows that allow 60 cfm of fresh air each. However, the local sustainable design ordinance requires new houses to provide three fresh air changes per hour.

How many additional 3’ x 4’ windows are required to comply with the ordinance?

a. 3 windows

b. 5 windows

c. 8 windows

d. 11 windows

A

3 windows

CALCULATIONS

1) House volume: 1,200 square feet x 8 foot ceiling height = 9,600 cubic feet

2) Cubic feet per hour required by ordinance: 9,600 cubic feet x 3 fresh air changes per hour = 28,800 cubic feet per hour

3) Cubic feet per minute required: 28,800 cubic feet per hour / 60 minutes per hour = 480 cubic feet per minute

4) Cubic feet per minute provided by five windows: 5 windows x 60 cubic feet per minute = 300 cubic feet per minute

5) Cubic feet per minute deficit: 480 cubic feet per minute required - 300 cubic feet per minute already available = 180 cubic feet per minute still needed

6) Additional windows required: 180 cubic feet per minute / 60 cubic feet per minute (each window) = 3 windows

Topic: Project Integration of Program & Systems

This version keeps the numbering but avoids formatting that breaks copying.

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3
Q

The preliminary bids for a 40,000-square-foot high school addition are over budget. The polished concrete floor originally specified for the floor assembly costs $6 per square foot. The owner requests a seamless flooring product and the contractor suggests the following alternative flooring materials:

Vinyl composition tile (VCT): $1.50 per square foot

Luxury vinyl tile (LVT): $4.50 per square foot

Epoxy flooring: $1.75 per square foot

What are the cost savings of switching to the preferred alternative flooring material?

a. $60,000

b. $170,000

c. $180,000

A

B
_____

$170,000

The owner wants a seamless flooring product and epoxy flooring is the only option that meets this requirement.

CALCULATIONS

  1. Cost of the originally specified polished concrete flooring material: $6.00 x 40,000 sf = $240,000
  2. Cost of the preferred alternative flooring material, epoxy flooring: $1.75 x 40,000 sf = $70,000
  3. Cost savings of switching flooring material: $240,000 - $70,000 = $170,000

Topic: Project Costs & Budgeting

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4
Q

Refer to the exhibit.

An architect is designing a 4,000-square-foot restaurant building. The kitchen will occupy 30% of the space and the remaining space will be for dining with tables and chairs. The local code requires 0.5 parking spaces per occupant.

How many parking spaces are required?

a. 96 parking spaces

b. 97 parking spaces

c. 192 parking spaces

d. 193 parking spaces

A

B
_____

97 parking spaces

CALCULATIONS

  1. Kitchen: 4,000 square feet x 30% = 1,200 square feet / 200 (occupant load factor) = 6 people
  2. Dining: 4,000 square feet x 70% = 2,800 square feet / 15 (occupant load factor) = 186.66 people, rounded up to 187
  3. Total occupants: 6 + 187 = 193 occupants
  4. Total parking spaces required: 193 occupants x .5 = 96.5 parking spaces, rounded up to 97

Topic: Codes & Regulations

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5
Q

Refer to the exhibit.

An architect is determining the size and number of doors for a large, rectangular assembly room that will be used as an exhibition gallery. The assembly room will be 150’-deep by 250’-long. The AHJ requires that all means of egress components other than stairways use an egress capacity factor of 0.2 inches per occupant. All assembly room exits will use double doors.

How many 60-inch clear width double door exits are required?

a. 4 double door exits

b. 5 double door exits

c. 8 double door exits

d. 9 double door exits

A

B
_____

5 double door exits

CALCULATIONS

  1. Determine room size: 150 feet x 250 feet = 37,500 square feet
  2. 37,500 square feet / 30 square feet per occupant (occupant load factor for an assembly space for exhibit galleries) = 1,250 occupants
  3. Egress components other than stairwells require multiplying the occupant load served by a means of egress capacity factor of 0.2 inches per occupant
  4. 1,250 occupants x 0.2 inches = 250 inches of egress width required
  5. 250 inches of egress width / 60 inches (double doors) = 4.17 doors, rounded up to 5

Topic: Codes & Regulations

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6
Q

An architect is designing a building renovation and needs to add an accessible ramp at an existing entrance that currently only has stairs. The dimension between grade and the building entrance is 42”. A survey shows no changes in grade on the site around the building. Accessibility code requires wheelchair accessible ramps to be between a 1:12 and 1:20 slope, with a maximum rise of 30” between 60”-long landings.

Based on the accessibility code requirements provided above, what is the minimum length of the accessible ramp between the top and bottom landings?

a. 30’-0”

b. 42’-0”

c. 47’-0”

d. 75’-0”

A

C
_____

47’-0”

CALCULATIONS

  1. The ramp has a maximum rise of 30 inches at a 1:12 slope, so one intermediate landing of 60 inches (minimum) is required = 5 feet
  2. Minimum ramp length: 42 inches of vertical rise requires 42 feet of ramp
  3. 42 feet of ramp + 5 feet for the intermediate landing = 47 feet

Topic: Codes & Regulations

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7
Q

Refer to the exhibit.

A hospital considers converting a 5,000-square-foot office space into clinical space. The space is currently carpeted but will require a change to a nonporous surface. The following flooring materials are being evaluated based on their life expectancy:

  • Porcelain tile: 10 years
  • Epoxy terrazzo: 20 years
  • Inlaid vinyl sheet: 5 years

Assuming the same replacement material is used, what is the price of the most cost-effective flooring material over a 25-year period?

a. $135,000

b. $150,000

c. $165,000

d. $180,000

A

C
_____

$165,000

CALCULATIONS
Calculate the lowest cost of each material option over 25 years

  1. Porcelain tile: 3 installations x $11/sf (price + installation) = $33
  2. Epoxy terrazzo: 2 installations x $18/sf (price + installation included) = $36
  3. Inlaid vinyl sheet: 5 installations x $8/sf (price + installation) = $40

Comparing the above, three installations of porcelain tile are less expensive than two installations of epoxy terrazzo or five installations of inlaid vinyl sheet.

Calculate the cost of the porcelain tile over 25 years.

  1. $9.00 (price of porcelain tile per sf) + $2.00 (installation price per sf) = $11 per sf
  2. $11.00 x 5,000 (square footage of converted space) = $55,000
  3. $55,000 x 3 (number of installations over 25 years) = $165,000

Topic: Project Costs & Budgeting

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8
Q

An architect is adding a set of stairs from grade to the top landing of an existing ramp. Excluding all landings, the existing ramp is 28 feet long and has a 1:16 slope. A survey shows no changes in grade on the site around the building. Each riser must be no more than six inches high.

How many risers should the set of stairs include?

a. 3 risers

b. 4 risers

c. 5 risers

A

B
_____

4 risers

CALCULATIONS

Convert ramp length to inches:
28 feet × 12 inches = 336 inches

Calculate total vertical rise using 1:16 slope:
336 inches ÷ 16 = 21 inches of rise

Determine number of risers (max 6 inches each):
21 inches ÷ 6 inches = 3.5 risers → round up

4 risers required.

Topic: Codes & Regulations

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9
Q

Refer to the exhibit.

A new school is moving into an existing building. The school wants the spaces in the building to be used as efficiently as possible. The building code requires 20 nsf per student for classroom spaces.

A classroom for 20 students should be assigned to which of the following spaces?

a. A

b. B

c. C

d. D

A

D
_____

CALCULATION

20 nsf × 20 students = 400 nsf required

A classroom for 20 students requires a minimum of 400 net square feet. Space D most efficiently meets this requirement.

Topic: Project Integration of Program & Systems

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10
Q

Refer to the exhibit.

A developer is determining the best building configuration for Lot 4B, a suburban plot in a cold climate. The lot is 150’ × 100’ and the maximum building footprint is 15,000 square feet. The owner’s program requires a minimum of 48,500 square feet of office space.

To minimize heat loss in winter, which one of the following building configurations should the architect recommend?

a. A three-story 150’ × 110’ rectangular footprint

b. A four-story 120’ × 120’ square footprint

c. A four-story 120’ × 100’ rectangular footprint

d. A six-story 90’ × 90’ square footprint

A

D
_____
A six-story 90’ × 90’ square footprint

CALCULATIONS

Step 1: 90’ × 90’ = 8,100 sf per floor

Step 2: 8,100 sf × 6 floors = 48,600 sf

Step 3: 8,100 sf is less than the 15,000 sf maximum footprint allowed

A compact square form minimizes exterior surface area relative to volume, which reduces heat loss in cold climates while meeting the required square footage.

Topic: Project Integration of Program & Systems

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11
Q

An architect is in the programming phase of a tenant improvement project for a small university office suite in an existing building. The client has asked for five 120-square-foot offices for staff members, a 200-square-foot conference room, and a 100-square-foot storage room. The client has a limited budget and would like to minimize the area to be remodeled.

Other programming requirements follow:

  • Use a building efficiency ratio (net-to-gross) of 0.75 if a double-loaded corridor design is implemented.
  • Use a building efficiency ratio (net-to-gross) of 0.70 if a single-loaded corridor design is implemented.
  • At least two offices and conference rooms should be located along exterior walls for views.
  • The dimension of the longest length of existing space to remodel is 50 feet.

How much area is needed for the renovation?

a. 1,285 square feet
b. 1,200 square feet
c. 1,250 square feet
d. 1,575 square feet

A

B
_____
1,200 SQUARE FEET

A double-loaded corridor layout minimizes the overall remodeled area, so use the 0.75 net-to-gross efficiency.

Step 1
Total office area = 120 sf x 5 offices = 600 sf

Step 2
Total net area = 600 sf (offices) + 200 sf (conference) + 100 sf (storage) = 900 nsf

Step 3
Gross area needed = 900 nsf / 0.75 = 1,200 sf

Topic: Project Integration of Program & Systems

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12
Q

An architect is renovating an existing building with 10,080 sf of glazing. The architect must assess the energy cost savings of re-glazing the existing wood windows instead of installing new aluminum windows. Assume the following energy cost information:

  • Anticipated energy costs are $60,000 per year.
  • There will be 20% savings on energy costs if the windows are re-glazed.
  • There will be 18% savings on energy costs if new aluminum windows are installed.

Over a 30-year period, what is the anticipated energy cost savings of re-glazing instead of installing new aluminum windows?

a. $1,200
b. $10,800
c. $12,000
d. $36,000

A

D
_____
$36,000

Step 1
Savings per year with re-glazing = $60,000 × 20% = $12,000

Step 2
Savings per year with new aluminum windows = $60,000 × 18% = $10,800

Step 3
Difference in annual savings = $12,000 − $10,800 = $1,200

Step 4
30-year savings difference = $1,200 × 30 = $36,000

Topic: Project Costs & Budgeting

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13
Q

Refer to the exhibit.

An architect is renovating an existing sports arena. There are 52 suites on the arena’s suite level at 250 square feet each. Each suite has 12 fixed seats only with views to the field below. Suites are the only spaces on this level. There are currently two female lavatories on the suite level.

How many additional female lavatories are required on the suite level?

a. 1 lavatory

b. 2 lavatories

c. 3 lavatories

d. 4 lavatories

A

A
_____
1 LAVATORY

Step 1

Occupant load = 52 suites × 12 fixed seats = 624 occupants

Step 2

Female occupants = 624 ÷ 2 = 312 females

Step 3

Lavatories required = 312 ÷ 150 = 2.08 → round up to 3 required

Step 4

Additional lavatories needed = 3 required − 2 existing = 1 additional lavatory

Topic: Codes & Regulations

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14
Q

A client asks an architect to perform a feasibility study for a rectangular 50’ × 100’ urban lot. The 50’ side fronts the street. The zoning ordinance stipulates the following:

  • Front and side setbacks: 5’
  • Rear setback: 25’
  • Maximum impervious coverage: 2,400 sf
  • FAR: 2.0 (based on total land area, including setbacks)
  • Maximum building stories on site: 4

What is the maximum gross building area?

a. 5,600 square feet

b. 9,600 square feet

c. 10,000 square feet

d. 11,200 square feet

A

B
_____
9,600 SQUARE FEET

Step 1

Lot area = 50 ft × 100 ft = 5,000 sf

Step 2

Max gross floor area allowed by FAR = 2.0 × 5,000 sf = 10,000 sf

Step 3

Buildable footprint inside setbacks:
Depth = 100 ft − 5 ft (front) − 25 ft (rear) = 70 ft
Width = 50 ft − 5 ft (side) − 5 ft (side) = 40 ft
Buildable area = 70 ft × 40 ft = 2,800 sf

Step 4

Max footprint allowed by impervious coverage = 2,400 sf (this controls, since 2,400 < 2,800)

Step 5

Max gross building area based on impervious coverage and max stories = 2,400 sf × 4 stories = 9,600 sf

Step 6

Check against FAR: 9,600 sf ≤ 10,000 sf, so 9,600 sf is allowed

Topic: Codes & Regulations

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15
Q

The architecture firm is determining the off-street parking capacity for the market-rate housing, which will consist of seven two-bedroom units per floor.

Givens:
* 7 two-bedroom units per floor
* 4 floors total
* 1 parking space required per bedroom per Zoning Ordinance

How many off street parking spaces are required for the market rate housing?

a. 28 spaces
b. 56 spaces
c. 112 spaces

A

B
_____
56 SPACES

The parking spaces needed are determined by the number of bedrooms, and the Zoning Ordinance resource provides the number of spaces needed per bedroom.

CALCULATIONS
1. Determine number of two-bedroom apartment units: 7 units x 4 floors = 28 units
2. Determine total number of bedrooms: 28 units x 2 bedrooms per unit = 56 bedrooms
3. Determine number of spaces for market-rate housing: 56 bedrooms x 1 space per bedroom = 56 parking spaces

Topic: Codes & Regulations

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16
Q

The housing portion of the mixed-use office and housing facility is to include 48 dwelling units that consist of the following:

  • 16 two-bedroom units
  • 32 one-bedroom units

Givens:
* 24,600 square feet of office space
* 1 parking space required per 300 square feet of office space
* 2 parking spaces required per two-bedroom unit
* 1 parking space required per one-bedroom unit

How many parking spaces will be required for the mixed-use office and housing facility?

a. 64 parking spaces
b. 82 parking spaces
c. 130 parking spaces
d. 146 parking spaces

A

D
_____
146 PARKING SPACES

Number of parking spaces required for the offices: 24,600 square feet / 300 square feet per parking space = 82 parking spaces. Number of parking spaces required for the two-bedroom units: 16 x 2 = 32 parking spaces. Number of parking spaces required for the one-bedroom units: 32 x 1 = 32 parking spaces. Total parking spaces required: 82 + 32 + 32 = 146.

CASE STUDY RESOURCES USED
Scenario
Zoning Ordinance

Topic: Codes & Regulations