Structural integration

The grid study that started the team's first argument comes back to the big room in week four. Ingrid and Tomasz have drawn three versions of the building's structure, with Adaeze consulted on each, and they have brought them to the session as overlays on the clinic and housing plans. Marta Szymańska, the structural engineer who taught the architecture students their two structures courses, has come to listen. She says nothing for the first hour, which Tomasz later says was the most stressful hour of his degree.

Three ways to meet

The first version carries the tower's grid down through the clinic and the ground floor. The tower wants columns at 20 feet along its length, which suits two homes of 20 feet frontage between each pair of columns or one larger home, and three bays across its depth of 23, 20 and 23 feet, with the corridor in the middle bay. Carried down, this grid puts columns in the clinic every 20 feet, which the clinic's exam room pods can live with if each exam room is 10 feet wide and two of them share a bay. It also puts columns in the transit hall, which the hall can take, because a waiting hall with columns is no worse than a train station with columns.

The second version carries the clinic's preferred grid up through the tower. The clinic would prefer 30 feet bays, which fit pods of three exam rooms each side of a work area. Carried up, the 30 feet bays make the tower's floors span further, which a timber floor can do only by getting much deeper, and they put columns in the middle of the homes, which Lafontaine has said she will not accept.

The third version gives each part its own grid and changes from one to the other with a transfer at the podium roof: a thick slab or a set of deep beams that collects the tower's columns and carries their loads sideways to the clinic's columns. Transfers are common in mixed-use buildings, and sometimes unavoidable. But a full transfer at the podium roof is expensive, heavy, high in carbon and deep, and its depth adds to the building's height and to every stair and riser that passes through it.

Szymańska's first comment, when she speaks, is about the third version. 'In practice,' she says, 'nobody chooses a full transfer if there is any way to avoid it. You choose it when the uses below truly cannot take the columns above, and then you pay for it.' The team chooses the first version, the tower's grid carried down. The clinic team led by Courchesne's facilities manager reviews it and agrees, provided the procedure rooms and the group room, which need wider spaces, go at the east end of the clinic floors, outside the tower's footprint, where the podium roof is only one floor above and the grid can open to 40 feet with deeper beams.

The one transfer the team keeps

One problem remains. At the lane, the loading bay must take a delivery truck and the refuse truck, which need a clear opening of about 40 feet to turn in from the lane. Two of the tower's columns fall in that opening. The team considers moving the loading bay, but the lane is the only place it can go. So it keeps a single local transfer: one deep girder at the podium roof, spanning the opening and carrying the two tower columns at its third points. Tomasz pre-sizes it with the loads from the floors above.

# Pre-sizing the transfer girder over the clinic entrance: two tower columns picked up on a 40.0 ft span
span = 40.0                         # ft
a = 13.3                               # ft from each support to the column it carries
p_dead, p_live = 520, 120           # kips per column from the floors above (unfactored)
pf = 1.2 * p_dead + 1.6 * p_live      # factored load per column
m = pf * a                            # moment between the two point loads (simply supported)
v = pf
print(f"factored load per column {pf:,.0f} kips; moment {m:,.0f} kip-ft; shear {v:,.0f} kips")
for depth in [36, 48, 60, 72]:                 # trial depths in in
    ratio = span * 12 / depth
    print(f"  depth {depth:>6} in: span/depth {ratio:4.1f}" + ("  <- typical for a heavy transfer" if 8 <= ratio <= 12 else ""))
b = 24; d = 60                        # width and effective depth, in
z = 0.9 * d
steel = m * 12 / (0.9 * 60 * z)  # required bottom steel area
print(f"with a {b} x {66} in girder: bottom steel about {steel:,.0f} in2 ({steel / 1.56:.0f} #11 bars)")

factored load per column 816 kips; moment 10,853 kip-ft; shear 816 kips
  depth     36 in: span/depth 13.3
  depth     48 in: span/depth 10.0  <- typical for a heavy transfer
  depth     60 in: span/depth  8.0  <- typical for a heavy transfer
  depth     72 in: span/depth  6.7
with a 24 x 66 in girder: bottom steel about 45 in2 (29 #11 bars)

A girder about 48 to 60 inches deep, with about 29 large bars at the bottom, is a substantial piece of concrete, but it is one girder rather than a whole floor of them. Its depth will be hidden in the podium roof's soil and drainage layers, which are deep anyway. Szymańska points out that the loads on it depend on the tower's material: a timber tower weighs much less than a concrete one, so the girder over the loading bay is a place where the choice of tower structure shows up directly in cost and carbon.

The tower's structure

The material of the tower is the decision Kostyshyn warned about at the brief review. Minnesota's current code is based on the 2018 International Building Code, which allows mass timber only in the older heavy timber type, limited to far fewer stories for a residential building than the team needs. The tall mass timber types, which allow encapsulated or partly exposed mass timber up to eighteen stories, were added in the 2021 edition, and the state's rulemaking to adopt the 2024 edition has begun but has no effective date. A timber tower of eleven stories would therefore need approval as an alternative method, with the building official, the fire department and probably a peer review, and the team cannot count on it. Tomasz proposes a post-tensioned concrete flat plate tower, which is fast to build, thin and well understood, and keeps a mass timber tower as an alternative to be priced and submitted if the state adopts the new code before the permit.

The concrete tower has the advantages of familiarity and thin floors: an eight-inch flat plate gives a floor-to-floor height of ten feet with room for a fan coil above the bathroom ceilings. Its disadvantages are much higher upfront carbon, a heavier load on the foundations and the transfer girder, and a longer construction period on a constrained site. Marcus Oyelaran, the builder's preconstruction manager, says his firm could build either, and asks that the team decide early, because the two need different cranes, different trades and a different schedule.

Either way, the floor-to-floor heights are now fixed, and the team writes them into the decision log: 18 feet for the ground floor, so that the transit hall is generous and the services can run above the shops; 15 feet for each clinic floor, because the clinic needs deep ceilings for its ducts; and 10 feet for each housing floor. The building's roof is at about 128 feet.

Standing up to wind

The tower must resist wind and, in principle, earthquakes. Both Minneapolis are in regions of low seismic hazard, so for a building of this weight and height, wind will govern the lateral design, as it did for the students' housing in second year. The team uses two concrete cores to resist it: the west core with the main stair, two elevators and the main shaft; the east core with the second stair and the electrical and telecom rooms. Concrete cores are stiff and strong, they are needed anyway to enclose the stairs and elevators with fire-rated walls, and they connect the timber or concrete floors of the tower to the foundations without any other bracing.

Tomasz estimates the wind on the tower's long face, the worst direction, using a simplified version of the code method: a reference velocity pressure, increased with height, multiplied by combined pressure and gust factors for the windward and leeward faces and by the area of each band of the facade. The result is the base shear and the overturning moment that the cores must resist, and the shear per unit length of core wall.

# Quick wind base shear on the tower and podium, to size the cores
height = 128.0                          # ft to the roof
width = 131.0                           # ft, face receiving the wind (long side)
q = 24.9                               # reference velocity pressure, psf
def exposure(z):                      # how wind pressure grows with height (simplified)
    return max(0.70, 2.01 * (max(z, 30) / 1200) ** (2 / 7))
cpcg = 1.105                           # combined pressure and gust factor, windward plus leeward
layers = 10                     # stories grouped in bands of 12.8 ft
shear = 0.0; moment = 0.0; z = 0.0
for n in range(layers):
    top = min(height, z + 12.8)
    mid = (z + top) / 2
    f = q * exposure(mid) * cpcg * width * (top - z) / 1000
    shear += f; moment += f * mid; z = top
print(f"wind base shear about {shear:,.0f} kips; overturning moment about {moment:,.0f} kip-ft")
core_len = 105.0                     # ft of core wall resisting in this direction
print(f"shear per ft of core wall {shear / core_len:,.1f} kips; factored ({1.0}) {1.0 * shear / core_len:,.1f} kips")

wind base shear about 397 kips; overturning moment about 27,521 kip-ft
shear per ft of core wall 3.8 kips; factored (1.0) 3.8 kips

About 400 kips of base shear spread over about 105 feet of core wall in that direction is a modest load for concrete walls of 10 to 12 inches, so the cores can be sized for their fire and elevator requirements and checked for wind, rather than the other way around. Szymańska points out what the estimate does not include: the drift of the tower, which governs comfort and the movement of the facade; the torsion if the cores are not balanced; and the overturning on the foundations, which with a tower of this weight needs checking at the cores. She asks Tomasz to show that the two cores are placed so that the center of their stiffness is close to the center of the wind's pressure, so the tower does not twist.

What integration changed

At the end of the session, Solberg asks the team to list what the structural decisions changed in the other disciplines. Ingrid's clinic plan now has a 20 foot rhythm and its widest rooms at the east end. Adaeze's ventilation ducts must cross the beam lines in the clinic, and the team agrees to keep the clinic's main ducts in the corridor zone between two beam lines, where the beams can be shallower. Rafael's electrical rooms are now in the east core, stacked from the ground to the roof. Hamid's foundations must avoid the contaminated soil at the old pump island, which by good luck falls between two column lines. And the cost plan has one transfer girder in it instead of a transfer floor. Szymańska's last comment is that the best structural decision in the building was made by moving the clinic's procedure rooms, which is not a structural decision at all.

Exercise 5: structural integration

• Draw at least two ways for the tower and podium to meet, and compare them for cost, carbon, depth, and the plans they force on each use.
• Choose the grid, fix the floor-to-floor heights and locate the cores; record the decisions and the reasons.
• Pre-size any transfer you cannot avoid, and estimate the wind base shear on the cores.
• Compare at least two materials for the tower, including what the code in your jurisdiction allows.

Self-check

• Can you show that every tower column reaches the foundations, and how?
• Have you listed what your structural decisions changed in the other disciplines?
• Are your cores balanced so the tower does not twist?