Lateral stability · Pascal Architecture

A one-bay timber frame on a test floor, pulled sideways by hanging weights. Unbraced, its joints turn and it racks over; cross rods, a shear wall or rigid joints each hold it square, and the readout shows how far each one sways.

Gravity is the easy load: it always points down, and a post standing on end carries it by being squeezed. Wind and earthquakes push sideways. Wind presses on one face of a building and sucks on the other; an earthquake moves the ground and the building’s own mass lags behind. Either way the frame is asked to keep its corners square while something shoves it along. A frame that cannot do that racks over, however strong its members are.

Why a frame racks

Four bars pinned at their corners form a mechanism: the rectangle can fold into a parallelogram without any bar getting longer or shorter, so nothing inside it pushes back. Choose None in the figure and hang a single weight: the bay leans until the catch post stops it. With no load it stands, but only in the way a pencil balances on its point.

There are three ways to lock the shape. Each one appears when you choose it, dropped into the same bay so you can compare them under the same pull.

Three ways to stay square

Braced frame: A diagonal divides the rectangle into triangles, and a triangle cannot change shape unless a side changes length. Steel rods and cables only work in tension, so they come in crossed pairs: whichever way the load comes, one rod is stretched and carries it while the other goes slack. Watch the slack rod bow at full load. Rigid diagonals, knee braces and K-braces work the same way and can push as well as pull.
Shear wall: A stiff sheet fixed all round its edges resists being sheared into a parallelogram. Here it is plywood nailed to posts, studs, sill and beam; concrete and reinforced masonry walls do the same job. The nailing carries the load into the sheet, and the sheet hands it down to the foundation. The pull also tries to tip the wall over, lifting one end, which is why real shear walls are anchored at both ends with hold-downs.
Rigid frame: Make the joints themselves stiff, with steel knee plates or welded and cast connections, and the angle between beam and column can no longer change. The frame can still sway, but only by bending its members: the posts curve one way near the foot and the other near the head. It leaves the bay completely open, and of the three it is the least stiff for the material it uses.

Which of the three a building uses is mostly a question of where it needs to stay open, and what it is made of:

How does a frame resist a sideways push?

Decided by where the openings must be · how stiff the building must be · the material of the frame · wind and earthquake forces

Braced frame
Diagonals of steel rod, strap or timber turn each rectangle into two triangles.
Choose it when steel and timber frames where some bays can be crossed; the stiffest resistance for the least material.
The catch a crossed bay cannot hold a door or a window; rods only pull, so they come in pairs; the joints carry large forces.
Shear wallThis house
A wall stiff in its own plane: sheathing nailed to a frame, or a wall of masonry or concrete.
Choose it when the walls are needed anyway, as in every house; concrete and masonry buildings; stiffness at little extra cost.
The catch enough solid length between openings; hold-downs at the ends so the wall cannot tip over; open plans and walls of glass leave too little.
Shear walls in the house No. 04 →
Moment frame
Columns and beams joined so rigidly that the corners cannot turn: the frame resists by bending.
Choose it when openings must stay open: shopfronts, garage doors, glass walls; steel and concrete buildings of several storeys.
The catch it sways more than a braced bay with the same members; heavy members and costly joints.

Here The house's sheathed walls are its shear walls: the cheapest stiffness there is, in walls that need sheathing anyway.

What the numbers say

At full load, eight 100 kg weights pull with 7.85 kN, and the floor shares it equally between the two bents: 3.92 kN each across a 2.4 m by 2.4 m bay.

System	Drift	Drift ratio	Working element
Cross rods	0.58 mm	H/4,100	Rod in tension, 5.5 kN
Shear wall	1.75 mm	H/1,370	Sheathing, 1.64 kN/m
Rigid frame	6.8 mm	H/350	Posts in bending, 2.4 kN·m
None	until it falls	none	Nothing

A common limit for sway under wind is about H/400, so the rigid frame passes at light load and fails it at full load; its posts would need to be deeper. The braced bay is twelve times stiffer with two 16 mm rods.

Each drift comes from a small model of the bay. The rods stretch as steel does (E = 200 GPa) and their pins are taken as tight. The shear wall uses the standard three-part wall deflection, with an apparent shear stiffness of 13 kips/in for 15/32 in plywood nailed at 6 in on its edges, and its anchors taken as not slipping. The rigid frame has fixed bases and fully rigid knees, with Douglas fir at 11 GPa. Real connections give a little, so a built bay of each kind would sway somewhat more. In the drawing the sway of the three braced systems is shown forty times larger than life; the unbraced bay is drawn true.

The floor ties it together

The pull does not reach the bents directly. It enters the floor through a steel spreader at one edge, and the floor carries it across to both bents like a beam lying flat: plywood skin as the web, the edge members as its flanges. This horizontal diaphragm is what lets a few walls or braced bays stabilise a whole floor plate. Roofs do the same job. Cut a large hole in one, or make it much floppier than the floors above and below, and it stops delivering the load.

Every direction, and symmetry

Bracing works in its own plane and nowhere else. The test bay is held the other way by rods in its end planes, lighter in the drawing because they take no part in this test. A building needs lateral resistance in both of its main directions. In a long rectangular building the short direction is the critical one, so the stiffest walls or braced frames usually run that way. The frames that cross the building’s length are called bents.

Where the stiff elements go matters as much as how many there are. Wind and inertia act through the centre of a floor’s mass; the floor is held at the centre of its resistance. Put all the bracing on one side and the two centres part company: the floor twists as well as slides, and the far side moves much further. Page 2.23 lists the other irregularities that cause trouble in earthquakes: a soft storey much weaker than the ones above it, re-entrant corners on L-shaped plans, and shear walls or diaphragms that are interrupted.

In a house

A wood-frame house is braced almost entirely by shear walls, because its outside walls are sheathed anyway. In the reference house every outside wall is 7⁄16 in (11) OSB nailed at 6 in (150) on its edges, and the panels cross the rim joists so each storey is fastened to the one below; the load path follows the wind from those walls down to the anchor bolts. Codes call it continuous sheathing, and allow lighter methods where wind and earthquakes are mild and stronger ones beside big openings.

What keeps the walls from racking?

Decided by wind speed and earthquake risk · how much solid wall there is between openings · the sheathing the wall gets anyway · inspection and labour

Structural sheathingThis house
OSB or plywood nailed on every edge to studs, plates and rims, over the whole wall: every wall a shear wall.
Choose it when almost always: it is the strongest and stiffest light-frame method; it also ties each storey to the next and gives the siding something to nail to; taped, it doubles as the air barrier.
The catch the nailing schedule must be kept, 6 in at edges and 12 in in the field; every panel edge must land on framing or blocking.
Sheathing on the frame No. 14 →
Let-in braces
A 1×4 set into notches cut across the studs, diagonally from top plate to sole plate.
Choose it when low wind and low earthquake risk; walls sheathed with foam or fibreboard that cannot brace.
The catch far weaker than sheathing; needs clear wall at each end of every wall line; cannot cross an opening.
Steel strap braces
Flat galvanized straps nailed diagonally across the studs, in crossed pairs.
Choose it when steel stud walls; sheathing that is not structural; a quick brace.
The catch a strap only pulls, so they go in pairs; they slacken if not tensioned; nailed at every stud they cross.
Portal frames
A narrow wall panel beside a big opening, its header strapped and its base held down so it acts as a small rigid frame.
Choose it when garage fronts and window walls with little solid wall; panels as narrow as 16 in (405).
The catch engineered nailing, straps and hold-downs; costs more per foot of wall; a careful inspection item.

Here Every outside wall is sheathed in 7⁄16 in OSB anyway, so nailing it to a schedule makes the whole skin bracing. The panels lap the rims, tying each storey to the one below.

The rig

Each cast disc is 100 kg and pulls with 0.98 kN once the cable has turned the corner over the pulley. A load cell in the cable reads the pull; the reaction post carries it back into the strong floor through a stiffened base plate; and the catch post stands ready for a specimen that cannot resist. Laboratories test real wall panels and frames in rigs much like this one, pushing them back and forth with hydraulic actuators until they fail.

The loads themselves are in chapter 2: wind loads in 2.09, earthquake loads in 2.10, and how tall buildings brace themselves in 2.24.