Construction · Lesson 2 of 13Intermediate9 min read

Loads and Structure

Every pound in a house, from the shingles to the people in the kitchen, has to find its way down to the ground. Builders call that route the load path. This lesson follows it, names the four ways a part can be loaded, and shows why a deeper joist is so much stiffer.

Dead, live, snow and wind

A house carries several kinds of load at once:

Dead load is the weight of the building itself: framing, sheathing, drywall, roofing, flooring.
Live load is everything that moves or changes: people, furniture, appliances, stored things.
Snow load is the weight of snow on the roof, which can be large in snowy places.
Wind load pushes on walls and the roof. At the roof’s edges, wind creates both the biggest pushes and the biggest pulls, so a roof has to be held down as well as held up.

Designers plan for the loads the local code sets for their area. A house in snow country carries a bigger roof load than one on the Gulf Coast, and a house near the coast plans for stronger winds.

The load path

Follow a pound of snow. It presses on the roof sheathing, which rests on the trusses or rafters. They sit on the top plates of the walls. The studs carry it down to the bottom plate, through the floor’s rim joist, sill plate and foundation wall, into the footing, and finally into the soil. Inside the house, floor joists hand part of their load to a beam, the beam rests on posts, and each post stands on its own footing.

Every link in that chain has to carry its share, and so does every connection between links: nails, plates, bolts and straps. The foundation is tied to the framing with anchor bolts or straps at the sill plate.

Physics sees each piece as an object in equilibrium. Nothing in a sound house is speeding up, so the forces on every piece add to zero: the load pushing down on a stud is matched by the plate pushing up. In the end the soil pushes up on the footings exactly as hard as the house pushes down, which is Newton’s third law at work.

Drag the sliders to add snow and furniture, change the footing width, or open a window in the wall. Only the loads you add are counted; the house’s own weight would add more. Pressure = force ÷ area.

pressure on the soil = load on the footing ÷ footing area (P = F / A)

Compression, tension, bending and shear

A part can be loaded four basic ways. Compression squeezes it shorter, like a post or a stud. Tension stretches it longer, like the bottom chord of a roof truss that keeps the walls from spreading. Bending does both at once: a loaded joist is squeezed along its top edge and stretched along its bottom edge. Shear is a sideways force that makes one layer try to slide past another, as at a bolted joint.

Materials handle these differently. Concrete can withstand compression well, which is why it works for footings and columns, but its tensile strength is only about 10 to 15 percent of its compressive strength. That’s why concrete is almost always reinforced with steel, which takes the tension (Lesson 3).

Most parts of a house feel more than one of these at once. Sources: OpenStax College Physics 2e (tension, compression and shear).

Why triangles are stiff

Nail four boards into a rectangle and push on a corner: the frame racks over into a parallelogram, because nothing about four side lengths fixes the angles. Three boards in a triangle can’t do that. Three side lengths fix all three angles, so the only way to change the triangle’s shape is to stretch or squeeze one of its sides. The push turns into tension and compression in the members, which wood handles well.

That’s the idea behind a roof truss, a frame built entirely of triangles. Walls use the same trick another way: wood sheathing panels nailed to the studs make the wall act like one stiff sheet that can’t rack. Walls built to resist sideways forces from wind this way are called shear walls.

That’s why trusses are built from triangles, and why walls get a stiff skin of sheathing or a diagonal brace. Geometry: a triangle’s three sides fix its three angles.

Beams, and why depth matters so much

A joist, rafter, header or beam works in bending. How much it sags depends on four things: the load, the span, the stiffness of the material (its modulus of elasticity, E), and the shape of its cross-section (its moment of inertia, I). For a beam resting on two supports with the load spread evenly along it, the sag at the middle is:

sag = 5 × w × L⁴ ÷ (384 × E × I) where w = load per inch of length, L = span
I = b × h³ ÷ 12 for a rectangle b wide and h deep

Depth cubed, span to the fourth

Two exponents explain a lot about houses. Depth is cubed in the stiffness, so a board twice as deep is eight times as stiff. That’s why joists stand on edge, and why a 2×4 laid flat bends like a diving board. Span is raised to the fourth power in the sag, so doubling the span of a joist under the same load per foot makes it sag sixteen times as much. Wood species matters too: in the USDA Wood Handbook’s tables, measured at 12 percent moisture, Douglas-fir’s E is about 1.95 million pounds per square inch and ponderosa pine’s about 1.29 million.

Pick a size, stand it on edge or lay it flat, and change the span and the load. The sag is drawn bigger than life so you can see it; the number is the real one. The joist’s own weight, knots, long-term creep and code limits are left out.

StopNever cut, notch or remove structure without a plan

Load-bearing walls, beams, joists, headers, posts and truss members are links in the load path. Removing a wall, cutting a joist for a pipe, or notching a beam can overload the parts left behind. These changes need a permit and, often, an engineer’s design. Real joist and beam sizes come from the span tables in the local code or from an engineer, not from a calculator like this one.

Check yourself

Tap an answer to check it, or open “Show the answer.”

Furniture and people in a house are what kind of load?
Show the answer
Live load. Live loads move or change. The weight of the building itself is dead load.
What carries the load over a window opening to the studs on each side?
Show the answer
The header. The header is a short beam that carries the load sideways to the jack studs.
A 2×12 (11¼ inches deep) is about twice as deep as a 2×6 (5½ inches). Under the same load and span, how does its sag compare?
Show the answer
About one-eighth as much. Stiffness grows with depth cubed: 2.05³ ≈ 8.6, so the 2×12 sags about 8.6 times less.
Why is concrete reinforced with steel?
Show the answer
Concrete is weak in tension. Concrete’s tensile strength is only about 10 to 15 percent of its compressive strength, so steel carries the tension.
If you make a footing twice as wide and the load stays the same, the pressure on the soil…
Show the answer
is cut in half. Pressure is force divided by area. Twice the area, half the pressure.

Go deeper

Science Lab: Forces at Work: Free-Body Diagrams Free-body diagrams: how to draw every force on an object.
Science Lab: Newton’s Laws of Motion The three laws behind every load path.
OpenStax, College Physics 2e, 9.2 The Second Condition for Equilibrium The second condition for equilibrium: why beams don’t rotate.
OpenStax, College Physics 2e, 5.3 Elasticity: Stress and Strain Tension, compression, shear and Young’s modulus, with worked examples.
Lesson 4: Framing Next stop on the load path: studs, plates and headers.

Sources

I finished this lessonSaved on this device only.

A free course from Teddy Rook Book. It explains how houses are built in general and follows U.S. sources; the local building code, the building department and the manufacturer’s instructions are the final word.