Can You Design an Earthquake-Safe House?: Going Further 9–12

What shaking does to a house

You met earthquake waves in Grade 9 Grade 9: Waves all around us: rock slips along a fault, and the energy travels out as seismic waves that shake the ground. (How the waves travel through the Earth, and why Nepal has great earthquakes, is in Why Is Everest Still Rising?.) The most damaging part of the shaking is sideways: the ground jerks back and forth, several times a second.

Think of standing in a bus when it starts suddenly. Your feet go with the floor, but your head and body are left behind, and you lurch backwards. That is inertia Grade 9: Grade 9: Inertia. A house does the same. Its foundation moves with the ground; its heavy walls and roof are left behind for a moment, and the walls bend. To drag the roof along, the walls must push on it, and the roof pushes back on the walls just as hard.

Figure 47.2 a. When the ground jerks sideways, the base of a house goes with it but the heavy roof lags behind, so the walls lean (drawn far more than real: a few millimeters). b. Seen from above: in a stone house without bands, the walls only touch at the corners, so the corners split and the long walls fall outwards. c. A band running round the top of all four walls ties them into one box.

How big is that push? Newton’s second law, F = ma Grade 9: Grade 9: Newton’s second law, says it depends on two things: the mass of the house, and the ground’s acceleration. Engineers give the acceleration as a share of g, the acceleration of a falling body (9.8 m/s²). Shaking of “0.3 g” is ground accelerating at 0.3 × 9.8 = 2.94 m/s². Then a house that moved stiffly with the ground would feel a sideways force of 0.3 times its own weight.

Worked example

The force on a stone house

A one-storey stone house has walls 26 m long in all, 2.8 m high and 0.45 m thick. Stone laid in mud has a density of about 2,000 kg/m³. a. What is the mass of the walls? b. What sideways force is needed to move them with the ground at 0.3 g? c. A light house of timber and sheet metal of the same size has a mass of about 8,000 kg. What force does it need?

Answer

a.Volume of the walls = 26 m × 2.8 m × 0.45 m = 32.8 m³. Mass = density × volume = 2,000 kg/m³ × 32.8 m³ = 65,600 kg, about 66 tonnes.
b.a = 0.3 × 9.8 m/s² = 2.94 m/s².

$F = ma = 65\,600\ \text{kg} \times 2.94\ \text{m/s}^2 = 193\,000\ \text{N} \approx 190\ \text{kN}$
That is about the weight of 20 tonnes, pushing sideways, back and forth, several times a second.
c. F = 8,000 kg × 2.94 m/s² = 23,500 N, about 24 kN: eight times less. A light house feels a light force.

Why stone in mud falls

Mud is a very weak glue. A wall of stones in mud can hold up its own weight for centuries, because the stones are pressed together from above. But it can hardly hold any pull. When the shaking pushes a long wall sideways, the wall tries to bend, the stones on one side are pulled apart, and it falls outwards. The corners, where two walls only touch, crack first. Once the walls have gone, the roof falls in (Figure 47.2).

The cure is to make the house act as one box. If the four walls are tied together, a wall pushed sideways is held up by the walls at its ends, which are very stiff along their own length. That is the job of seismic bands: belts of reinforced concrete or timber running round all the walls at several heights, like the hoops round a barrel.

Two houses of the same size are shaken in the same earthquake. One has a roof of stone slates; the other a roof of corrugated iron sheets. Which is more likely to stay standing, and why?

Pick an answer to see why.

Every house has its own swing

Push the top of a young tree, or a tall bamboo, and let go: it sways back and forth at its own steady rate. A building does the same. The time for one full sway is its natural period. A rough rule engineers use is about 0.1 s for every storey: a two-storey house sways about 5 times a second, a ten-storey building about once a second. Tall buildings are more flexible, and sway more slowly.

Shaking that matches a building’s natural period makes it sway more and more, the way small pushes at the right moments make a swing go higher and higher. This is called resonance. So how hard a house is shaken depends not only on the earthquake, but on the match between the ground’s shaking and the house.

And the ground matters. Hard rock passes on quick, sharp shaking. Soft ground, like the deep clay of the old lake under the Kathmandu Valley (Why Do People Live Where They Do?), shakes harder and more slowly, like a bowl of jelly.

Step 1: what does “safe” mean?

You may have met the engineer’s way of starting a design: write down the criteria (what the solution must do) and the constraints (the limits it must stay within) (Designing for a crash). For a helmet that is fairly simple. For houses after a great earthquake it is much harder, because the problem is shared by hundreds of thousands of families, the government, the masons, the villages and the country.

“The house must be safe” is too vague to design with. Safe in how big an earthquake? Safe means no damage at all, or that it may crack but must not fall? Engineers turn a want into something they can measure: a quantitative criterion, with a number. Some things can’t be measured, like whether a house looks right in its village: those are qualitative criteria, and they matter too.

A stone-paved lane between houses with walls of rough stone and roofs of gray stone slates; people carry big baskets along the lane — **Figure 47.3** Houses of stone, with roofs of stone slates, in Barpak, Gorkha district. The 2015 earthquake began beneath this village. Photo: Krish Dulal, CC BY-SA 3.0

Here is how the problem of rebuilding a family’s house in a hill village might be written down:

	What	Kind
Safety	must not collapse in shaking of 0.35 g (stronger than most of Nepal felt in 2015); may crack	constraint, quantitative
Cost	the family has the government’s grant of Rs 3 lakh and about Rs 3 lakh of its own, so at most Rs 6 lakh	constraint, quantitative
Size	two rooms and a kitchen, about 40 m²	constraint, quantitative
Time	a roof over the family before the next winter	constraint, quantitative
Building it right	local masons can build it correctly with little training	criterion, qualitative
Warmth	warm enough in winter at 2,000 m without burning much firewood	criterion, quantitative (indoor temperature)
Look	fits the village’s houses; has the rooms a family needs for worship and storing grain	criterion, qualitative
Environment	uses little cement and steel, which take a lot of energy and release a lot of CO₂ to make	criterion, quantitative

Notice how each one comes from people’s needs (shelter, safety, warmth) and wants (a house that looks like home, built quickly). A design that ignores the wants can fail even if it is strong: families who don’t like their new house add rooms to it in the old way, without bands, and undo its safety.

A story from science

The schools that were ready

In the 1990s, a Nepali engineer, Amod Mani Dixit, and his colleagues at the National Society for Earthquake Technology (NSET) began strengthening school buildings, adding steel and concrete to old walls, at first only a few schools a year. When he first talked about it, Dixit later said, nobody trusted them: how could a poor country like Nepal do that? But school by school the work spread, and by 2015 between 350 and 400 of Nepal’s 35,000 schools had been strengthened, many of them in the Kathmandu Valley.

When the great earthquake came, the strengthened schools stood (reports found none that collapsed), while thousands of other schools across Nepal were destroyed or badly damaged. Many of the strengthened ones became shelters for families whose houses had gone. The earthquake struck on a Saturday, when schools were closed. On a school day, the unstrengthened classrooms would have been full.

Which of these is a quantitative criterion for a new house?

Pick an answer to see why.

Step 2: break the problem down

“Design a house that won’t fall” is too big to solve in one go. Engineers break a big problem into smaller problems that can each be solved, tested and checked on its own. For a masonry house, the sub-problems follow the way a house fails:

Sub-problem	Solution	Why it works
The house must not slide or sink	a wide foundation, below the ground, on firm soil	spreads the weight; soft or loose ground sinks unevenly
The walls must act as one box	bands of reinforced concrete or timber at plinth, sill, lintel and roof level	ties the walls together, so each is held by the walls at its ends (Figure 47.2)
The corners must not split	steel bars running up every corner, tied into each band	the bars carry the pull that mud and stone can’t
Openings must not weaken the walls	small windows and doors, well away from corners, with steel bars beside them	a wall full of holes is weakest exactly where it must be strongest
A wall must not split in two layers	through-stones: long stones that cross the whole thickness of the wall	a thick stone wall is really two thin walls with rubble between, unless something ties them
The roof must not add force or fall	a light roof, tied down to the roof band; a gable band along the sloping tops of the end walls	less mass means less force, and a tied roof can’t slide off

Figure 47.4 The front wall of a one-storey stone house built to resist earthquakes: the big problem broken into parts, each solving one way a house fails. Bands of concrete or timber (gray), steel bars inside the walls (red, dashed), through-stones (dark), small openings away from the corners, and a light roof tied down.

Breaking a problem down only works if you then put it back together. The parts interact. Bands do little unless the corner bars tie them together. A light sheet roof cuts the force, but it is noisy in the rain, hot in summer and cold in winter, so it changes the warmth criterion. Small windows make the walls stronger and the rooms darker. Every solution to one sub-problem must be checked against the others, and against the whole.

Try it

Break down another problem

A village needs a new water tank that will still hold water after a strong earthquake. Break the problem into at least three smaller problems, and suggest a solution to each.

Answer

For example:

a.The tank must not slide or topple: a wide, deep foundation on firm ground, and the tank fixed to it.
b.The walls must not crack and leak: reinforced concrete walls, or a steel or plastic tank that can bend a little without breaking.
c.The water sloshing inside must not break it: a tank of the right shape, and walls strong enough for the sloshing water’s push (water is heavy: a full 10,000 liter tank holds 10 tonnes).
d.The pipes must not snap: flexible joints where the pipes enter and leave the tank, so the tank and the ground can move a little differently.
e.If it does leak, the village must still have water: a second, smaller tank, or a way to close a broken pipe quickly.

Step 3: test it on a computer

How do you know a design will work before the earthquake comes? You can’t wait for one. You can build a model and shake it: on a shake table, a platform that machines move back and forth to copy a real earthquake. One of the biggest, E-Defense in Miki, Japan, is 20 m × 15 m and can shake a whole building of up to 1,200 tonnes. But a shake-table test costs a lot, and destroys the model. So engineers first test their ideas on a computer simulation: a model made of numbers.

A full-size six-storey concrete building with balconies and outside stairs, standing inside a huge hall on the flat floor of the E-Defense shake table — **Figure 47.5** A full-size six-storey concrete building on the E-Defense shake table in Japan, in 2006. The whole building, not a model, is shaken as a real earthquake would shake it. Photo: hibino from Kanagawa, Japan, CC BY 2.0

Two small model buildings of thin posts and flat floors, several storeys tall, standing side by side on the platform of an outdoor shake table — **Figure 47.6** Two model buildings on a shake table in California. The one on the left is fixed to the table; the one on the right stands on special bearings that let the ground move under it. Shaking them side by side shows which design works better. Photo: Shustov, CC BY-SA 3.0

How the computer does it

The simplest model of a house is a heavy mass (its roof and walls) on a spring (the walls, which bend and spring back). The computer doesn’t solve the problem in one go. It takes a tiny step in time, again and again:

Where is the ground now? (From a record of a real earthquake, or a made-up one.)
How far is the top of the house bent away from the ground? The spring pushes back with a force in proportion to that bend.
From F = ma: the force gives the acceleration of the top of the house.
From the acceleration, a new speed; from the speed, a new position, a tiny moment later.
Go back to 1.

Each step is simple arithmetic. A computer can do millions of them in a second, so it can “shake” a hundred designs in the time it takes to read this sentence.

Worked example

Two steps of a simulation

In a model of a two-storey house, the spring’s push on each kilogram of the house is 987 × (how far the ground is from the top of the house, in meters), in newtons. The time step is 0.01 s. At the start, the top of the house is at 0 and not moving. In the first step the ground is at 2 mm (0.002 m), in the second at 3 mm. Work out the top’s acceleration, speed and position after each step.

Answer

Step 1. Distance from the ground to the top: 0.002 − 0 = 0.002 m.
Acceleration (force per kg): a = 987 × 0.002 = 1.97 m/s².
New speed: v = 0 + a × 0.01 s = 0.0197 m/s.
New position: 0 + v × 0.01 s = 0.000197 m, about 0.2 mm.
Step 2. Distance: 0.003 − 0.000197 = 0.002803 m.
a = 987 × 0.002803 = 2.77 m/s².
v = 0.0197 + 2.77 × 0.01 = 0.0474 m/s.
Position: 0.000197 + 0.0474 × 0.01 = 0.000671 m, about 0.7 mm.
The top of the house is following the ground, but lagging behind it. At step 2 the force on the walls is 2.77 ÷ 9.8 = 0.28 times the house’s weight. The computer goes on like this for every hundredth of a second of the earthquake (the simulator below takes even smaller steps, 500 a second, to be more exact).

Now try it. The simulator below is this model. Each run uses the same made-up earthquake, so the only things that change are the ones you change: the house, the ground and the strength of the shaking. That is what makes it a fair test, with one independent variable at a time, just as in an experiment Grade 10: Grade 10: Variables of scientific research.

Choose a kind of house, the ground it stands on, how many storeys it has and how strong the earthquake is, then press Shake. The blue line is the force on the walls, as a share of the house’s weight; the gray line is the force a house that couldn’t bend at all would feel; the dashed lines are where heavy damage and collapse begin. Start with two storeys of stone in mud, at 0.3 g. Then change one thing at a time. Which kinds of house survive 0.3 g? On which ground is a four-storey concrete frame safest?

House:

Ground:

Storeys: 2 Earthquake (shaking on rock): 0.30 g

Biggest force on the walls: –
Biggest sway at the top: –
Heavy damage / collapse at: 0.30 / 0.60 × weight

Choose a house, the ground and the earthquake, then press Shake.

A teaching model, not a design tool: each house is one mass on a spring, and the strengths are typical values for each kind of house.

In the simulator, a four-storey concrete frame on rock comes through a strong earthquake far better than the same building on soft clay. Why?

Pick an answer to see why.

Run the simulator for every natural period, from a squat one-storey house to a tall tower, and plot the biggest force on each. The result is a graph engineers design with, a response spectrum.

Figure 47.7 The biggest sideways force on houses of every natural period, in the same earthquake (0.15 g on rock), from the computer model, averaged over six made-up earthquakes. On rock, one- and two-storey houses are hit hardest. On soft clay they are hit about as hard as on rock, but taller buildings far harder, most of all buildings of about six to eight storeys.

A model is only a model

The computer’s answers are only as good as the model. Ours leaves out a lot: a real house is not one mass on one spring, a cracked wall is not as springy as a new one, and a real earthquake is different every time. Engineers check their programs against shake-table tests and against what real earthquakes did to real buildings, and they design with a safety margin, for the earthquake that might be stronger than the one they modeled.

Step 4: weigh the trade-offs

Now the family has to choose. There are several possible houses, and none is best at everything. Choosing one means giving up something to get something else: a trade-off. A good choice comes from three steps:

Rule out every design that breaks a constraint (too costly, not safe enough).
Decide which criteria matter most: the priorities.
Compare what’s left, with the most important criteria counting most.

You may have used a decision matrix for this before (Can a Forest Come Back?): rate each design from 1 (poor) to 5 (very good) on each criterion, give each criterion a weight for how much it matters, multiply, and add up. Here are five ways to rebuild a small two-room house. The numbers are rough, for practice; a real family would get prices from masons and advice from an engineer.

Design	Cost (Rs lakh)	Doesn’t collapse up to	Easy to build right	Warm in winter	Traditional look	Low CO₂
a.Stone in mud, as before	4	0.15 g	5	5	5	5
b.Stone in mud with timber bands	5.5	0.35 g	4	5	5	4
c.Brick in cement with concrete bands	8	0.5 g	3	4	3	3
d.Concrete frame with brick walls	14	0.5 g	2	2	1	1
e.Light timber frame, sheet roof	5	0.5 g	3	2	2	5

Worked example

Choosing for a family in the hills

The family in Step 1 has at most Rs 6 lakh, and the house must not collapse at 0.35 g. Being easy to build right matters most (weight 3), then warmth (weight 2); look and CO₂ matter a little (weight 1 each). Which design should they choose?

Answer

Constraints first. a. is out: it would collapse at 0.35 g. c. and d. are out: over Rs 6 lakh. That leaves b. and e.
Score what’s left (weight × rating, added up):

b.3 × 4 + 2 × 5 + 1 × 5 + 1 × 4 = 12 + 10 + 5 + 4 = 31
e.3 × 3 + 2 × 2 + 1 × 2 + 1 × 5 = 9 + 4 + 2 + 5 = 20

The best possible is 5 × (3 + 2 + 1 + 1) = 35, so b. scores 31 ÷ 35 = 89 % and e. 20 ÷ 35 = 57 %.
Stone in mud with timber bands wins. It is nearly the old house, built by the same masons with the same stone, made far safer by the bands, corner posts and through-stones.

Try it

A school in an old town

A school in an old town has Rs 15 lakh for a small building, which must not collapse at 0.5 g (it will be full of children). The town cares most about the look of its old streets (weight 3); easy to build right has weight 2; warmth and CO₂ weight 1 each. Which design wins?

Answer

Constraints: a. (0.15 g) and b. (0.35 g) are not safe enough. All are within Rs 15 lakh. That leaves c., d. and e.

c.2 × 3 + 1 × 4 + 3 × 3 + 1 × 3 = 6 + 4 + 9 + 3 = 22, 22 ÷ 35 = 63 %
d.2 × 2 + 1 × 2 + 3 × 1 + 1 × 1 = 4 + 2 + 3 + 1 = 10, 29 %
e.2 × 3 + 1 × 2 + 3 × 2 + 1 × 5 = 6 + 2 + 6 + 5 = 19, 54 %

Brick in cement with concrete bands wins. Notice that the safety constraint decided more than any weight: it removed the two designs that look most traditional.

Set the family’s budget and the shaking the house must survive: designs that break either constraint are ruled out. Then set how much each criterion matters. Which constraint changes the winner most? Can you find priorities that make the light timber frame win?

Budget: Rs 8 lakh

Must not collapse in shaking of:

Easy to build right: matters Warm in winter: matters Traditional look: matters Low CO₂: matters

Stone in mud with timber bands wins: nearly as cheap and warm as the old houses, and much safer. It fails only the strictest safety need.

Costs, safe shaking and ratings are rough numbers for practice, for a small two-room house; a real family would get quotes from local masons and an engineer’s advice.

Costs and impacts beyond the family

Some trade-offs reach far beyond one house:

Society. Nepal’s government gave each family whose house was destroyed a grant of Rs 3 lakh, in three parts, the second and third paid only once the house was being built to one of the approved earthquake-safe designs. That turned the safety criterion into a rule every family had to meet, and thousands of masons were trained in earthquake-safe building along the way. By the end of 2021, when the reconstruction authority closed, about nine families in ten had rebuilt.
Culture. In the rush to rebuild, many villages and towns lost the look they had had for centuries, as cement blocks and concrete frames replaced stone, brick and carved wood. Some towns decided that their look was worth paying for. As long ago as 2001, Bhaktapur’s municipality paid three-quarters of the cost of the wood, and all of the bricks and tiles, for families who gave new houses a traditional front.
Environment. Making cement and steel takes a great deal of energy and releases a lot of CO₂; bricks are fired in kilns that burn coal. Stone and timber from nearby need much less, but timber has to come from forests that can regrow it.
Reliability. A design that is safe only if it is built perfectly is a risky design. Engineers prefer designs that are forgiving: still fairly safe when the work is less than perfect.

Build a shake table

Activity

A shake table on the floor

You need: two flat pieces of cardboard or thin board (about 30 cm × 40 cm), four round pencils or marbles, a rubber band or two, a ruler, and to build with: drinking straws or thin sticks, sticky tape, and small blobs of clay or dough as weights.

Lay one board on a table or the floor. Put the pencils on it, and the second board on top, so that the top board rolls freely. Loop a rubber band from the top board to something fixed, so it springs back when you pull it. This is your shake table.
Build a two-storey “house” from straws and tape, about 15 cm tall, with a blob of clay on each floor and on the top, as the mass. Tape its feet to the top board.
Shake the board by pulling it about 2 cm and letting go, or by pushing it back and forth with your hand. Keep the shaking the same each time: count the shakes in 10 seconds, and keep the distance the same.
Write down what happens: does it lean, wobble, break?
Now improve it, one change at a time: add diagonal straws (bracing) on the walls; tie a “band” of tape round each floor; move the clay lower; make it taller. Test each change with the same shaking.
Then try shaking quickly and slowly. Does the tall model or the short one wobble more at each speed?

What you should see

Without bracing, the straw frame leans over and folds at the joints. Diagonal straws make each wall stiff, and the house hardly bends. Tape round each floor holds the walls together. Moving the clay down (a lighter top) makes it wobble less. And you should find resonance: shaken slowly, the tall model sways a lot, while shaken quickly, the short one does, and the tall one barely moves. That is exactly what the computer model shows, and why engineers have to know both the building and the ground.

In short

In an earthquake the ground jerks sideways; the house’s heavy parts lag behind, and the walls must push them along with a force F = ma. A lighter house feels a smaller force.
Every building has a natural period, about 0.1 s per storey; shaking that matches it makes the building resonate. Rock shakes short houses hardest, soft clay taller ones.
Engineers start by turning needs and wants into criteria (the more the better) and constraints (pass or fail), as numbers where they can (quantitative) and in words where they can’t (qualitative).
They break a big problem down: foundation, bands, corner bars, openings, through-stones, a light roof. Then they check that the parts work together.
They test ideas on a computer simulation before building: many tiny steps of F = ma, one variable changed at a time. A model leaves things out, so it is checked against real tests and used with a safety margin.
To choose, they rule out designs that break a constraint, set priorities, and weigh the trade-offs of cost, safety, reliability and looks, and the effects on society, culture and the environment.

Questions

A family wants a house that “will survive the next big earthquake”. What should an engineer do first?

Pick an answer to see why.

Which is a constraint rather than a criterion?

Pick an answer to see why.

a.

a. A house has a mass of 50,000 kg. What sideways force is needed to move it with the ground at an acceleration of 0.25 g (take g = 9.8 m/s²)? b. The owners replace a stone-slate roof of 12,000 kg with a sheet-metal roof of 1,500 kg. By how much does that reduce the force?

Answer

a.a = 0.25 × 9.8 = 2.45 m/s². F = ma = 50,000 kg × 2.45 m/s² = 122,500 N, about 123 kN.
b.The mass falls by 12,000 − 1,500 = 10,500 kg. The force falls by 10,500 kg × 2.45 m/s² = 25,700 N, about 26 kN, or about a fifth of the total.

b.

A town on soft clay has many one- and two-storey brick houses and a few new seven-storey apartment buildings. An engineer says the apartments are at greater risk than the houses. Use the idea of natural period to explain why.

Answer

A building’s natural period is roughly 0.1 s per storey: about 0.1–0.2 s for the houses, and about 0.7 s for the apartments. Soft clay shakes hardest at slow periods, around 0.5–1 s at many soft sites. The apartments’ natural period matches the ground’s shaking, so they resonate and sway more and more; the houses swing much faster than the ground, so they respond less. (On rock it would be the other way round.)

c.

Break the problem “make a two-storey stone house earthquake-safe” into at least four smaller problems, and give a solution to each and the reason it works.

Answer

For example:

a.Walls separate at the corners: bands of concrete or timber round all the walls at plinth, sill, lintel and roof level tie them into one box.
b.Corners crack and open: steel bars up every corner, tied into each band, carry the pull that stone and mud can’t.
c.Walls are weakened by openings: small windows and doors, well away from the corners, with steel bars beside them.
d.A thick wall splits into two thin skins: through-stones that cross the whole wall tie the two faces together.
e.A heavy roof adds force and falls on people: a light roof tied down to the roof band.
f.The house slides or sinks: a wide foundation, below the ground, on firm soil.

d.

Describe how a computer simulation of a house in an earthquake works, in steps. Give two things a simple model leaves out, and say how engineers make sure their designs are safe anyway.

Answer

The house is modeled as a mass on a spring. For each tiny step in time (a hundredth of a second or less), the computer: finds where the ground is, from an earthquake record; works out how far the top of the house is bent from the ground; works out the spring’s force; uses F = ma to find the acceleration; updates the speed and then the position; and repeats, thousands of times, for the whole earthquake. It records the biggest force and sway, and compares them with what the walls can take.
It leaves out, for example: that a real house is many masses and springs, not one; that cracked walls get weaker and less springy; that it may not be built as designed; that the next earthquake will be different from the one modeled; that the ground may slide or sink.
Engineers check their models against shake-table tests and against real buildings in past earthquakes, and design with a safety margin, for shaking stronger than they expect.

e.

A family has Rs 7 lakh, and their house must not collapse at 0.35 g. Their priorities: warmth (weight 3), look (weight 2), easy to build right (weight 1), low CO₂ (weight 1). Using the table in Step 4, which design should they choose? Show your working.

Answer

Constraints: a. is not safe enough (0.15 g); c. (Rs 8 lakh) and d. (Rs 14 lakh) are over budget. That leaves b. and e.

b.3 × 5 + 2 × 5 + 1 × 4 + 1 × 4 = 15 + 10 + 4 + 4 = 33 out of 35, 94 %.
e.3 × 2 + 2 × 2 + 1 × 3 + 1 × 5 = 6 + 4 + 3 + 5 = 18, 51 %.

They should choose b., stone in mud with timber bands: it meets both constraints, and it is warm and traditional.

f.

After 2015, many families in hill villages rebuilt with concrete frames and cement blocks, even where an engineer said a banded stone house would be safe and cheaper. Suggest reasons, and say what was gained and what was lost.

Answer

Reasons: concrete looked modern and was seen as a sign of doing well; families had seen stone houses fall and didn’t trust stone, even with bands; some masons knew concrete work better; cement and steel could be bought, while good stone and timber were hard to find or carry; a concrete house can be extended upwards later.
Gained: if well built, strength in very strong shaking; a house that looks modern; room to add storeys.
Lost: much more money (often borrowed); warmth, as concrete houses are cold in the hills; the village’s traditional look and building skills; more CO₂ from cement and steel. And a concrete frame built without an engineer can be less safe than a well-built banded stone house, so the safety gained may not be real.

Think about it

Who should decide?

The government set the rules every rebuilt house had to follow, engineers checked them, and families chose among the designs that passed. Was that a good way to share the decision? What would you change?

Answer

There is no single right answer. Rules set by the government make every house meet a minimum of safety, which protects people even when they don’t believe an earthquake will come, and protects their neighbors (a house that falls into the street blocks it). But families know best how they live, and designs they don’t like get changed, often unsafely. Many engineers now argue for both: a safety constraint set by law, and the design worked out with the family and the village, using local materials and masons, with the costs and trade-offs explained so that the family can choose.

Where to go next

Why Is Everest Still Rising? Why Nepal has great earthquakes, how seismic waves travel, and why western Nepal is waiting for its next one.
Why Do People Live Where They Do? How water, soil and hazards like earthquakes and floods shaped where people settle, and the chance of a hazard over a lifetime.
Does the Fix Actually Work? How engineers test whether a solution, like the rebuilt brick kilns of the Kathmandu Valley, really does what it was meant to, with data.