Hip Rafter Design Step by Step - How to Size a Hip Beam, Worked Example (NDS 2024)

Hip Rafter Design - Sizing a Hip Beam on a Sloped Roof

0:00A hip rafter is the one roof member that breaks every convenient assumption at once. It is not on the pitch of the roof it carries. It does not carry a uniform load. And its two governing load cases are measured on two different lengths. This example works one all the way through, by allowable stress design to NDS 2024: a nineteen point eight foot hip carrying the corner of a clay tile roof, sized as a six by twelve Douglas Fir-Larch number two. At the end we enter the same design in StructSuite and watch it reproduce every number.

0:32Three things, and each one is a trap. First, the hip is not on the pitch of the roof it carries — it runs diagonally across the corner, so its own slope is flatter than the common rafters framing beside it. Second, it does not carry a uniform load: the jacks dying into it get longer and longer, so the load it picks up is a triangle. Third, its two governing load cases are measured on different lengths — dead load per square foot of the sloped surface, roof live load per square foot of the horizontal projection.

1:01Get any one of them wrong and the answer is off by anywhere from three to twenty five percent. And here is the part worth remembering: the biggest error is not in the moment. It is in the reaction at the top of the hip — which is what sizes the post and the connection nobody drew.

The structure - what we're designing

1:17Here is the building. A rectangular house, forty feet by twenty eight, hip roofed at six in twelve on all four planes. Because it is twelve feet longer than it is wide, the ridge is exactly twelve feet long, and four hips run from the building corners up to the ridge ends. Jack rafters at twenty four inches on center frame into them. The ceiling is vaulted, so the hip is exposed below. In amber, the one we are designing. In dashed green, its tributary area in plan — ninety eight square feet, which we will derive shortly.

Why a hip is never on the roof's pitch

1:49Now the single most common hip rafter mistake — and it is a geometry mistake, not an engineering one. A common rafter runs perpendicular to the eave. Its horizontal run is half the building width, fourteen feet, and it rises fourteen times six twelfths — seven feet. The hip runs diagonally across the corner to the same point on the ridge. Its horizontal run is the diagonal of a fourteen by fourteen square: fourteen root two, nineteen point eight feet. But its rise is the same seven feet, because it ends at the same ridge height. Same rise, longer run. So the hip is flatter.

2:22On the left, in plan: the hip is the forty five degree diagonal of that corner, giving a nineteen point eight foot run. On the right, the two members in elevation. Gray is the common rafter, six in twelve, twenty six point five seven degrees. Amber is the hip, four point two four in twelve, nineteen point four seven degrees. Both reach the same ridge height, so the hip's flatter angle comes entirely from its longer run.

2:47Side by side. Horizontal run, fourteen feet against nineteen point eight. Rise, seven feet for both. Pitch, six in twelve against four point two four in twelve. Angle, twenty six point five seven degrees against nineteen point four seven. Length along the member, fifteen point six five feet against twenty one. And the sloped length factor — the number that converts loads — one point one one eight for the roof planes, one point zero six one for the hip.

3:11Carpenters have known this forever, and they say it the other way round. They lay hips out on a framing square using seventeen inches of run instead of twelve — twelve root two, sixteen point nine seven, the plan diagonal of a twelve inch square. It is the same fact as the table: the hip rises six inches per seventeen inches of its own run. The engineer's four point two four in twelve and the carpenter's six and seventeen describe one member.

3:36Because the hip is flatter, its sloped length factor is one point zero six one, not one point one one eight. Using the roof's factor on the hip over converts dead load by five point four percent — conservative, but it is money. And the same confusion running the other way, using the hip's flatter factor on the roof planes, is unconservative. Two numbers, two jobs, not interchangeable.

Choosing the inputs - where every value comes from

3:58Before any arithmetic, every input. Every input is either a code prescribed value with its section cited on the row, or a geometry fact read off the framing plan. Nothing is a guess. Span for analysis, nineteen point eight feet — the horizontal projection, never the twenty one foot sloped length. Pitch, four point two four in twelve, derived. Pinned at the eave corner, roller at the ridge end. Tributary, ninety eight square feet, triangular. Dead load, seventeen pounds per square foot of roof surface. Roof live load, eighteen pounds per square foot of horizontal projection.

4:29No snow. A six by twelve Douglas Fir-Larch number two, Beams and Stringers. Dry service. Three and a half inch bearing seats. And limits of L over 240 live, L over 180 total. And the dead load takeoff, all of it per square foot of the sloped roof surface, because that is how roofing is sold and installed. Clay tile, ten pounds. Underlayment and battens, six tenths. Five eighths plywood, two. Two by eight jacks at twenty four on center, one point three. R thirty insulation, thirty five hundredths. Five eighths gypsum ceiling, two point seven five. Seventeen pounds per square foot on the roof surface.

Step 1 - Hip geometry

5:05Step one. Everything downstream comes from four numbers, so derive them once and carry them. Horizontal run: fourteen root two, nineteen point eight zero feet. Rise: fourteen times six twelfths, seven feet. Length along the hip: the square root of nineteen point eight squared plus seven squared — the square root of four hundred forty one, exactly twenty one feet. And the sloped length factor, twenty one over nineteen point eight: one point zero six one.

5:30The analysis span is nineteen point eight feet, the horizontal projection — and that is not a simplification. For vertical gravity loads it is statically exact: the moments and shears in the sloped member about its strong axis are identical to those of a horizontal beam on the projected span carrying the projected loads. It is also the basis every IBC span table is written on. What the slope changes is not the span. It is which loads have to be re-measured onto it — which is Step four, and nothing else.

Step 2 - Why a hip carries a triangle

6:00Step two. Why the load on a hip is a triangle. Walk along the hip from the building corner toward the ridge. At the corner, the jacks dying into it are a few inches long. At the ridge end, they are full length commons. Each one delivers half its load to the hip and half back to the wall. So the load the hip picks up grows linearly, from nothing at the corner to a maximum at the ridge end. That is a triangle, and it is not an approximation — it falls straight out of the framing.

6:28On the left, the corner in plan. Every jack is drawn in two tones — the lighter half spans back to the wall, the darker half is what the hip carries. The green dots are the mid points, and the dashed tributary boundary is nothing more than the line through them. That is why the tributary width is zero at the corner and nine point nine feet at the ridge end. On the right, the consequence: a triangular line load, with two thirds of the total landing on the ridge end support.

6:54In plan the tributary is the quadrilateral with corners at zero zero, fourteen seven, fourteen fourteen, and seven fourteen. Its area is one half times fourteen squared — ninety eight square feet. The maximum width, measured square to the hip, is fourteen over root two, nine point nine feet — exactly half the hip's own span. Check it as a triangle: one half times nineteen point eight times nine point nine is ninety eight. Now, that is a plan area. The roof it represents is inclined at six in twelve — the roof plane's pitch, not the hip's — so the surface hanging on this hip is ninety eight times one point one one eight, one hundred nine point six square feet.

7:30And there it is, shaded green on the framing plan — one eighth of the roof, delivered to one member. Stop on this one, because it is the second classic hip error. Two different slope factors are in play on one member, doing two different jobs. The tributary surface uses the roof plane's factor, one point one one eight, because that is the surface the tiles sit on. The load conversion coming up uses the hip's own factor, one point zero six one, because that is the length the load gets spread along. Swap them and nothing will announce itself.

Step 3 - Loads: two intensities, two lengths

8:02Step three. Two load intensities, measured on two different lengths. Dead load is defined on the roof surface, so start from the surface area. One hundred nine point six square feet times seventeen pounds per square foot: one thousand eight hundred sixty three pounds hanging on this hip. The distribution is triangular, so the peak is twice the average — two times eighteen sixty three, divided by the hip's own twenty one foot length: one hundred seventy seven point four pounds per foot, measured along the hip.

8:30Roof live load is a different animal. ASCE 7-22, section 4.8.2 defines it per square foot of horizontal projection — so it needs no surface correction at all. R one is one point zero, because ninety eight square feet is under two hundred. R two is one point two minus zero point zero five F, where F is six, the rise of the roof plane the hip supports — not the hip's own four point two four.

8:54That gives zero point nine. So L r is twenty times one times zero point nine, eighteen pounds per square foot, inside the twelve to twenty bounds of equation 4.8 dash 1. Times the nine point nine foot maximum width: one hundred seventy eight point two pounds per foot, on the projection. The module adds the beam's own weight from the section — fifteen point four pounds per foot along the hip — and being dead load, it converts exactly like D. Now notice something. The dead load peak is one hundred seventy seven point four. The roof live load peak is one hundred seventy eight point two. Almost identical, a complete accident of this roof, and a useful one — because it makes the two entered numbers look interchangeable while the analysis is about to treat them completely differently.

Step 4 - The slope conversion (horizontal-projection method)

9:38Step four. The slope conversion. Back to the hip's own geometry, because the factor this step uses comes from exactly one number on this drawing: four point two four in twelve. The beam is analysed on its horizontal projection. Loads defined along the sloped length get re-expressed per horizontal foot, which makes them larger, because one horizontal foot of hip is one point zero six one feet of actual member.

10:04Loads already defined on the projection are left exactly as entered. On top, each load drawn on the length it is defined on. In amber, the dead load block, parallel to the member over its twenty one foot sloped length. In blue, the roof live load block, on its own horizontal line over the nineteen point eight foot projection. Both are vertical gravity vectors — the only difference is the length each is measured on. Below, the analysis model: a horizontal beam on the projection, carrying the converted load.

10:35Load by load. Dead roof load, entered as zero to one hundred seventy seven point four, times one point zero six one, becomes zero to one hundred eighty eight point two on the projection. Self weight, fifteen point four, times the same factor, sixteen point three. Roof live load, times one point zero zero — unchanged, because it is already a projection intensity. Snow likewise. And wind also times one, for a subtler reason: it acts normal to the surface, and the cosine theta in the vertical component and the cosine theta in the projection cancel exactly.

11:08Deflection is computed and limited on the projection as well — the span table convention, and the one IBC Table 1604.3 is written on. Model the member on its twenty one foot sloped length instead and you get two errors pointing opposite ways: the deflection grows while the limit loosens. We will price that mistake later.

Step 5 - Section and material: Table 4D, not Table 4A

11:28Step five. The section and the material — and the table you read them out of is not the one most engineers reach for. A six by twelve is five and a half by eleven and a half inches dressed. That width puts it in the timber size class, so its design values come from Supplement Table 4D, Beams and Stringers — not Table 4A, which covers two to four inch dimension lumber. And this is not a formality.

11:52Same species, same grade name, two different tables. Select Structural: fifteen hundred pounds per square inch in 4A, sixteen hundred in 4D. Number one: one thousand against one thousand three hundred fifty — a thirty five percent difference. And number two, our grade, goes the other way: nine hundred against eight hundred seventy five. Different grading rules, different assumed uses. A six by twelve read off Table 4A is simply the wrong number, in either direction depending on grade.

12:20StructSuite ties the two selections together, per NDS 4.1.3. The design value table you choose strictly drives which Table 1B size classes are selectable: pick 4D and only timber sizes open. The others stay visible but grayed, with a note naming the table that would enable them, so you can see what exists rather than wondering where it went. And picking across the five by five boundary clears the selection the new table cannot design and flags it required, rather than silently re-reading it off the wrong page. We will watch that in the app shortly.

12:53So here is the member. Five and a half by eleven and a half. Area, sixty three point two five square inches. Section modulus, one hundred twenty one point two. Moment of inertia, six hundred ninety seven point one. Bending, eight hundred seventy five pounds per square inch. Shear, one hundred seventy. Compression perpendicular, six hundred twenty five. And a modulus of one point three million.

Step 6 - Analysis: reactions, shear, and moment

13:17Step six. The analysis, with the converted loads on a nineteen point eight foot simple span. The governing combination is ASCE 7-22, combination three a — D plus L r. For a triangular load rising to its peak at the far end, the classical results are: near reaction w L over six, far reaction w L over three, maximum moment w L squared over nine root three. Our triangle peaks at three hundred sixty six point four pounds per foot, giving twelve hundred nine pounds at the low end and two thousand four hundred eighteen at the high end. Add one hundred sixty one pounds of self weight at each end and the reactions are one thousand three hundred seventy at the eave corner, two thousand five hundred seventy nine at the ridge end.

14:03And the maximum moment is nine thousand nine hundred ninety six pound feet, at eleven point three one feet from the low end. Fifty seven percent of the span, not midspan — because a triangle does not put its peak in the middle. At the top, the load: sixteen point three pounds per foot of self weight plus the converted triangle running to three hundred sixty six point four. Below it, the shear — and look how asymmetric it is. Plus one thousand three hundred seventy at the eave corner, crossing zero at eleven point three feet, minus two thousand five hundred seventy nine at the ridge end.

14:35That asymmetry is the triangular load, made visible. And below that, the moment: one sagging peak of nine thousand nine hundred ninety six, at the point where the shear crossed zero. And now the part this whole example exists for. Two thousand five hundred seventy nine pounds — two thirds of the total load — arrives where the hip, the ridge, and two king common rafters converge. A ridge board cannot carry that; it is a nailing spacer with no bending capacity. That reaction needs a real load path: a post down to a bearing wall, a girder truss, or a hip supporting header. Sizing the hip and then hanging it off a two-by ridge board is exactly how hip roofs sag at the corners.

Step 7 - Adjustment factors, and CD per combination

15:15Step seven. The adjustment factors. The load duration factor is one point two five for D plus L r, because roof live load is a seven day construction load under NDS Table 2.3.2 — and zero point nine for the dead only cases. Applied per combination, never once globally. Wet service and temperature are both one: dry, under a hundred degrees. The size factor is one, because Table 4D tabulates timbers directly and C sub F only appears above twelve inches deep — ours is eleven and a half. The stability factor is one, because the jacks and sheathing brace the compression edge continuously, and in any case the depth to breadth ratio is two, for which NDS 4.4.1.2 requires no lateral support at all. Flat use, incising and repetitive member all one.

16:04So the adjusted bending value for the governing combination is eight hundred seventy five times one point two five: one thousand ninety four pounds per square inch. And because the duration factor belongs to the combination rather than the member, the dead only case runs against seven hundred eighty eight and produces its own ratio of zero point six nine three. Lower, but worth seeing — on a tile roof the permanent case is closer than engineers expect.

Step 8 - Flexure

16:31Step eight. Flexure — and this is the check that governs. The bending stress is the moment over the section modulus: nine thousand nine hundred ninety six, times twelve, over one hundred twenty one point two — nine hundred ninety pounds per square inch. And the capacity, per NDS equation 3.3 dash 1, is the adjusted value times the section modulus over twelve: eleven thousand forty seven pound feet. Nine thousand nine hundred ninety six against eleven thousand forty seven: zero point nine zero five. It passes, and it is the governing check on this beam.

Step 9 - Shear

17:06Step nine. Shear — taken at the support face from statics, and the high end governs, because two thirds of the load lands there. The adjusted shear value is one hundred seventy times one point two five, two hundred thirteen pounds per square inch. The capacity, per equation 3.4 dash 2, is two thirds of that times the area: eight thousand nine hundred sixty pounds. And the shear stress is one point five V over A — sixty one pounds per square inch.

17:31Two thousand five hundred seventy nine against eight thousand nine hundred sixty — zero point two eight eight. Shear passes comfortably, as it usually does on a member this deep. One note on that number. NDS 3.4.2.2 permits you to neglect uniform load acting within a distance d of the support, which would lower the demand. StructSuite does not take that reduction. It is a permission the engineer may exercise, with knowledge of the framing — not a default the software should quietly apply on your behalf. And the detailed calculation says so, in those words.

Step 10 - Deflection

18:06Step ten. Deflection. The hip supports a vaulted gypsum ceiling, so the limits are L over 240 live and L over 180 total, both on the nineteen point eight foot projection. And the total load case is not dead plus roof live. IBC Table 1604.3, footnote d, limits it to the creep component of long term dead load deflection plus the short term live load deflection — and for wood dry at installation and used dry, that creep component may be estimated as the immediate deflection from half the dead load. So the case actually checked is zero point five D plus L r.

18:42Roof live load alone: zero point three four one inches against L over 240, zero point nine nine zero — a ratio of zero point three four four. The footnote d case: zero point five five two against L over 180, one point three two zero — zero point four one eight. Both pass, with real margin. And this is the drawing to keep in mind for what comes next:

19:05nineteen point eight feet of projection, twenty one feet of actual member. Notice what the slope did not do here. The dead load deflection rose, because the converted load is larger. But the span used for the calculation and for the limit stayed nineteen point eight feet. Model the member on its twenty one foot sloped length and the limits loosen from zero point nine nine and one point three two inches to one point zero five and one point four zero, while the deflection itself grows. Two errors pointing opposite ways — worse than one, because the total still looks plausible.

Step 11 - Bearing

19:36Step eleven. Bearing — the last check, and the one where the two ends of this member behave very differently. Both ends bear on three and a half inch seats — a double top plate at the corner, a post cap at the ridge — over the full five and a half inch width, so nineteen point two five square inches at each. At the eave corner, one thousand three hundred seventy pounds gives seventy one pounds per square inch against six hundred twenty five:

20:01zero point one one four. At the ridge end, two thousand five hundred seventy nine pounds gives one hundred thirty four: zero point two one four. Nearly twice the stress at the top of the hip, for the same reason everything else about this member is asymmetric. The bearing area factor is one point zero at both ends. NDS 3.10.4 grants it only to bearings at least three inches from the end of a member, because the reference value already covers bearings of any length at a member end — and both of ours are end bearings. And the load duration factor never applies to compression perpendicular to grain, per Table 2.3.2, footnote one. Six hundred twenty five is six hundred twenty five, in every combination.

20:45Two practical notes the numbers do not show. First, compression perpendicular to grain belongs to whatever actually gets crushed. If the plate under the hip is a softer species, name that species in the app so the lower value governs — otherwise you are checking the beam, not the connection. Second, a hip bears on a sloped cut, so the reaction arrives at an angle to the grain, and NDS 3.10.3's Hankinson formula would give a higher allowable than plain perpendicular bearing. Checking against the perpendicular value alone, as we have, is the conservative simplification.

Five mistakes that show up on hip beams

21:21Five mistakes that show up on hip beams. Every alternative here was run through the same engine, so the cost of each is a real number, not a warning. One. Assuming the load is uniform. Spread the same total evenly and the moment barely moves — nine thousand seven hundred seventy six against nine thousand nine hundred ninety six, two percent low. Which is exactly why this mistake survives review: the number a checker looks at first is almost right. The reactions do not survive. One thousand nine hundred seventy five pounds at both ends instead of thirteen seventy and twenty five seventy nine, so the post and connection at the top are under designed by twenty four percent. A hip's danger is at its high end, and only the triangle shows it.

22:04Two. Using the roof's pitch for the hip. Convert the dead load at one point one one eight instead of one point zero six one and the moment goes to ten thousand two hundred ninety four, a ratio of zero point nine three two — three percent conservative here, pure waste on a bigger beam. Three. Modelling the beam on its sloped length. Enter twenty one feet and forget the conversion and the moment becomes ten thousand eight hundred eighty nine, zero point nine eight six — nine percent heavy — while the deflection limits quietly loosen. Two errors in opposite directions, and the total looks plausible.

22:37Four. Forgetting the conversion entirely — entering the dead load and leaving the member horizontal. Nine thousand six hundred eighty pound feet, zero point eight seven six. Only three percent unconservative, and it is tempting to conclude the whole conversion is a rounding error. It is not. Three percent is what a four point two four in twelve hip costs you, because that hip is nearly flat. On a twelve in twelve roof the hip runs at eight point four nine in twelve, its factor is one point two two five, and the same omission would understate the dead load moment by eighteen percent.

23:09And five. Sizing the hip and stopping there. The six by twelve passes at zero point nine zero five. The six by ten, one size down, same grade, does not: one point three zero eight. Depth is the lever on this member — but grade is a cheaper lever than it looks, because Table 4D's number one drops the same six by twelve to zero point five eight six. Between them lies the honest answer: a six by twelve number two uses ninety percent of its bending capacity, and nothing is wasted.

Summary of results

23:36And the summary. Every check on one page. Flexure, nine thousand nine hundred ninety six against eleven thousand forty seven — zero point nine zero five, and it governs. Shear, zero point two eight eight. Roof live deflection, zero point three four four. The footnote d total load case, zero point four one eight. Bearing at the ridge end, zero point two one four; at the eave corner, zero point one one four. The beam works, and flexure decides it.

24:04And the combinations that did not govern. Dead load alone, zero point six nine three. D plus three quarters L r, zero point eight zero three. Zero point six D, zero point four one six. The engine runs each with its own duration factor, which is why one report shows different capacities for the same member. And look again at the first: on a heavy tile roof, the permanent case reaches sixty nine percent of capacity by itself.

FAQ - slope, sizing, and snow

24:29Three questions worth closing on before we open the app. What slope do you design a hip rafter for? Its own — and on an equal pitch roof with a square corner, that is always flatter than the planes it carries. The rise is the same as the common rafter's, but the plan run is root two longer, so the hip's pitch is simply the roof pitch divided by root two. A four in twelve roof gives a two point eight three in twelve hip. Six gives four point two four. Twelve gives eight point four nine. If the two planes meeting at that corner have different pitches, or the corner is not ninety degrees, the hip is neither at forty five degrees in plan nor at that ratio, and you work the geometry out from the two plane equations — but the principle does

25:10not change. Use the hip's real rise over its real plan run. No size answers that without the tributary and the loads, and a hip is the worst member to guess at — because its triangular tributary makes it lighter than its length suggests. This one spans nineteen point eight feet and carries only three thousand nine hundred fifty pounds in total, an average of two hundred pounds per foot, because ninety eight square feet of roof is all that ever reaches it. A six by twelve handles it at ninety percent. But double the tile weight or the tributary and you are into a six by fourteen, a glulam, or a five and a quarter inch PSL very quickly.

25:47Enter the sloped roof snow load, p s, from Chapter 7, as a type S load — same triangular shape, no slope conversion, because p s is already a projection intensity. Two things change. The duration factor drops from one point two five to one point one five, the two month snow value, so capacities fall about eight percent. And the combination reads D plus, in brackets, L r or zero point seven S or R — that zero point seven is there because ASCE 7-22 moved to strength level ground snow loads. Let the module take whichever produces the greater effect.

Now in StructSuite - entering the same hip

26:21Now let's enter this exact hip in StructSuite's Wood Beam module, starting from a completely blank project, and watch it reproduce every number we just found by hand.

App Step 1 - Geometry & Configuration

26:31Step one, Geometry and Configuration — the spans, the supports, and the one toggle this whole example turns on. Blank. Wood is already the design material — the module also does steel to AISC 360-22, by LRFD, if you ever want to compare a wood and a steel option for the same member. We stay on wood, NDS 2024, allowable stress design. One span: nineteen point eight feet. And this is the first decision that matters — that is the horizontal projection, not the twenty one foot length of the member. The span box on a sloped beam always wants the projection.

27:09Pinned at the eave corner, which is the default, and the ridge end becomes a Roller. Simple span. The other options are Fixed, for a real moment connection, and Free, which is what makes a cantilever — neither applies to a hip sitting on a plate at one end and a post cap at the other. And now the toggle this example exists for — watch what the app does with the two numbers on this drawing.

27:33Sloped member — rafter or pitched beam. It is an opt in, because most beams are horizontal, and turning it off returns the member to horizontal rather than leaving a hidden slope behind. The rule is stated right on the label: D and self weight convert by the sloped length factor to the horizontal projection, while L, L r, S and W stay exactly as entered. Now the slope, and here is a detail worth knowing: the rise and run boxes take any run, not just twelve. So you can type the hip's real geometry instead of pre-converting it in your head. Rise, seven.

28:06Run, nineteen point eight. And there it is — the module reports the slope back as four point two four in twelve, nineteen point four seven degrees. The exact two numbers we derived from a fourteen by fourteen corner, without ever asking us to do the division. And the figure below the entry is the same picture we drew in Step four: the inclined member, the horizontal projection it is analysed on, and the conversion factor stated on the drawing — one point zero six one.

28:31It is drawn from the analysis slope rather than your keystroke, so the figure can never quote a factor the results behind it were not computed with.

App Step 2 - Load Definition

28:42Step two, Load Definition — where the triangle gets entered. Look at the first line of this step, because it has already changed: slope four point two four in twelve, D and self weight converted by one point zero six one to the horizontal projection, enter L, L r, S and W on the projection as usual. The app states the rule before you type a number — and it is quoting your slope, not a generic one.

29:07Include member self weight is checked by default and grayed out until Step three has a section. The moment we pick a six by twelve, this row fills itself in at fifteen point four pounds per foot and adds itself to D — and the note below states the conversion that will be applied to it. The first load row. Type D. Distribution: Linearly varying, triangular or trapezoidal — a first class option here, not a workaround. Then w one equals zero at the eave corner and w two equals one hundred seventy seven point four at the ridge end, over the full span. That is the triangle, entered exactly as we derived it: measured along the hip, and the app does the converting.

29:46The second row, and this is where the two loads part company. Type L r — roof live, not L. Same linearly varying shape, same zero to the ridge end, w two of one hundred seventy eight point two. Two numbers that look almost identical, in almost identical boxes — and the analysis behind them multiplies one by one point zero six one and the other by one. Both rows in. And when the step collapses, its summary states the conversion on the affected value itself: the dead load row reads one hundred seventy seven point four, then times one point zero six one at four point two four in twelve, gives one hundred eighty eight point two on the horizontal span. Never a silent conversion — the number you typed and the number the solver used are both on screen.

App Step 3 - Material & Section

30:31Step three, Material and Section — where the Table 4A versus Table 4D distinction stops being a lecture and becomes a click. Six product categories, grouped by where their design values come from. Sawn Lumber and Glulam under the NDS Supplement; then LVL, LSL, PSL and I-Joist, whose values come from manufacturer ICC-ES evaluation reports instead. A hip beam out of the yard is Sawn Lumber, already selected. And here is the choice. Table 4A, visually graded dimension lumber, two to four inches thick. Table 4B, the same for Southern Pine. Or Table 4D, visually graded timbers, five by five and larger. A six by twelve is a timber, so we take 4D — and the moment we do, the size table below reshapes itself around that choice.

31:20The whole of Table 4D, as printed in the Supplement, with Douglas Fir-Larch pinned to the top. Expand it and every grade is there with its full row: bending, tension, shear, both compression values, modulus, specific gravity, grading agency. Number two, Beams and Stringers — and notice the grade name carries its size classification. Table 4D splits within itself: Beams and Stringers for a section loaded on its narrow face, Posts and Timbers for something roughly square loaded axially. They carry different tabulated values, so the module names the class on the grade rather than letting a six by twelve quietly read a Posts and Timbers row. Eight hundred seventy five p s i in bending — our number.

32:01Down in section size, Table 1B — and here is the gating. Boards and Dimension Lumber are grayed, with a note saying they become available under Table 4A, 4B or 4C. Only the two timber groups are live, because Table 4D is what we chose. Expand Beams and Stringers. Six by twelve. Area sixty three point two five, section modulus one hundred twenty one point two, moment of inertia six hundred ninety seven point one — read straight off the Supplement, exactly the three numbers the hand calculation used. And had we picked a two by twelve here instead, the module would have cleared the Table 4D species and flagged it required, rather than silently re-reading Douglas Fir-Larch off the wrong page.

App Step 4 - Design Parameters

32:43Step four collects every NDS adjustment factor in one place, each tagged either calculated by the program or user defined by you. Wet service and temperature both default to dry and normal — one point zero each. The size factor is calculated: Table 4D tabulates timbers directly and C sub F only appears above twelve inches deep, so at eleven and a half it stays at one. The duration factor is calculated per combination, which we will watch change from row to row. And each factor opens to show the actual code table it came from, with your row highlighted.

33:17Bearing length is optional — leave it blank and the app omits the bearing check rather than inventing a seat length for you. We enter three and a half inches, matching the top plate at the corner and the post cap at the ridge, so the check runs at both supports. And the deflection limit, straight off IBC Table 1604.3: ceilings with flexible finishes — L over 240 live, L over 180 total. That is the row a vaulted gypsum ceiling under a roof member sits on, and the row our hand calculation used.

33:50One factor deserves a word even though it stays at one point zero: C sub L, the beam stability factor. It defaults to one on the assumption that the compression edge is continuously braced — an assumption the app makes on your behalf, not something it read off your framing plan. For this hip it is true: the jacks and sheathing brace the top edge along its whole length. A hip standing bare during construction is a different member, and the unbraced length box here is where you say so.

34:17And one more thing the slope does, which is easy to miss. Step five is the Simpson Strong-Tie hanger selector — and on a sloped member it deactivates itself and says why. The selector sizes level seat face mount hangers. A member sloped at four point two four in twelve bears on a sloped cut, so it needs a slopeable or skewable model chosen from the manufacturer's literature. Rather than sizing a hanger that cannot be installed, the module refuses and tells you what to look up.

App Step 6 - Design Verification

34:44Step six, Design Verification — where we check the app's answer against every number we found by hand. Six rows. Four strength combinations for moment and shear — D alone, D plus L r, D plus three quarters L r, and zero point six D — and two separate deflection cases, because deflection is a serviceability check running under its own rules. Every ratio is a demand over capacity, so anything at or under one point zero passes. And there is our governing number: zero point nine zero five, on D plus L r.

35:16Click a row and the full derivation opens for that combination. Dead load alone first: the same eight hundred seventy five p s i reference value, but multiplied by a duration factor of zero point nine instead of one point two five — and a ratio of zero point six nine three. It never governs here, but on a tile roof it is closer than you would guess, and the app runs it whether or not you ask.

35:40D plus L r — the one that matters. And here is the app's own derivation, line for line what we did by hand. F b prime equals F b times C M times C t times C F times the lesser of C L and C V times C D: eight hundred seventy five, times one, times one, times one, times one point two five — one thousand ninety four p s i. Times a section modulus of one hundred twenty one point two, over twelve: M n equals eleven thousand forty seven pound feet, against a demand of nine thousand nine hundred ninety six. D over C, zero point nine zero five.

36:12Scroll the same combination and the shear derivation adds something the hand calculation only mentioned. It computes shear two ways — an analytic value from the support reaction and a sampled value off the finite element diagram — and takes the larger, because a coarse sample could otherwise miss the true peak. It also states explicitly that it is not taking the 3.4.2.2 allowance. And further down, bearing: two supports, two reactions, one hundred thirty four p s i at the ridge end against six hundred twenty five — zero point two one four, exactly as we found.

36:46D plus three quarters L r: the same combination with roof live load knocked down to seventy five percent, at zero point eight zero three. One of the four ASCE combinations you check even when it never governs — for a member carrying several different variable loads at once, this is the row that sometimes wins instead. And zero point six D, at zero point four one six — dead load alone at sixty percent, the combination whose job is to see whether a reduced dead load paired with wind or seismic elsewhere in a load path could flip a reaction into tension. This example carries no wind, so it is simply the lightest of the four.

37:24The two deflection rows sit apart from strength and open their own derivations. Roof live load alone: zero point three four one inches against L over 240 on the nineteen point eight foot projection, zero point nine nine zero inches. D over C, zero point three four four. Matches. And zero point five D plus L r, the total load case — where the app states the IBC footnote d reasoning explicitly, the same reasoning we walked through: long term creep estimated as the immediate deflection from half the dead load, plus the full short term live load, and not to be combined with the NDS 3.5.2 creep factor. One or the other, never both. Zero point five five two inches against one point three two zero.

38:04D over C, zero point four one eight. Matches.

App Step 7 - Visualization

38:09Step seven, Visualization — the diagrams, for every load case and every combination, not just the governing one. The sidebar lists the six combinations from Step six plus the two individual load cases, and it already tags which ones govern. First, dead load by itself: the converted triangle, zero to one hundred eighty eight point two, plus the sixteen point three pound per foot self weight — and no roof live load at all.

38:34Roof live load by itself: zero to one hundred seventy eight point two, unconverted, because it was already defined on the projection. Two triangles that look almost identical on screen and were arrived at completely differently. D plus L r — the governing combination, and the picture to compare against the figure from the first half of this video. The beam model on top, then shear, moment and deflection below. Same reactions, one thousand three hundred seventy and two thousand five hundred seventy nine. Same shear crossing zero at eleven point three feet. Same moment peak of nine thousand nine hundred ninety six, off center toward the ridge end. Drawn by the app, from its own solver.

39:14D plus three quarters L r — visibly a scaled down version of the same diagram, exactly as the combination name says. Zero point six D: both reactions shrink and both stay positive. No uplift signal here, which is what you would expect under a tile roof with no wind load entered. And the two deflection only views. Roof live load alone against L over 240 — — and zero point five D plus L r against L over 180.

39:41Eight views, one click apart, every governing tag matching what we found by working this hip through by hand.

Hand calculation vs. StructSuite - every number matches

39:49One last comparison, side by side, before we close. The hip slope, four point two four in twelve, both ways. The converted dead load, one hundred eighty eight point two, both ways. The roof live load, one hundred seventy eight point two, unconverted, both ways. The ridge end reaction, two thousand five hundred seventy nine pounds. The maximum moment, nine thousand nine hundred ninety six pound feet at eleven point three one feet. Flexure, zero point nine zero five. Shear, zero point two eight eight. Both deflection cases. And bearing at the ridge end, zero point two one four. Every governing number, worked two completely different ways, agrees.

40:26Every figure, every table, every formula in this video came straight from the written guide. Every field you watched us enter in the app is a number this video derived first, by hand, from the code. And the number that actually matters is not the one that governed the member. It is the two thousand five hundred seventy nine pounds landing at the top of the hip — which now has a load path, because the triangle showed it to you. Read the article, or watch this video: either way, you get the same hip, checked the same way, twice.