Theory of Structures

Assn 14 - Rafter Tie Investigation

2009-11-12T13:02:00.001-08:00

Gang, here is assn 14 - it is the investigation of the effect of the location of the tie in a `rafter' construction roof. Rafters are 2 x 6 DFL No. 1 spaced 24 in. o.c. and span 12 ft on the plan. Roof slope is 5/12. Each pair of rafters is connected by a tie ... however, the location of this tie will be allowed to vary, per our investigation. Ties are 2 x 4 DFL No.1. Yeah, they are potentially long ...

Scenarios:

1) tie connects rafters at their ends (ceiling tie)

2) tie connects rafters 1/3rd of the way up from the bottom.

3) tie connects rafters 1/3rd of the way down from the top (kind of a collar-tie scenario)

Roof load: 40 psf (snow)

Dead load: 15 psf

Roof load values are `as projected onto a horizontal plane' and may be applied to the rafters. And they may be assumed to include self weight.

The purpose of the tie is to prevent `pushout' of the ends of the rafters.

Find: for each rafter scenario:

a) maximum bending moment in rafter (lb-in., and indicate positive or negative ... positive being flexural tension on bottom),

b) pushout of right end relative to left, in in., and

c) axial force in tie, lb (indicate T or C).

Model one end as a pin and the other as a roller ... though in real life, perhaps both are `springs' as attached to the tops of walls.

For E use 1,700,000 psi x 1.03 ... (I'll explain the 1.03 in recitation).

Discuss ... especially how each scenario is effective at preventing pushout, or not.

Do in GROUPS.

Due before you leave (or I leave) for Thanksgiving Break.

Doc

... hinged arch frame under virtual load.

2009-11-07T10:29:00.000-08:00

Hey - this is kind of cool - though I discovered after the fact. Recall how I have been solving these with a load applied at a node as being shown applied to one adjacent member, or the other, but not both???? If you take the unit load applied to the top, and SPLIT it - one half to each, then each side is a mirror image of the other ...

Assn 3 ... DONE

2009-11-05T23:24:00.000-08:00

30 pages ...

Grueling.

Oh, and 6 page of Excel spreadsheet numerical integrations ...

Assignment 13 ... update!

2009-11-05T18:22:00.001-08:00

I just finished Delta B,x ... and I'm on page 19. Now for Delta B, y.

But I write big.

FIERCE!

E for Assn 13 ...

2009-11-05T17:59:00.001-08:00

Yeah, the E value for Assn 13 is ... 29,000,000 psi (29,000 ksi) ... as used in recit.

Assn 13 ...

2009-11-05T17:03:00.001-08:00

Member EC ... remember how I flopped how I was looking at it? ... top vs. bottom. You can do it either way - just be sure you are consistent in the way you look at each member for both virtual and real loads ...

Frame with tapered section ... Assn 13

2009-11-05T12:14:00.001-08:00

Assignment 13 ... here.

This is a frame with tapered sections ... we'll work on it in Recit. today.

Doc.

2-D Stat Det Frames ...

2009-10-31T13:03:00.001-07:00

A sort of `STEPS' ... here.

Second Exam ...

2009-10-28T17:27:00.000-07:00

Okay, I just made the second exam. One problem with 3 parts ... one truss, five members. Be able to handle thermal and structural loads. My solution is 10 pages long, but I write fairly spread out (and big compared to some). You might want to bring an energy drink or two, and/or food, but if you bring food - I get some. I think if you know virtual work, you will survive, if you can last (all three parts).

I will probably NOT be in my office tomorrow morning, except briefly ... (but my solution notebook will be).

Doc

Equations of Condition

2009-10-28T13:37:00.001-07:00

Dang, this is good! ...

... look at these jewels ...

2009-10-21T17:05:00.000-07:00

Added to the Index Page (for the Course) ...

Thermal Deflections by Virtual Work (Trusses) ... here.

Equations Page ... here.

BABY!

Plug and Chug ...

2009-10-20T20:59:00.001-07:00

I am impressed from the `Poll' that you people are getting a decent handle on (understanding of) this virtual work stuff. That is my mission. Computers can `plug and chug', or do `math'. Interns in sweat shops in foreign countries can plug and chug. But if you know what is going - what the plugging and chugging is all about ... the real world behavior described by equations ... you will amount to something as engineers. And I think your careers will be far more interesting.

Virtual Work ... more formal blurb

2009-10-20T16:58:00.000-07:00

Okay, I worked up a more formal blurb on the Virtual Work Method (statically det. truss) ... enjoy it ... here.

Assignment 10

2009-10-20T16:49:00.000-07:00

Okay, Assn 10 is up ... here.

With the assignment is a `steps' of sorts, for solving this kind of thing ... not as good as our talk in class (IMO), but here it is ... http://serioushunter.com/edu/engr/342/stat-ind-truss-steps.html. (Plus, the formatting is a bit weird.)

Stat Indet Truss

2009-10-19T14:00:00.000-07:00

So, here is what we get when we `add' (superpose) the statically determinate and applied reaction cases:

It's kind of wild in that the top member forces go to zero. In reality, those top members would carry load ... certainly their self weights, and perhaps the load from the deck (if, say, part of a bridge.)

Also, in reality, there will be some allowance for (some) movement in (some of) the joints.

Second Exam ...

2009-10-19T13:34:00.001-07:00

... second exam is moved to 10/29 ...

http://serioushunter.com/edu/engr/342/Schedule.html

Doc

... work-energy method.

2009-10-17T17:43:00.001-07:00

So, I typed up a more formal blurb on this work-energy method.

It is ... here.

Doc

Work - Energy and Virtual Work ...

2009-10-15T21:34:00.001-07:00

Okay, though these methods sound similar, and look similar, ... it is somewhat `illusionary'.

The Work - Energy method looks at the REAL WORK done by the REAL FORCES as the truss is loaded, and deformed.

The Virtual Work method looks at the `imagined' work done by `virtual' forces ... as the truss is loaded with (real) loads (and deforms under these real loads).

YIKES! ...

(I don't know if this helps, or not.)

Assignment 9 ...

2009-10-15T21:33:00.000-07:00

This problem would be easy to solve (or CHECK) using `geometry'.

Assignment 9 ...

2009-10-14T16:26:00.001-07:00

Assignment 9 is up! ... Due in Groups; due a week from today ... but start TODAY, while it's fresh!

http://serioushunter.com/edu/engr/342/Assn-9.html

Doc

Truss Deflections by Virtual Work ...

2009-10-12T14:23:00.000-07:00

Gang,

I formalized this Virtual Work method ... here.

And here is our class example hammered out ... (here).

I said I'd probably have you finish this one as homework, but I am changing it a bit ... here (Assignment 8).

COOL!

Doc

... finding mid-point deflection ...

2009-10-11T15:10:00.000-07:00

Q: ... is there a way to find the deflection just using the lengths and angles, without having to `draw' a model?

A: ... yeah.

Q: ... (I'm waiting ...)

A: ... find a line that connects ends A and E, and the distance of F from that line is the deflection of F.

But I suggest at least doing a sketch of the deformed truss - so you'll see what I am talking about.

It's basically the same thing that we discussed in class, except that I described the `additional' visualization of rotating this line (from A to E) so that it is oriented horizontally - since that's what the boundary conditions are requiring.

Assignment 7 is up ...

2009-10-07T20:24:00.000-07:00

Assignment 7 (2 Problems) ... here.

Assignment 6

2009-10-05T16:30:00.001-07:00

Assignment 6 is up, as promised ...

http://serioushunter.com/edu/engr/342/Assn-6.htm

Trusses ...

2009-09-30T14:28:00.001-07:00

Today we started trusses. Your assignment is up on the "Assignments and ... " page (here).

I modified the assignment just a bit. In class we started number crunching with P = 4080 lb. In the assignment you'll see I want you to use a normalized load P = 1000 lb. Then at the end you can get the (reactions and internal) loads corresponding to P = 4080 lb simply by multiplying by 4.08.

Often when setting up a structural model it is convenient to load it with a nice number like 1000 ... and once you get it working, then multiply by 4.08 to get total loads, 4080 x 60/85 to get Snow loads only, ... 20/85 to get dead loads, and so on.

Enjoy.

Review

2009-09-23T16:07:00.001-07:00

So, here is a little review outline I came up with ...

REVIEW … CE 342 … FIRST EXAM …

1. Stability

1) Internal
2) External
3) Global

2. External Stability

1) Sliding
2) Overturning
3) Bearing

Typical min FOS values …

Sliding … 1.5
Overturning 1.5
Bearing
Flexible Systems 2.0
Rigid Systems 3.0

* Remember in the FOS calcs … keep the overturning effects and gravity (righting) effects separated … don’t use `net’ values.

3. Bearing Pressures

* Make sure you are clear on this `middle third’ thing. Remember, soils cannot take negative pressures.

… f = P/A +/- M/S

And if your resultant is not in the middle third, you better make some adjustments until it is!

4. Loads

1) Dead loads
2) Wind loads
3) Snow loads
4) Lateral soil pressure loads
5) Load combinations

5. Dead loads

*Make sure you are all over this stuff. If I bring in a piece of `Material X’ and a tape measure and a bathroom scale, can you determine specific weight, weight per linear foot, weight per square foot, and so on.

*Make sure you can deal with tributary width, area, etc.

* Make sure you can take material weights, say, in a roof plane, and translate them to a `footprint’ weight.

*Also, remember that `truss’ problem we did? … where we determined the weight of the timber truss, and then I asked how much do they contribute to the roof dead load (footprint) value, spaced 8 ft o.c.? …

… f = W / area = 1000 lb or so / (8 ft o.c. x 24 ft wide) = about 5 psf added …

* And it would be a good idea to have that one handout of `weights of construction materials’ or whatever it’s called, at your fingertips, unless you have found a better list (to have at your fingertips).

6. Wind loads

* You need to have some grip on the terminology …

MWFRS … versus … C&C

7. Snow Loads

* Have the snow load `lesson’ from the course Schedule printed off … so if I gave you some information dealing with `Exposure Category’, exposed or sheltered, heated or cold, slippery unobstructed or not, and slope, importance, and a value for ground snow load / ft of elevation (like 0.033 psf/ft), you could sort through the equations

… pf = 0.7 Ce Ct I pg … and … ps = Cs pf

and

… come up with a design roof snow load.

8. Load Combinations

* Make sure you understand that foundation calc we did, with the gravity loads D, S, and L coming down, and how we combined the loads to look at soil pressure … and how we came in later and added the (overturning) effect of wind … and also how we were allowed to increase the allowable soil pressure in resisting load combinations including wind.

9. Anything that I emailed you, or emphasized or directed you to on the blog … you should probably consider important.

10. Anything that I wrote on the board, and especially underlined … you should consider (real) important.

Assignment # 2 Solution - Errata

2009-09-21T16:51:00.000-07:00

1. In my `published' solution my roof height is a bit off … it should be 1 ft x 5/12 higher … resulting in slightly larger Fo and Mo values.

Solutions ...

2009-09-21T15:17:00.001-07:00

... grading assignments and have some solutions already up. More to follow. Site is here:
http://serioushunter.com/edu/engr/342/assignments-and-solutions-342.html

In general, for submitting materials in this (342) or any (e.g. 357) class ...

Each submission should be self-contained ... in other words, should include the given and wanted information, and how you went about your solution. A good format to consider is:

1. Given
2. Wanted
3. Assumptions
4. Strategy
5. Solution (calcs, sketches, etc.)
6. Answer
7. Discussion

If I say you can put your `answer' in a `table' ... don't show `just' the table, but how the information in the table was obtained.

CON*MAT SHIRT

2009-09-21T14:33:00.000-07:00

That shirt for 357 was made at Shirt Shack ... we could do something like that for 342 ... so far the talk has been for SAFETY ORANGE! Maybe 342 on the front and T.O.S. on the back? If a bunch of us want shirts - maybe the gal at S.S. will cut us a deal???

Segmental Block Ret. Wall ...

2009-09-17T19:13:00.000-07:00

... I was walking about and came past this ret. wall near home. It's not over 4 ft high so it probably did not have engineering. ??? The blocks are set back each course giving it some batter. I like how the sidewalk provides (some) sliding resistance (intended or not). There is a lawn above that gets plenty of water. WATER. This is not an old wall, and look at the (forgot the word) stains! Not only does water make a wall unstable - it can stain a wall. Even on `non-engineered' walls - make sure they have good drainage.

( ... pic taken from my cell phone and text'd to my email account and then uploaded to the blog. Probably there is a way to send straight to the blog ...)

Dead Loads ... OUTLINE

2009-09-15T22:19:00.000-07:00

I'm thinking we should talk more about dead loads ... OUTLINE is ... here.

Due Date on Assn 3 ...

2009-09-14T14:24:00.000-07:00

Assn 3 Due Date indicates 9/17 ... that's unrealistic. Instead, we will use Recitation that day to determine the site-specific ground snow loads for your groups, and the Assignment will be due some time after that. Probably 9/21???

Loads and Load Combinations ...

2009-09-13T09:21:00.000-07:00

here is some more reading on ...

LOADS ... http://www.associatedcontent.com/article/1402844/introduction_to_loads_and_forces.html?cat=6

... and ...

LOAD COMBINATIONS ... we will talk more about on Monday ...

Outline for `talk' ... http://serioushunter.com/edu/engr/342/Load-Combinations-ASD.htm

Example on AC: http://www.associatedcontent.com/article/1476848/load_combinations_in_allowable_stress.html?cat=15

... a few photos on sliding snow, or not ...

2009-09-13T09:19:00.000-07:00

Here are some photos of snow, sliding, accumulating, or not.

(Yeah, there is a deck, and maybe even furniture, under the pile.)

http://www.associatedcontent.com/slideshow/9584/snow_on_roofs_and_decks.html?cat=58

Wind Exposure Category ...

2009-09-12T11:58:00.001-07:00

... here are the `Exposure Categories' for wind design from the 2003 IBC. You will need these for your homework problem. My intent here is educational (not that you use these instead of `buying' your own). Before you start designing in real life (IRL) you will want to get a current copy of the applicable code for your project ... and/or ... a current copy of ASCE-7.

Enjoy ... (And let me know if there are typos.)

Borrowed from … 2003 IBC

1609.4 …

(WIND)

Exposure B. Urban and suburban areas, wooded areas or other terrain with numerous closely spaced obstructions having the size of single-family dwellings or larger. Exposure B shall be assumed unless the site meets the definition of another type …

Exposure C. Open terrain with scattered obstructions, including surface undulations or other irregularities, having heights generally less than 30 ft … This exposure shall also apply to any building located within Exposure B-type terrain where the building is directly adjacent to open areas of Exposure C-type terrain in any quadrant for a distance of more than 600 ft. This category includes flat open country, grasslands and shorelines in hurricane-prone regions.

Exposure D. Flat, unobstructed areas exposed to wind flowing over open water for a distance of at least 1 mile … inland waterways, the Great Lakes and coastal areas of California, Oregon, Washington and Alaska. This exposure shall apply only to those buildings and other structures exposed to the wind coming from over the water … extends inland 1500 ft or 10 times the height of the building or structure, whichever is greater.

D + W ... and ... 0.6 D + W

2009-09-11T16:45:00.000-07:00

Gang, don't panic on the notation of Assn 4. We have talked about it a bit already - and will probably talk more ... (but) all the Assignment is driving at is this: in class we analyzed the tie-down force needed based on an estimate of the roof weight and the calculated wind forces. But what about a light roof? The building code requires that we also design the tie-down for the possibility that our roof ends up lighter (less heavy) than we estimated. A lighter roof will likely demand more from the tie-down.

Note: D + W and 0.6D + W are NOT algebraic equations. They are more `prescriptions' of what to analyze. The first one is saying: `analyze the effects of the (full) dead load and the (calculated) wind loads'. The second one is saying: `analyze the effect of (the same) wind load but with ligther dead load'.

(The wind forces themselves stay the same in these two combos.)

Oh, here is 4 ...

2009-09-10T18:03:00.001-07:00

Assignment 4 ... http://serioushunter.com/edu/engr/342/assignment-4-ce342.htm

Easy! Do Individually!

Assn 2 Solution is up ...

2009-09-10T16:44:00.000-07:00

Here is my solution to assignment 2 ... your numbers might vary if you took into account thickness of far wall, and so on. Actually, the more I think about it, if you take into account the thickness of the far wall, and bring the far wall dead loads `in' ... and also count the near wall, which are the same amount of inches out ... you'll probably get the same answer as if you only count the far wall dead loads, and put them at the outside-to-outside dimension (distance). Enjoy.

http://serioushunter.com/edu/engr/342/assn-2-solution.pdf

Doc

Solutions ...

2009-09-10T13:52:00.001-07:00

I revised the `index' page for the course: http://serioushunter.com/edu/engr/342/

On it you will see a link to an `assignments and solutions page' ... here: http://serioushunter.com/edu/engr/342/assignments-and-solutions-342.html

I have my solution to Assn 1 up ... with more to follow.

Doc

... stuff recently added to Schedule, etc.

2009-09-09T20:55:00.001-07:00

I have added Assn 3 to the Schedule, which we will begin talking about in Recitation tomorrow. Also, for Monday, some stuff on load combinations.

Item 10 of the Assn 3 is iffy ... I'm not sure how we are going to handle that yet.

http://serioushunter.com/edu/engr/342/Assn-3-Snow-Loads.htm

http://serioushunter.com/edu/engr/342/Load-Combinations-ASD.htm

http://serioushunter.com/edu/engr/342/Schedule.html

Some important concepts

2009-09-08T17:51:00.001-07:00

... here are some concepts that are really important, but often `slip through the cracks' in the academic world:

Tributary width calcs ...

http://www.associatedcontent.com/article/1286453/this_thing_called_tributary_width.html?cat=15

Self-weight calcs ... (we have already done some of these)

http://www.associatedcontent.com/article/1267641/calculating_self_weight_of_structural.html?cat=69

Snow Loads ...

2009-09-08T16:34:00.000-07:00

Okay, gang, I have revised the schedule a bit, to include a link to an outline on our talk tomorrow on snow loads ...

schedule ... http://serioushunter.com/edu/engr/342/Schedule.html

outline ... http://serioushunter.com/edu/engr/342/snow-loads.htm

Andrew is awesome ...

2009-09-03T17:01:00.000-07:00

Whoa! ... Andrew was in my office and he had different values than I do for the location of Resultant Weight W at the different batters, AND HE IS RIGHT! As I hammered through the problem - and as I helped many of you, I stated that the centroid of the wall is located at L/2 + (H/2 x tan phi) back from the front of the first block. If one does (and Andrew and I did) a centroid calc using 6 discrete blocks, ... the location of the centroid is slightly less (less into the hill). In other words, my calc is incorrectly slightly more stable. Using the L/2 + H/2 tan phi is like using an infinite number of infinitely thin blocks, battered at phi, or, more simply, a parallelogram.

All that said, I would not count the way I did it as necessarily wrong (even though it is, technically). If you did it the Andrew way - you'll get slightly different numbers.

Maybe before I post my solution ... I'll do it both ways.

And if you did it my way - don't necessarily re-do it.

BABY!

Turning in Assignments ...

2009-09-03T10:58:00.000-07:00

Okay, when an assignment is due at the beginning of class, they should be on the table/desk at the front, in a nice, neat pile, at the beginning of the lecture, before I start talking. If I am already talking and you come up to the front, I will probably stop talking, and stare, or worse.

If I have given you a `drop off at CE' date and time, come on in to the main CE Office (BEL 102), and graciously ask one of the office staff to accept your paper for me. (They will get it to me.)

Assignment 2 ...

2009-09-02T15:39:00.000-07:00

I posted a slightly revised schedule which includes a link to Assignment 2 ...

Schedule ... here

Assignment 2 ... here

Bring Assignment 2 to recit tomorrow and we'll start on it. It spawns from a consulting assignment I just finished.

Doc

... middle third ...

2009-08-31T15:27:00.000-07:00

Okay, in class today we talked about the `middle third'. Well, for a round section it is the `middle fourth'. In other words, for a round section the line of action of the resultant must be within 1/8th of the diameter.

Check this out (from another blog of mine) ... http://reinforced-concrete.blogspot.com/2009/02/oh.html

FOS Soils ...

2009-08-30T15:16:00.000-07:00

Make sure you are clear on:

1. Flexible walls vs. rigid ...

Also ...

2. As mentioned in recit. ...

... for flexible walls we use a FOS of 2.0 for soil bearing ...

... for rigid walls we use FOS of 3.0 ...

Remember, when `allowable' pressures are provided, the FOS has already been `factored' in.

3. Rigid walls / foundations must be embedded below frost depth ... flexible walls not necessarily.

Doc

Course index

2009-08-30T14:56:00.000-07:00

Gang! ...

I have put together a course `index' page, with links to updated syllabus and schedule. The schedule has links to some brief outlines of stuff covered ... and an outline for the talk tomorrow!

http://serioushunter.com/edu/engr/342/

NOTE: I updated Assignment # 1 a bit (link to from the schedule) ... in addition to `answers' (numbers) ... I want you to discuss:

1) does batter matter?

2) if you run into a condition that is `not good' ... what might be some remedies?

OH, BABY!

Doc

Assignment # 1

2009-08-26T17:14:00.000-07:00

Gang, here is Assn # 1 ...

Deals with External Stability Calcs for a SBRW (Segmented/Segmental Block Retaining Wall) ...

http://serioushunter.com/edu/engr/342/assn-1-sbrw-stab.pdf

We will start working on it in `Recitation' tomorrow. The room scheduled is TLC 146. I'd like to get us a different room, but for now, show up there.

A more detailed sketch of the wall is ... http://serioushunter.com/edu/engr/342/sbrwsketch.pdf

Bring paper, calculators, etc.

Doc

Sliding ...

2009-08-26T16:17:00.001-07:00

A couple of people have asked, so let me elaborate. For sliding resistance we used 130 psf of contact area in our example in class. This is a `code' value based on concrete (sliding) on clay bearing soil. A lot of times when we think of sliding resistance we use weight times a coef of friction. And in some cases (rock, gravel) that is indeed the case. (See table link: here.) The clay stuff around here acts more like a `fluid'. (Remember from fluid mechanics that fluid friction doesn't depend on normal force.)

Tentative Schedule / List of Topics

2009-08-24T17:51:00.000-07:00

And here is a (VERY) tentative schedule: http://woodengineering.com/edu/engr/342/ce342-schedule.pdf

Syllabus ...

2009-08-24T17:29:00.000-07:00

Syllabus for 342 is up ... here: http://woodengineering.com/edu/engr/342/syllabus-4-342.pdf

On it (above) there is a link of my professional resume/background, if interested.

Theory of Structures

Assn 14 - Rafter Tie Investigation

... hinged arch frame under virtual load.

Assn 3 ... DONE

Assignment 13 ... update!

E for Assn 13 ...

Assn 13 ...

Frame with tapered section ... Assn 13

2-D Stat Det Frames ...

Second Exam ...

Equations of Condition

... look at these jewels ...

Plug and Chug ...

Virtual Work ... more formal blurb

Assignment 10

Stat Indet Truss

Second Exam ...

... work-energy method.

Work - Energy and Virtual Work ...

Assignment 9 ...

Assignment 9 ...

Truss Deflections by Virtual Work ...

... finding mid-point deflection ...

Assignment 7 is up ...

Assignment 6

Trusses ...

Review

Assignment # 2 Solution - Errata

Solutions ...

CON*MAT SHIRT

Segmental Block Ret. Wall ...

Dead Loads ... OUTLINE

Due Date on Assn 3 ...

Loads and Load Combinations ...

... a few photos on sliding snow, or not ...

Wind Exposure Category ...

D + W ... and ... 0.6 D + W

Oh, here is 4 ...

Assn 2 Solution is up ...

Solutions ...

... stuff recently added to Schedule, etc.

Some important concepts

More Reading on Snow ...

Snow Loads ...

Andrew is awesome ...

Turning in Assignments ...

Assignment 2 ...

... middle third ...

FOS Soils ...

Course index

Assignment # 1

Sliding ...

Tentative Schedule / List of Topics

Syllabus ...