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DoodleBug Reloaded!!
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Her Vital Statistics
September 2016 -- Website Update: DoodleBug has been "reloaded" and has made the transition from rental boat to cruising boat. I have moved all of the 2015 "blog" to "trip logs" which you can accessing by clicking the catamaran picture to the right. I finally ADDED PICTURES to the trip logs. I also just completed updating all of the e-Books so that the pictures display properly when using Apple's iBook app. I have tested these on an iPad3.
January 2016 -- Website Update: We have bid Australia a sad farewell for a while and our Toyota Coaster RV HAS BEEN SOLD!!! Thank You Ray at Koolah Kampers!! (see www.koolahkampers.com.au). I have re-ordered the daily entries into time order, moved the trip-logs to a new page and ADDED PICTURES!!. You will find the link to the right (click on the white bus picture).
The logs of our sailing circumnavigation were moved down a level and you will find the link to the right (click on the S/V DoodleBug picture to get to the "old" web-site).
We have also "cleaned up" the sailing logs and reformatted them into .epub files, so that they may be downloaded and read at your convenience on an iPad or Kindle reader as "e-books". Because there are about 6,000 embedded photos in the original website, I needed to split the log of the cruise into 18 "volumes". To date, I have tested these eBook files on both a "Kindle Fire" and an "iPad3". Click right on the "books" icon to access the files for download.
I have also finished the task of converting the Australia "Walkabout" blog to 11 volumes of "e-books", also accessible here.
August 6 - August 13, 2016
This week began with a vague report, gradually fleshed out during the following days, of an attack on a cruising couple, Mark and Sue, who had been anchored off nearby Hog Island. Mark had been walking their dog ashore when he was kidnapped by a couple of men with a handgun. They demanded that he transport them in his dinghy to his nearby yacht and then insisted that they raise anchor and sail to Puerto Rico. As they were leaving the bay, they ran aground on a coral reef and were unable to free the vessel. The men assaulted the couple and then left in the dinghy with the Sue, "as a hostage" to return to the main island. Here she was raped and assaulted for several hours. The men were at large for a week and then captured by police. The attack was a dreadful occurrence that the locals would like to pretend never happened.
We realize that a there is a level of crime just about everywhere throughout the Caribbean but there is a big step between the accustomed petty theft and physical assaults. This is one of the several reasons why Annette and I prefer the Pacific islands. A Google search on crime rates puts the overall murder rate in the Caribbean Islands around 30 per 100,000 population. By comparison the USA comes in at around 4 per 100,000, Samoa and Fiji at 1 or less. The usual excuses about poverty and lack of opportunity evaporate when compared to Pacific Islands where crushing poverty also exists and yet people neither steal from each other nor kill each other. Both societies are predominantly Christian but the Pacific lacks the Universal and Perpetual excuse of having experienced a slave economy 150 years ago.
Annette put the finishing touches to her current painting whilst I updated the website by adding pictures to the blog. I also began the task of converting our Australian "walkabout" tour to eBooks. We are leaving next week and searched the various hardware stores for art shipping tubes before settling upon a section of 4 inch diameter drainpipe. Annette carefully removed her works from their frames and the painted canvases were separated with wrapping paper, courtesy of the local butcher, before being rolled and placed inside the plastic drainpipe tubing.
The packaging of sand samples has been problematic as it is obvious that she has over 50 pounds collected. In addition to the logistics of hauling a suitcase full of "dirt", there is the problem that the USA Customs controls the import of "soil". The proposed solution is to use the US mail to ship the bulk of the sand samples after Doodlebug next reaches the Virgin Islands. Annette has discovered that one of her fellow members of the sand collectors society specializes in "ant" sand – that is the sand that ants bring to the surface of their nests. Naturally Annette wanted to collect some Grenada "ant" sand for him and finished up with 14 bites when the Grenadian fire ants objected.
Monday was the start of "Carnival" proper and this began around 4 a.m. with "Jab Jab". The participants, or at least the younger set, strip down to near nudity, smear their bodies with used motor oil and wear horned "devil" masks and the like, sometimes with chains and padlocks around their feet and parade through the streets accompanied by hammering reggae music. The meaning of this depends upon who you hear it from. There are multiple internet references to slavery, the revolt burning of the cane fields and plantations. Supposedly the slaves were not allowed to participate in Carnival before emancipation and Jab Jab was a form of protest. The revelers traditionally fling dirty motor oil and paint at anyone and everyone and old clothes are highly recommended. We decided that this was not for us and instead traveled downtown to see "Pretty Mas" in the early afternoon. This is another parade but here the marchers / dancers are wearing the scant and gaudy costumes that had been under preparation for the past year. We noticed the road surface was coated with a thin layer of fine sand in attempt to soak up some of the earlier broadcasting of dirty motor oil. This parade was a family affair and we had learned that you could purchase a ticket to march with a particular band and would be provided with a matching costume. Early afternoon near the equator is both hot and humid and we were impressed that the dancers moved non-stop. Not all were as energetic however and we saw one young man, presumably an earlier Jab Jab participant, fast asleep in the cab of one of the trucks bearing the sound system as it came by. These trucks bore huge electric generators and were lined with monster speakers to ensure that even the inhabitants of the local cemetery could enjoy the music.
We tried to find a source for a dehumidifier to run whilst the boat was in storage but struck out here. We will just have to rely on the use of packs of deliquescent crystals that will then need to be traded out every couple of weeks. To do this we contacted Denise, who runs a local yacht services company. Denise was just recovering from an attack of Zika. We have met several couples recently who have suffered the same fate.
Just as we were packing up in anticipation of our departure, the port toilet pump began making noises of a terminal nature. I noticed that there was rust stains on the floor beneath the pump and assumed that the seals had gone allowing sea water to leak into the motor. Fortunately I had a spare pump and it was quickly replaced. I always intend to rebuild the "old" pump but every time I have removed one of these pumps, I have promptly pitched it into the trash can and vowed to buy a new one. Then I washed my hands.
Of course the big event of the week was when we left the dock on Wednesday and motored about five miles to drop anchor in Woburn Bay. We somehow managed to get our suitcases packed and the following day, DoodleBug was hauled "onto the hard" at Clarke's Court marina. It was late afternoon before she was settled into her assigned parking spot and we spent the night at a hotel near the airport. We returned the following morning to do all the fun tasks such as stowing all of the fenders and lines, cleaning out the fridge and the like but by afternoon it was done and we are officially land-lubbers.
Our final "hash" was Saturday and we rode "Shademan's" bus north to the town of Victoria. The "hash" began from the beach where we had examined the Petroglyphs a couple of months ago and turned out to be a "Goldilocks" run – not too far, not too steep, not too muddy, not too hot. A couple of stream crossings and a pleasant route winding between ancient bamboo groves, banana and mango plantations. We even managed to be far enough ahead of the crowd that we had to do some route finding rather than just follow the mob. A pleasant event to wrap up our Grenada visit.
July 30 - August 5, 2016
This has been a slow sort of week. We attended the "hash" on Saturday which was enjoyable and not too strenuous. These events are such a super way of meeting local residents and seeing parts of the island we would never see as "tourists". People will set out on their stoop or garden wall and watch as a couple of hundred strangers walk across their property. They are invariably polite and will offer water, directions, or silence their dogs as appropriate. We were passing one house when the lady ahead of us stopped to talk to one of the householders. She began by explaining where on the island she lived, thereby establishing her bona fides as a local. As we passed, I heard her say, "We go up, we go down, we go behind!" Presumably she had been just been asked what was she doing, wandering around with what is decidedly a diverse crowd and I thought her explanation was admirable. I don't know the exact demographics of the Hash club but I would estimate they about 20 percent cruisers and 80 percent locals. The locals are split about 70 / 30 between "native" Grenadians and ex-patriots.
We also attended the "Mango Festival" that was held at the National Stadium in St. Georges. This was a delightful family affair, with stalls selling mango themed food, booming music from a disc-jockey, parades and competitions. We watched the mango sucking (means "eating") competition where three adult ladies competed to eat three mangoes in under 60 seconds. The winner was nicely dressed, with makeup and jewelry but the fact that she was carrying a towel was a dead giveaway that this was a professional, probably a ringer from Trinidad. She devoured the mangoes with ten seconds to spare, an amazing performance. Around us there were stilt-walkers and a group of thirty or so children in costume and masks who wore some kind of heavy boot, or at least footwear with enhanced stomping ability. They stamped around the stadium facility in tight formation and were obviously enjoying the attention immensely.
I tried the mango ice-cream and declared it delicious. It was too. Poor Annette had to watch me devour it as she ranks amongst the lactose intolerant, so I let her eat some of my sugar cone as a consolation.
When we left the stadium, we transited the highway to the beach front and perambulated a highway bridge across a rank and smelly stream that disgorged its suspicious contents into the bay. Annette had spotted "beach glass" from the vantage point of the bridge and we found a small gap in the wall where we were able to work our way through the bush and down to the beach, with Annette scouring the beach for treasure whilst I was looking for dead bodies and axe murderers, lurking like the troll, fol de rol, below the bridge. This was indeed the mother lode of beach glass, the difficulty of access plus the distinct possibility of sewage contamination having scared off any normal scavenger.
Although there was transportation organized for the cruisers, we chose to take the local bus to the downtown bus terminal and walk from there. We had not visited the bus terminal before and when we saw the Number "1" bus unloading, we were encouraged to board. What we learned is that the driver was supposed to join the end of a long line of buses, rather like a taxi rank at the airport. He used our presence to bully his way past the line of waiting drivers as though he had to look after these dumb tourists. He drove along the lane bypassing the parked buses and then parked blocking the lane so that he could a buy a bottle of beer from the bus station kiosk. By the time we hit the road his bus was packed with other passengers and we found ourselves stuck in a traffic jam in downtown St. Georges in airless conditions. A passenger at the back yelled out, "Driver, give it cold man!" The driver leaned forwards and turned the air-conditioner on while passengers slid the windows closed as though they were part of a drill team. This is the first and only time we have enjoyed air-conditioning on these buses and I had assumed up till this point they were inoperative.
The first tropical disturbance of the season had formed just west of the Cape Verde Islands and we carefully watched its progress as what was to become hurricane Earl headed towards us across the Atlantic and passed by to our north. The forecast area of high waves and high winds extended through the Grenadines but never included Grenada. We are currently tied up to a "fixed" dock by a network of six lines but these lines are necessarily slack to allow for a two foot tidal change, plus the two bow lines are attached to submarine anchors of unknown integrity. The bottom line is I would not want to be at this dock dealing with even a two foot swell, let alone with what a hurricane might bring. Our "hurricane plan", filed with our insurer, states that if we are floating at the time, we will run to either Trinidad or Tobago in the event that Grenada is directly threatened with a tropical storm. Our plans in fact call for us to be "lifted" next week and stored "on the hard" at the Clarke's Court marina where we travelled to use their crane for the generator swap-out out a couple of weeks ago.
Last night we experienced the passage of a "tropical wave" with lightning and some rain. Since we received lightning damage three times in six years aboard the original "DoodleBug", we tend to be a little wary of such conditions but this event was but a "moon cast shadow" of the real thing and I slept through it.
July 23 - July 29, 2016
On Sunday morning we were leisurely drinking our respective morning coffee and tea when the VHF sprang to life with a call for a medical emergency. The boat name was S/V Adagio and from the tone of the caller, the situation was past dire. The cruising community responded instantly yet it still took an hour for an ambulance plus doctor to arrive. In the meantime volunteers had attempted CPR, raised anchor and brought Adagio to the fuel dock alongside DoodleBug. We helped with lines, fenders and the like and provided water to the waiting volunteers but the 65 year old captain was obviously dead and had been for some time. This nightmare is one that we all face but it is still hard to contemplate the inevitability.
Annette continued to paint this week and is working on a canvas themed around the Grenada Carnival celebration. I spent some time analyzing the undocumented add-on wiring for the generator compartment exhaust fan, before discovering that the fan itself was corroded into immobility. It took a couple of days to find a replacement fan and install it. The unit still didn't work and since I had previously tested the wiring and relay, the only remaining issue was the power supply. Sure enough, the wire that was supposed to supply juice, dove back somewhere inside the boat in the direction of the house battery bank. This was silly, the obvious place to get clean power was from the generator alternator and its battery connection, just a few inches away from the relay. I abandoned the original wiring, ran a new power line and the fan worked!
The Grenada Carnival is celebrated next week and we joined a tour of one of the junior "pan" bands that is performing and competing during the parades. The "pan" band is what we call a steel drum band and these kids were awesome! We learned that this group has competed in 38 national and international competitions and have won 33 of them. We can well believe it. We listened to the band practice their competition number and then they performed a short concert for us. We learned that the drums, that can cost around $1,500 apiece, are limited to two simultaneous notes, since the drummer has but two arms and drumsticks. Most musical chords have three notes and the chords are achieved by another section of the drum orchestra playing the missing complementary note. There was obviously considerable skill involved in adjusting the various sections to finely balance the necessary volume and we could surmise that this band director is a perfectionist. We also toured the facility where volunteers were assembling the hundreds of costumes that the celebrants would wear, an explosion of colors, feathers and bling. This was a great tour and we really enjoyed the music.
July 16 - July 22, 2016
On Monday we left the dock and motored a little less than five miles, to drop anchor in Woburn Bay. This is a quiet little bay to the east of Prickly Bay, where we have been roosting for the past month. The anchor launched itself with just a little grumbling from the windlass. The new chain has acquired some twists and we will have to straighten these out at sometime in the future. We have read of sailors who have lowered their anchor in deep water, to allow the chain to untwist naturally and then discovered that the vertical deadweight was beyond the lift capacity of their windlass. We won't do this.
We launched our dinghy and scouted the boat yard, visiting with the yard manager on the procedure for tomorrow's arrival. We followed this with a visit to Palm Tree Marine's office to check on their schedule. The operation manager was still at the St. George's dock awaiting the release of the generator. We determined that we will just proceed on the assumption that everything will "somehow work out".
The Clarke's Court boatyard is still under construction and the restaurant and bar have yet to open for business. We dinghied across the inlet to the opposite side to visit the Whisper Cove Marina. At their dinghy dock we met "Bob", who was attempting to lift 4 large batteries from his ancient dinghy onto the dock. We stayed to help him and after Annette had rustled up a pair of dock carts, I hauled a pair of batteries up the steep slope to the Marina office whilst Annette and Bob hauled the second pair. By this time we were more than ready for our beer and invited Bob to join us.
Bob is 78 years old and had circumnavigated the globe at least once. When he mentioned anchorages in the Indian Ocean, we asked him if he had stopped at Cocos Keeling and further, if he knew Bea and Diane on S/V Sortilege. He said, "You mean that small white catamaran?". I had received an e-mail from Bea and Diane the previous week regarding Bea's new book that has just been published ("Yowie Country", "Jungle Rescue"[the sequel] and "Metamorphosis" by Robin Freeman). Bob insisted that they would surely remember him as the single hander on S/V Tasmine who broke his shoulder in 2003 and sailed "back" for four or five days to seek medical care at Cocos Keeling. This is surely a small world.
The following morning we tied up at the Clarke's Court dock and waited for the arrival of the crane. The latter showed up just before lunch and by 1:30 p.m. the old generator had been lifted from DoodleBug and the replacement unit craned into place. The only anxious time was when the mechanic began cleaning underneath the old generator whilst the latter hung directly above his head, all of its 600 pounds of iron suspended from a single rusty shackle. There is no way I could have done this, I have too much imagination. The crew continued to leisurely hook up the various hoses and umbilicals but seemed more interested in the painting that Annette was working on in the cockpit. Meanwhile I attempted to find some power for the night, that would allow us to run our bedroom air-conditioner. I "hotwired" an extension cord to our power cord and plugged it into a yard transformer that dropped the Grenada voltage from 220 volts to the USA standard of 110 volts. When I threw the switch, the dock power went off. The yard electrician disappeared for some minutes and the power came back on. I tried again. As I watched the input voltage carefully, the voltage began to fall and the amperage correspondingly increased until I was forced to switch the air-conditioner off to avoid damaging it. A miserable hot night, as the yard is infested with no-see um's who found their way inside and were seemingly proof against any normal concentration of insecticide.
The following morning the generator install crew were back aboard and by noon had completed the installation. We motored off the dock and anchored again in the Bay with the new generator and air-conditioners going full blast. A definite improvement on last night and by morning we were almost refreshed when we raised anchor and motored back to Prickly Bay to tie up again at the dock.
The new generator is very pretty in its pristine white sound enclosure and there are just a couple of minor items to correct, one being that the compartment exhaust fan is not running. There is always something!
July 9 - July 15, 2016
This week was the annual chore known as "the boat insurance renewal challenge". The insurer requires you to outline your cruising plans for the next twelve months and this necessitates you actually having some intentions, or at the very least, creating the fiction of some goals. Then they require a detailed hurricane plan. This is trickier because they want specifics on items such as the thickness of mooring lines and the contact information on the party claimed to be looking after the boat when the owner is absent. If you fabricate this information, they could deny the claim in the event of a mishap. This year however, no inspection or survey of the vessel was demanded. The latter would have involved considerable expense as well as the aggravation of finding an appropriately licensed surveyor, plus arranging for a haul-out so that the hull could be inspected. A typical boat inspection can easily cost as much as the annual insurance premium.
On Saturday we again signed up for the "HASH" (see previous posts if you don't know what this is) and headed "downtown" St. George's to their national stadium where a couple of hundred hashers stood around chatting and visiting. This was a diverse group (a heavily overused word that means entirely different things to different people), ranging from those carrying babes in backpacks through ancient people like us. I have no idea how many nationalities were represented but conversations were ongoing around us in French, German, Spanish and Dutch plus the local patois of Grenada Creole. There were dogs on leashes and dogs running free, families with children and some very serious looking lycra-clad running types. The organizers had scoured the crowd looking for "virgins" (people who had never "hashed" before), particularly those with new running shoes. The victims had a single shoe confiscated and were invited to stand in front of the podium where the hash leader explained that the shoes needed to be tested before they could be allowed on the course. On this particular day there were three young Grenadian girls who looked on with initial puzzlement and then shock as a bottle of beer was poured into each shoe to test them for "leaks" followed by the admonition to "drink it or wear it".
The hash course ran from the stadium, across a park and then near vertically up a steep muddy hillside towards the prison perched atop Richmond Hill. If the steep slope wasn't muddy enough from the recent rains, the single file passage of a couple of hundred hashers guaranteed that the "hike" was a muddy scramble, pulling on any branch or twig that might possibly bear weight. We had taken a couple of one inch diameter dowels (used for flying Annette's kites) to use as hiking sticks and these turned out to be invaluable as they could be thrust into the mud to act as anchors or jammed between trees for handholds. For a time we followed a less than athletic Venezuelan lady who had been told that this would be a pleasant walk. She was now perched high on a muddy hillside with a line of people both ahead and behind her, struggling to get up a hold-less slope whilst muttering dire imprecations in Spanish. At one point she was straddled across a log when she toppled backwards and slid headfirst down the hill until arrested by a tree-stump. Annette helped to her feet while quizzing her. "Are you broken, are you bleeding?" A shaken negative and Annette assured her, "You have both earrings, you're OK". This was a tough "hike" needing more upper-body work than footwork and the clumsy folks were easily identified by the amount of mud on their clothing and bodies.
That night it rained heavily across Grenada putting nearly four inches of water into our dinghy. I can only imagine what that hash would have been like either during or just after such a rain.
Our current plans call for us to cruise in the Caribbean next year and since we had now settled the insurance issue, we decided we will park DoodleBug "on the hard" next month and spend late summer in Santa Fe. We are still expecting our generator to be replaced next week at Clarkes Boat yard, located a couple of bays east of where we are now. Just finding dock space to enable the generator to be craned out of its locker has been a problem and similarly catamaran lift capability and storage space is hard to find. We did eventually make arrangements to be lifted at the same boat yard a few weeks after the generator swap-out.
July 2 - July 8, 2016
In the morning we generally listen to a "cruiser's radio net" that begins at 0730 hours and generally runs for 45 minutes or so. The "net" is run by volunteers and after the call for "emergencies" medical or otherwise, begins with a marine weather forecast. I usually don't pay much attention to this because I have already researched this a couple of hours earlier but this particular morning the local weather report gave the humidity at 94%. Wow! I used to think that Houston was humid.
Annette has been producing more paintings and is currently experimenting with "minimalist art". I don't pretend to understand but I do know that her version involved painting with a brush made from rubber bands and she is constructing another brush using dog hair. I mentioned that using the whole dog would be more efficient but this suggestion was "brushed off".
Yesterday we participated in the Grenada Hash House Harriers event known as a "HASH". For the uninitiated, the concept of a HASH was founded in 1937 by Albert Gispert, an English chartered accountant who had been transferred by his employer to Malaya and is based upon the centuries old game of "Fox and Hounds". The Malaysian authorities required that organizations be registered with the government and since Albert's buddies typically ate at the Selangor club, not famous for the quality of its food and derogatorily referred to by the members as the "hash house", his club was registered as the "Hash House Harriers". "Hash" clubs are scattered all around the globe and the reader will likely find one in whatever town they are resident.
The "Fox" is given a start of some number of minutes and takes off into the bush / jungle laying a trail of shredded paper (or flour as we experienced in Micronesia). The Fox can set false trails that terminate in an "X" and when branching trails are experienced, it takes some casting around by the "Hounds" to find the correct trail. It is debatable whether the the point of the game is to catch the "Fox" or simply to to imbibe a large quantity of beer and get a little exercise in the process. To arrive with the lead "Hounds" it is usually not necessary to be the swiftest runner since the lead harriers will be searching for the trail markers and backing up when they are lost. The "lost"parties yell out, "Are You?" and when the trail markers are spotted, the lead "Hounds" yell, "On! On!". Annette and I stayed up with the main body of the group until we found a trail split with an arrow sending the "runners" in one direction and the "walkers" in an another. The walkers thinned out in the thick brush and we were alone, having to find our own trail markers instead of following the mob and enjoying the scenery. There was a short section where the runners rejoined the trail we were following and then a second trail split that almost all of the other "walkers" missed. Now we were truly alone with no sound of shouts either ahead or behind us. We were also both ready for a beer as the trail wound on and on through dense undergrowth and several times we had to cast around in wide circles to pick it up again. We would have likely shortcut back to the terminus of the run if we hadn't been so thoroughly lost. As it was we just continued to follow the clumps of shredded paper in the fading light. We came upon a steep road under construction and the workers halted the operation of their diggers and the like to allow us to pass down the steep muddy incline beside their idling equipment. We weren't the last people to arrive at the finish but not too many folks were behind us. We felt superior however in that we may have been the only "walkers" to have followed the "correct" trail, due of course to our superior aboriginal tracking skills derived in part from watching old Crocodile Dundee flicks.
Wednesday was "shopping bus day" where a special bus is laid on to take shoppers on a swing through banks, supermarkets, pharmacies and the like for about US$5 per head. As we waited for the bus, Les and Louise of S/V Bali walked by and invited us to join them on a private bus charter to visit the Grenada chocolate factory (www.grenadachocolate.com). We hastily swapped out our shopping bags for cameras and headed off up the west coast of the island to the village of Hermitage. Here we toured the only chocolate manufacturing facility in a cocoa producing country.
The facility was a surprise in that this was a real manufacturing operation tucked away in a tiny village off the main drag. Chocolate manufacture is a complex process – here I am talking about "real" chocolate, not that brown waxy crap that Cadbury's and Hershey sell. We began our tour by visiting the sheds where the cocoa beans are "fermented" before being dried, roasted and ground. The various machines for the processing of the dried beans were a curious melange of vintages and origins. Some were made in the USA but there were also ancient Italian and British devices that might have originated in a museum. In spite of the age of the equipment, the whole set-up looked very businesslike, well laid out and obviously a source of pride to the local community. Of course we tasted the chocolate and declared it to be excellent. A really interesting tour.
Later I was looking on the internet and discovered that the enterprise was begun in 1999 by owner and founder Mott Green with the note that he was formerly "David Friedman". Huh? This bore further investigation. Mott Green was the son of Staten Island physicians who decided to cast aside his life of privilege, dropped out of college and became an anarchist / squatter / environmentalist in the early 90's and who nevertheless was able to afford to move to Grenada, build himself a hut somewhere and equip the latter with sufficient solar power to run his stereo system. The internet reports that Ella Fitzgerald was on his playlist. He and friends put together the machinery and had all shipped to Grenada to set up operations. The business was supposedly financially in the black after a mere 14 years of operations, a few months before his accidental death of electrocution whilst repairing some solar powered equipment. I learned that the Grenada chocolate is the darling of the environmental industry with all sorts of international awards and a documentary narrated by Susan Sarandon underway at the time of his demise. He was just 47 when he was killed and with his business finally beginning to take off.
The week ended with a truly spectacular fireworks display at the marina. The display was allegedly for a private birthday party for the American Ambassador to Grenada but the State Department website gives the ambassador's birthday in October. Maybe they really wanted to celebrate on the 4th. but were hunkered down behind sandbags and S.W.A.T. teams that day. We are tied up on the dock here at Prickly Bay and the fireworks were being launched from inside the marina grounds about 40 yards from our fly-bridge where we were sitting, beers in hand. I researched "fireworks displays" to see what they might cost for a private party ($3K and up) and discovered all of the lengthy permitting rules as well as the admonition that the firing point must be at least 50 yards from any people or structure. Apparently this particular rule is not applicable to Grenada.
June 25 - July 1, 2016
The Brexit vote was last week on the 23rd. so the bulk of the week's international "news" consisted of cloned articles echoing the same speculations of possible repercussions. That and the European soccer championship pretty much wrapped up the outside world. This is the first time we have stayed aboard our boat during hurricane season and interacted with the cruising community. In past years i.e. with the previous "DoodleBug", if we were parking the boat somewhere during hurricane / cyclone season, we had left the boat and returned to the USA for a few months to take the kettle off the stove and let the cat out.
We gave up our rental car after the first week and have been riding the local "buses". These are mostly Toyota vans that manage to cram 19 people inside, with five rows of seats including the driver. The bench seats will each seat three people but the port armrest folds down to create "space" for a fourth person. Of course there is no way you can exit these vehicles unless the folks sitting on the "fold down" seats get out of the van first. To add to the overall ambience of the experience, they never use air-conditioning and they play rap music at truly ear shattering volume levels that the famous rock band "Disaster Area" would be proud of. The driver usually has a partner who handles the cash (2.50 EC dollars per trip – just over 90 cents US) and acts as a spotter for potential riders. They do have a route and there is a number on the front of the van designating the route but this is more for guidance rather than a rule. The spotter would notice us coming out of a store and yell across the road at us, "Number one?". With an affirmative wave they would then hold up traffic so that we could cross the highway and board. Pretty neat really.
We continue to take care of a few boat chores and as the list whittles down, we have the boat in about as good a shape as it's going to get on the anniversary of its purchase. Annette has begun painting again and has a large 36" by 48" canvas under construction that I have already titled, "Chagos Sunset". I have offered it to sale to curious by-passers for a discount price of $18,000 but haven't had any takers yet.
My last "major" upgrade was to swap out the 40 ampere battery charger for a new 100 ampere unit. In its previous life, renters would run the 9 kW generator just about non-stop during the period of their charter and the 40 ampere unit drawing a mere half of a kilowatt, acted as a sort of trickle charger to the batteries. We added 600 watts of solar charging last August that on most days provides sufficient juice for lighting and to run the three refrigerator / freezers we operate. We only use the generator for air-conditioning and also to boost the batteries after a couple of cloudy days have impacted the solar output. What had irritated us was the use of only one eighteenth of the generating capacity to perform this function while burning generator diesel and we were about to rectify this with the new unit. I knew this would not be a simple swap-out with just a couple of wires involved. The battery charger is connected to the house batteries via a giant fuse buried behind intimidating cables. In addition it is also wired to the engine starter batteries and is "paralleled" to the solar array which kicks out a not inconsequential amount of power delivered at 36 volts. The swap out job began with disconnecting all of the house battery terminals from their respective batteries, removing the in-line fuses in the engine compartments to isolate the the engine starter batteries and similarly isolating the six solar panels by removing their fuses. The work-space for the charger is tiny and involved considerable contortion and a whole lot of cursing. Four hours later it was all installed and re-connected. I threw the input power breaker to the new charger and watched the monitor as it began to churn out nearly 90 amperes of charging power. My elation lasted about sixty seconds when the breaker popped. I knew this might happen and just hoped to get lucky. The respective manuals claim a recommended 6 ampere input breaker for the "old" unit and a 16 ampere breaker for the "new" one. This would be a "tomorrow" project.
The following morning I opened up the A/C power panel and found the installed battery charger breaker is rated at 10 amperes. Sitting next to it was a "spare" breaker, unused, already wired in and rated at 15 amperes. Sometimes you do get lucky! I swapped the output wires and powered up the new charger. It ran and produced lots of power until I shut is down a few hours later to let the solar panels do their work.
June 18 - June 24, 2016
Last week we had moved from a mooring onto a slip at the marina dock. This means we not only had a viable internet connection but "on demand" city power for air conditioning! Our generator could also provide this power but requires diesel fuel to make it hum and unfortunately, when the air conditioner cycles "off", the unloaded generator has more of a death rattle than a "hum". We decided to take this opportunity to call around to see what a new generator might cost. We also slowly attacked our "to do" list of boat chores, the chores you put off because you either don't want to do them, or they are remarkably tedious. We finally found a replacement LED anchor light bulb that fits the socket and in addition replaced more of our interior lighting with low power draw LED's. I also tackled the chore of calibrating the refrigerator thermostat. It's particular crime is that it is too cold and there are few more spirit crushing events we suffer in this life than discovering your beer is frozen and won't come out of the can.
We checked around on the price of anchor chain and discovered the best deal, on this island at least, was at the Budget Marine store across the bay. This meant we could drop the "old" chain into the dinghy, motor it across the bay to Budget and they in turn swapped this for new anchor chain to be loaded again into our dinghy. Removing the old chain had been entertaining in that the "boat" end of the chain was spliced into a length of nylon rode that I needed Annette to cut with a dive knife. I was underneath the catamaran at the time of cutting, holding the dinghy in place whilst the "old" chain lay in swathes on the floor around my feet. The last time I asked Annette to cut a perfectly good line was during a 2004 emergency and she couldn't bring herself to do it until too late. Again she needed multiple affirmations that it really needed to be done in this decidedly non-emergency application. In the event, it was very hard to cut, thereby indicating we really need a sharper knife for emergency line cutting.
I had serviced the windlass and taken the chain gypsy over to Budget to ensure that the new chain was really going to fit but it was still a huge relief when the new chain was sucked up from the dinghy into the boat and the anchor re-attached. I looked up the internet on how to make the chain to nylon rode splice and with the help of a non-frozen beer was able to make this splice myself instead of hiring someone to do this for me as I have in the past. The advantage of this splice over the typical "mixed rode" application is that my work is safely buried under 300 feet of chain so my workmanship is nigh impossible to criticize.
We took this opportunity to donate the old 45 pound anchor that was on the boat when we took possession, as well as its 145 feet of chain. We now have an 88 pound "self setting" anchor on 300 feet of chain, enabling us to anchor just about anywhere in the world we might want to go. Typically sailors use a "5 to 1" rule that the anchor chain deployed should be at least 5 times the water depth. To complicate this, the anchor and windlass are mounted five feet above the surface of the water so that in 20 feet of water, we would actually need 125 feet of chain to anchor safely, about what we carried previously. The new set-up will allow us to anchor in nearly 60 feet of water.
We did make a deal to buy a new generator and will hang on this dock for the full month whilst it is shipped from the manufacturer.
June 11 - June 17, 2016
We decided to spend at least a week at Prickly Bay, Grenada to "regroup", catch up on boat chores and see the island.
Our first step beyond the act of renting a car was to set out to investigate various boat storage options, thus we found ourselves in the island capital, downtown St. George's, trapped in their one way street system. Several of the the narrow streets were unlabeled as to the direction of traffic flow and in the absence of parked cars as an indicator, it was easy to find oneself on a one way street, headed against the oncoming traffic. More by accident than design, we found ourselves in the close proximity of Fort George, the citadel that overlooks the town and its harbors. We pulled into the parking lot at the fort and discovered it is currently used a a training academy for the Grenada police force. The policemen who were loitering on the sidewalk indicated that it would be fine for us to explore the facility and we wandered around the old fort with it's ancient rusting cannons and its sweeping view of St. George. The courtyard where we had entered bore a memorial tablet to Prime Minister Maurice Bishop and his cabinet members who had been shot during a coup. I then realized that I knew little about Grenada other than the fact that US Marines had invaded in 1983.
Grenada was occupied by Carib Indians from the South American mainland who displaced the earlier occupants, collectively referred to as Arawak Indians. The Caribs were fierce fighters and wiped out early attempts at European colonization until the French managed to gain a fortified foothold on the island in 1649. The driving force for colonization was again the production of sugar cane for the manufacture of alcohol and as in other places, the local Caribs were unsatisfactory as a source of labor and thus replaced by African slave labor. The discovery and implementation of northern latitude sugar beet agriculture in the mid-1700's wiped out the Caribbean cane industry and the Grenada plantations similarly collapsed. The British and French squabbled back and forth over the island until 1783 when the island became British once more. Once the economic requirement for slaves had evaporated, slavery was abolished in 1834 but unlike other islands where the former slaves were essentially abandoned to fend for themselves, nutmeg had been introduced here in 1843 and the island had become a global source of the spice.
In 1974 Grenada became independent of Britain with a Parliamentary system of governance. This lasted 5 years before a military coup put a Marxist group in control. They held power for the next four years until they fell out amongst themselves and began shooting each other. The Cubans had begun extending the runway in Grenada for all of the tourists who naturally flock to islands run by a bunch of armed thugs but Reagan believed that the Cubans, as surrogates for their masters the Soviets, intended to use Grenada to project military power throughout the Caribbean. Reagan organized a military incursion backed by US troops which the association of kleptocrats, dictators and psychopaths called the "United Nations" roundly denounced. The Grenada military and their Cuban allies were swiftly defeated, the US troops departed a few weeks later and a democratic government restored with elections in 1984.
Today the economy is described as 11% agriculture and 20% industry. The island still is a large exporter of the spices nutmeg and mace and there is also some degree of manufacturing. I noticed that Wikipedia has a chart showing the breakdown of exports and an astonishing 8% of export is claimed to be household quality toilet paper. The balance of the economy is tourism and services. The GDP per capita of over $14,000 certainly explains the overall look of prosperity of the island compared to some of the other places we have visited.


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Lemon Cake with whipped lemon and raspberry filling. Decoracted with Stargazer Lilies and buds, Briar Roses, and accent leaves and flowers. Celebrating the engagement of my eldest daughter to a wonderful man!
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Fixed-end beams, continuous beams, continuous trusses, and rigid frames are statically┬Āindeterminate. The equations of equilibrium are not sufficient for the deter┬Āmination of all the unknown forces and moments. Additional equations based on a┬Āknowledge of the deformation of the member are required.
Hence, while the bending moments in a simply supported beam are determined┬Āonly by the loads and the span, bending moments in a statically indeterminate┬Āmember are also a function of the geometry, cross-sectional dimensions, and modulus┬Āof elasticity.
Sign Convention
For computation of end moments in continuous beams and frames, the following┬Āsign convention is most convenient: A moment acting at an end of a member or at┬Āa joint is positive if it tends to rotate the joint clockwise, negative if it tends to┬Ārotate the joint counterclockwise.
Similarly, the angular rotation at the end of a member is positive if in a clockwise┬Ādirection, negative if counterclockwise. Thus, a positive end moment produces a┬Āpositive end rotation in a simple beam.
For ease in visualizing the shape of the elastic curve under the action of loads┬Āand end moments, bending-moment diagrams should be plotted on the tension side┬Āof each member. Hence, if an end moment is represented by a curved arrow, the┬Āarrow will point in the direction in which the moment is to be plotted.
Carry-Over Moments
When a member of a continuous beam or frame is loaded, bending moments are┬Āinduced at the ends of the member as well as between the ends. The magnitude of┬Āthe end moments depends on the magnitude and location of the loads, the geometry┬Āof the member, and the amount of restraint offered to end rotation of the member┬Āby other members connected to it. Because of the restraint, end moments are induced┬Āin the connecting members, in addition to end moments that may be induced┬Āby loads on those spans.
If the far end of a connecting member is restrained by support conditions against┬Ārotation, a resisting moment is induced at that end. That moment is called a carryover┬Āmoment. The ratio of the carry-over moment to the other end moment is called┬Ācarry-over factor. It is constant for the member, independent of the magnitude and┬Ādirection of the moments to be carried over. Every beam has two carry-over factors,┬Āone directed toward each end.
As pointed out in Art. 5.10.6, analysis of a continuous span can be simplified┬Āby treating it as a simple beam subjected to applied end moments. Thus, it is┬Āconvenient to express the equations for carry-over factors in terms of the end rotations┬Āof simple beams: Convert a continuous member LR to a simple beam with┬Āthe same span L. Apply a unit moment to one end (Fig. 5.60). The end rotation at┬Āthe support where the moment is applied is , and at the far end, the rotation is B.┬ĀBy the dummy-load method (Art. 5.10.4), if x is measured from the B end,
Carry-Over Factors. The preceding equations can be used to determine carryover┬Āfactors for any magnitude of end restraint. The carry-over factors toward fixed┬Āends, however, are of special importance.
The bending-moment diagram for a continuous span LR that is not loaded except┬Āfor a moment M applied at end L is shown in Fig. 5.61a. For determination of the┬Ācarry-over factor CR toward R, that end is assumed fixed (no rotation can occur┬Āthere). The carry-over moment to R then is CRM. The moment diagram in Fig.┬Ā5.61a can be resolved into two components: a simple beam with M applied at L┬Ā(Fig. 5.61b) and a simple beam with CRM applied at R (Fig. 5.61c). As indicated┬Āin Fig. 5.61d, M causes an angle change at R of . As shown in Fig. 5.61e, CR┬ĀM induces an angle change at R of CRMR.
With the use of Eqs. (5.107) and (5.111), the stiffness of a beam with constant┬Āmoment of inertia is given by
This equation indicates that a prismatic beam hinged at only one end has threefourths┬Āthe stiffness, or resistance to end rotation, of a beam fixed at both ends.
Fixed-End Moments
A beam so restrained at its ends that no rotation is produced there by the loads is┬Ācalled a fixed-end beam, and the end moments are called fixed-end moments. Fixedend┬Āmoments may be expressed as the product of a coefficient and WL, where W┬Āis the total load on the span L. The coefficient is independent of the properties of┬Āother members of the structure. Thus, any member can be isolated from the rest of┬Āthe structure and its fixed-end moments computed.
Assume, for example, that the fixed-end moments for the loaded beam in Fig.┬Ā5.63a are to be determined. Let MF be the moment at the left end L and MF the┬ĀL R
moment at the right end R of the beam. Based on the condition that no rotation is┬Āpermitted at either end and that the reactions at the supports are in equilibrium with┬Āthe applied loads, two equations can be written for the end moments in terms of┬Āthe simple-beam end rotations, L at L and R, at R for the specific loading.
Let KL be the fixed-end stiffness at L and KR the fixed-end stiffness at R, as┬Āgiven by Eqs. (5.112) and (5.113). Then, by resolution of the moment diagram into┬Āsimple-beam components, as indicated in Fig. 5.63ŲÆ to h, and application of the┬Āsuperposition principle (Art. 5.10.6), the fixed-end moments are found to be
Deflection of Supports. Fixed-end moments for loaded beams when one support┬Āis displaced vertically with respect to the other support may be computed with the┬Āuse of Eqs. (5.116) to (5.121) and the principle of superposition: Compute the fixedend┬Āmoments induced by the deflection of the beam when not loaded and add them┬Āto the fixed-end moments for the loaded condition with immovable supports.
The fixed-end moments for the unloaded condition can be determined directly┬Āfrom Eqs. (5.116) and (5.117). Consider beam LR in Fig. 5.64, with span L and┬Āsupport R deflected a distance d vertically below its original position. If the beam┬Āwere simply supported, the angle change caused by the displacement of R would┬Ābe very nearly d/L. Hence, to obtain the fixed-end moments for the deflected conditions,┬Āset @L =@R = d/L and substitute these simple-beam end rotations in Eqs.┬Ā(5.116) and (5.117):
where MF is the fixed-end moment at the left support and MF at the right support.┬ĀL R
As an example of the use of the curves, find the fixed-end moments in a prismatic┬Ābeam of 20-ft span carrying a triangular loading of 100 kips, similar to the┬Āloading shown in Case 4, Fig. 5.70, distributed over the entire span, with the maximum┬Āintensity at the right support.
Slope-Deflection Equations
In Arts. 5.11.2 and 5.11.4, moments and displacements in a member of a continuous┬Ābeam or frame are obtained by addition of their simple-beam components. Similarly,┬Āmoments and displacements can be determined by superposition of fixed-end-beam┬Ācomponents. This method, for example, can be used to derive relationships between┬Āend moments and end rotations of a beam known as slope-deflection equations.
These equations can be used to compute end moments in continuous beams.
Consider a member LR of a continuous beam or frame (Fig. 5.72). LR may have┬Āa moment of inertia that varies along its length. The support R is displaced vertically
The slope-deflection equations can be used to determine end moments and rotations┬Āof the spans of continuous beams by writing compatibility and equilibrium┬Āequations for the conditions at each support. For example, the sum of the moments┬Āat each support must be zero. Also, because of continuity, the member must rotate┬Āthrough the same angle on both sides of every support. Hence, ML for one span,┬Āgiven by Eq. (5.133) or (5.135), must be equal to MR for the adjoining span,┬Āgiven by Eq. (5.134) or (5.136), and the end rotation at that support must be the┬Āsame on both sides of the equation. One such equation with the end rotations at┬Āthe supports as the unknowns can be written for each support. With the end rotations┬Ādetermined by simultaneous solution of the equations, the end moments can be┬Ācomputed from the slope-deflection equations and the continuous beam can now┬Ābe treated as statically determinate.
See also Arts. 5.11.9 and 5.13.2.
(C. H. Norris et al., ŌĆśŌĆśElementary Structural Analysis,ŌĆÖŌĆÖ 4th ed., McGraw-Hill┬ĀBook Company, New York.)
Moment Distribution
The frame in Fig. 5.74 consists of four prismatic members rigidly connected together
at O at fixed at ends A, B, C, and D. If an external moment U is applied at ┬ĀO, the sum of the end moments in each member at O must be equal to U. Furthermore,┬Āall members must rotate at O through the same angle , since they are┬Āassumed to be rigidly connected there. Hence, by the definition of fixed-end stiffness,┬Āthe proportion of U induced in the end of each member at O is equal to the┬Āratio of the stiffness of that member to the sum of the stiffnesses of all the members┬Āat the joint (Art. 5.11.3).
can be taken when a member has a hinged end to reduce the work of distributing┬Āmoments. This is done by using the true stiffness of a member instead of the fixedend┬Āstiffness. (For a prismatic beam with one end hinged, the stiffness is threefourth┬Āthe fixed-end stiffness; for a beam with variable I, it is equal to the fixedend┬Āstiffness times 1 - CLCR, where CL and CR are the carry-over factors for the┬Ābeam.) Naturally, the carry-over factor toward the hinge is zero.
When a joint is neither fixed nor pinned but is restrained by elastic members┬Āconnected there, moments can be distributed by a series of converging approximations.
All joints are locked against rotation. As a result, the loads will create┬Āfixed-end moments at the ends of every member. At each joint, a moment equal to┬Āthe algebraic sum of the fixed-end moments there is required to hold it fixed. Then,┬Āone joint is unlocked at a time by applying a moment equal but opposite in sign┬Āto the moment that was needed to prevent rotation. The unlocking moment must┬Ābe distributed to the members at the joint in proportion to their fixed-end stiffnesses┬Āand the distributed moments carried over to the far ends.
After all joints have been released at least once, it generally will be necessary┬Āto repeat the processŌĆösometimes several timesŌĆöbefore the corrections to the fixed ┬Āend moments become negligible. To reduce the number of cycles, the unlocking of┬Ājoints should start with those having the greatest unbalanced moments.
Suppose the end moments are to be found for the prismatic continuous beam┬ĀABCD in Fig. 5.75. The I /L values for all spans are equal; therefore, the relative┬Āfixed-end stiffness for all members is unity. However, since A is a hinged end, the┬Ācomputation can be shortened by using the actual relative stiffness, which is 3Ōüä4.
Relative stiffnesses for all members are shown in the circle on each member. The┬Ādistribution factors are shown in boxes at each joint.
The computation starts with determination of fixed-end moments for each member┬Ā(Art. 5.11.4). These are assumed to have been found and are given on the first┬Āline in Fig. 5.75. The greatest unbalanced moment is found from inspection to be┬Āat hinged end A; so this joint is unlocked first. Since there are no other members┬Āat the joint, the full unlocking moment of +400 is distributed to AB at A and onehalf┬Āof this is carried over to B. The unbalance at B now is +400 - 480 plus the┬Ācarry-over of +200 from A, or a total of -120. Hence, a moment of 120 must┬Ābe applied and distributed to the members at B by multiplying by the distribution┬Āfactors in the corresponding boxes.
The net moment at B could be found now by adding the entries for each member┬Āat the joint. However, it generally is more convenient to delay the summation until┬Āthe last cycle of distribution has been completed.
The moment distributed to BA need not be carried over to A, because the carryover┬Āfactor toward the hinged end is zero. However, half the moment distributed to┬ĀBC is carried over to C.
Similarly, joint C is unlocked and half the distributed moments carried over to┬ĀB and D, respectively. Joint D should not be unlocked, since it actually is a fixed┬Āend. Thus, the first cycle of moment distribution has been completed.
The second cycle is carried out in the same manner. Joint B is released, and the┬Ādistributed moment in BC is carried over to C. Finally, C is unlocked, to complete┬Āthe cycle. Adding the entries for the end of each member yields the final moments.
Maximum Moments in Continuous Frames
In design of continuous frames, one objective is to find the maximum end moments┬Āand interior moments produced by the worst combination of loading. For maximum┬Āmoment at the end of a beam, live load should be placed on that beam and on the ┬Ābeam adjoining the end for which the moment is to be computed. Spans adjoining┬Āthese two should be assumed to be carrying only dead load.
For maximum midspan moments, the beam under consideration should be fully┬Āloaded, but adjoining spans should be assumed to be carrying only dead load.
For maximum midspan moments, the beam under consideration should be fully┬Āloaded, but adjoining spans should be assumed to be carrying only dead load.
The work involved in distributing moments due to dead and live loads in continuous┬Āframes in buildings can be greatly simplified by isolating each floor. The┬Ātops of the upper columns and the bottoms of the lower columns can be assumed┬Āfixed. Furthermore, the computations can be condensed considerably by following┬Āthe procedure recommended in ŌĆśŌĆśContinuity in Concrete Building Frames.ŌĆÖŌĆÖ
EB033D, Portland Cement Association, Skokie, IL 60077, and indicated in Fig.┬Ā5.74.
Figure 5.74 presents the complete calculation for maximum end and midspan┬Āmoments in four floor beams AB, BC, CD, and DE. Building columns are assumed┬Āto be fixed at the story above and below. None of the beam or column sections is┬Āknown to begin with; so as a start, all members will be assumed to have a fixedend┬Āstiffness of unity, as indicated on the first line of the calculation.
On the second line, the distribution factors for each end of the beams are shown,┬Ācalculated from the stiffnesses (Arts. 5.11.3 and 5.11.4). Column stiffnesses are not┬Āshown, because column moments will not be computed until moment distribution┬Āto the beams has been completed. Then the sum of the column moments at each┬Ājoint may be easily computed, since they are the moments needed to make the sum┬Āof the end moments at the joint equal to zero. The sum of the column moments at┬Āeach joint can then be distributed to each column there in proportion to its stiffness.
In this example, each column will get one-half the sum of the column moments.
Fixed-end moments at each beam end for dead load are shown on the third line,┬Ājust above the heavy line, and fixed-end moments for live plus dead load on the┬Āfourth line. Corresponding midspan moments for the fixed-end condition also are┬Āshown on the fourth line and, like the end moments, will be corrected to yield┬Āactual midspan moments.
Moment-Influence Factors
In certain types of framing, particularly those in which different types of loading┬Āconditions must be investigated, it may be convenient to find maximum end moments┬Āfrom a table of moment-influence factors. This table is made up by listing┬Āfor the end of each member in the structure the moment induced in that end when┬Āa moment (for convenience, +1000) is applied to every joint successively. Once┬Āthis table has been prepared, no additional moment distribution is necessary for┬Ācomputing the end moments due to any loading condition.
For a specific loading pattern, the moment at any beam end MAB may be obtained┬Āfrom the moment-influence table by multiplying the entries under AB for the various ┬Ājoints by the actual unbalanced moments at those joints divided by 1000, and summing┬Ā(see also Art. 5.11.9 and Table 5.6).
Procedure for Sidesway
Computations of moments due to sidesway, or drift, in rigid frames is conveniently┬Āexecuted by the following method:
1. Apply forces to the structure to prevent sidesway while the fixed-end moments┬Ādue to loads are distributed.
2. Compute the moments due to these forces.
3. Combine the moments obtained in Steps 1 and 2 to eliminate the effect of the┬Āforces that prevented sidesway.
Suppose the rigid frame in Fig. 5.77┬Āis subjected to a 2000-lb horizontal load┬Āacting to the right at the level of beam┬ĀBC. The first step is to compute the moment-
influence factors (Table 5.6) by┬Āapplying moments of 1000 at joints B┬Āand C, ┬Āassuming sidesway prevented.
Since there are no intermediate loads┬Āon the beams and columns, the only┬Āfixed-end moments that need be considered
are those in the columns resulting┬Āfrom lateral deflection of the frame┬Ācaused by the horizontal load. This deflection,┬Āhowever is not known initially.
So assume an arbitrary deflection, which┬Āproduces a fixed-end moment of┬Ā-1000M at the top of column CD. M is an unknown constant to be determined┬Āfr ┬Āthe columns and hence are equal in AB to -1000M x 6Ōüä2 = -3000M. The columnom the fact that the sum of the shears in the deflected columns must be equal to┬Āthe 2000-lb load. The same deflection also produces a moment of -1000M at the┬Ābottom of CD [see Eq. (5.126)].
From the geometry of the structure, furthermore, note that the deflection of B ┬Ārelative to A is equal to the deflection of C relative to D. Then, according to Eq.┬Ā(5.126) the fixed-end moments in the columns are proportional to the stiffnesses of ┬Āfixed-end moments are entered in the first line of Table 5.7, which is called a┬Āmoment-collection table.
from which M = 2.30. This value is substituted in the sidesway total in Table 5.7┬Āto yield the sidesway moments for the 4000-lb load. The addition of these moments┬Āto the totals for no sidesway yields the final moments.
This procedure enables one-story bents with straight beams to be analyzed with┬Āthe necessity of solving only one equation with one unknown regardless of the┬Ānumber of bays. If the frame is several stories high, the procedure can be applied┬Āto each story. Since an arbitrary horizontal deflection is introduced at each floor or┬Āroof level, there are as many unknowns and equations as there are stories.
The procedure is more difficult to apply to bents with curved or polygonal┬Āmembers between the columns. The effect of the change in the horizontal projection┬Āof the curved or polygonal portion of the bent must be included in the calculations.
In many cases, it may be easier to analyze the bent as a curved beam (arch).
(A. Kleinlogel, ŌĆśŌĆśRigid Frame Formulas,ŌĆÖŌĆÖ Frederick Ungar Publishing Co., New┬ĀYork.)
Rapid Approximate Analysis of Multistory Frames
Exact analysis of multistory rigid frames subjected to lateral forces, such as those┬Āfrom wind or earthquakes, involves lengthy calculations, and they are timeconsuming┬Āand expensive, even when performed with computers. Hence, approximate┬Āmethods of analysis are an alternative, at least for preliminary designs and,┬Āfor some structures, for final designs.
It is noteworthy that for some buildings even the ŌĆśŌĆśexactŌĆÖŌĆÖ methods, such as those┬Ādescribed in Arts. 5.11.8 and 5.11.9, are not exact. Usually, static horizontal loads┬Āare assumed for design purposes, but actually the forces exerted by wind and earthquakes┬Āare dynamic. In addition, these forces generally are uncertain in intensity,┬Ādirection, and duration. Earthquake forces, usually assumed as a percentage of the┬Āmass of the building above each level, act at the base of the structure, not at each┬Āfloor level as is assumed in design, and accelerations at each level vary nearly┬Ālinearly with distance above the base. Also, at the beginning of a design, the sizes┬Āof the members are not known. Consequently, the exact resistance to lateral deformation┬Ācannot be calculated. Furthermore, floors, walls, and partitions help resist┬Āthe lateral forces in a very uncertain way. See Art. 5.12 for a method of calculating┬Āthe distribution of loads to rigid-frame bents.
Portal Method. Since an exact analysis is impossible, most designers prefer a┬Āwind-analysis method based on reasonable assumptions and requiring a minimum┬Āof calculations. One such method is the so-called ŌĆśŌĆśportal method.ŌĆÖŌĆÖ
It is based on the assumptions that points of inflection (zero bending moment)┬Āoccur at the midpoints of all members and that exterior columns take half as much┬Āshear as do interior columns. These assumptions enable all moments and shears┬Āthroughout the building frame to be computed by the laws of equilibrium.
Consider, for example, the roof level (Fig. 5.78a) of a tall building. A wind load┬Āof 600 lb is assumed to act along the top line of girders. To apply the portal method,┬Āwe cut the building along a section through the inflection points of the top-story┬Ācolumns, which are assumed to be at the column midpoints, 6 ft down from the┬Ātop of the building. We need now consider only the portion of the structure above┬Āthis section.
Since the exterior columns take only half as much shear as do the interior columns,┬Āthey each receive 100 lb, and the two interior columns, 200 lb. The moments┬Āat the tops of the columns equal these shears times the distance to the inflection┬Āpoint. The wall end of the end girder carries a moment equal to the moment in the┬Ācolumn. (At the floor level below, as indicated in Fig. 5.78b, that end of the end┬Āgirder carries a moment equal to the sum of the column moments.) Since the┬Āinflection point is at the midpoint of the girder, the moment at the inner end of the┬Āgirder must the same as at the outer end. The moment in the adjoining girder can┬Ābe found by subtracting this moment from the column moment, because the sum┬Āof the moments at the joint must be zero. (At the floor level below, as shown in┬ĀFig. 5.78b, the moment in the interior girder is found by subtracting the moment┬Āin the exterior girder from the sum of the column moments.)
Girder shears then can be computed by dividing girder moments by the half┬Āspan. When these shears have been found, column loads can be easily computed┬Āfrom the fact that the sum of the vertical loads must be zero, by taking a section┬Āaround each joint through column and girder inflection points. As a check, it should┬Ābe noted that the column loads produce a moment that must be equal to the moments┬Āof the wind loads above the section for which the column loads were computed.
For the roof level (Fig. 5.78a), for example, -50 x 24 + 100 x 48 =┬Ā600 x 6.
Cantilever Method. Another wind-analysis procedure that is sometimes employed┬Āis the cantilever method. Basic assumptions here are that inflection points are at┬Āthe midpoints of all members and that direct stresses in the columns vary as the┬Ādistances of the columns from the center of gravity of the bent. The assumptions┬Āare sufficient to enable shears and moments in the frame to be determined from the┬Ālaws of equilibrium.
For multistory buildings with height-to-width ratio of 4 or more, the Spurr modification
is recommended (ŌĆśŌĆśWelded Tier Buildings,ŌĆÖŌĆÖ U.S. Steel Corp.). In this
method, the moments of inertia of the girders at each level are made proportional┬Āto the girder shears.
The results obtained from the cantilever method generally will be different from┬Āthose obtained by the portal method. In general, neither solution is correct, but the┬Āanswers provide a reasonable estimate of the resistance to be provided against┬Ālateral deformation. (See also Transactions of the ASCE, Vol. 105, pp. 1713ŌĆō1739,┬Ā1940.)
Beams Stressed into the Plastic Range
When an elastic material, such as structural steel, is loaded in tension with a gradually┬Āincreasing load, stresses are proportional to strains up to the proportional limit┬Ā(near the yield point). If the material, like steel, also is ductile, then it continues to┬Ācarry load beyond the yield point, though strains increase rapidly with little increase┬Āin load (Fig. 5.79a).
Similarly, a beam made of a ductile material continues to carry more load after┬Āthe stresses in the outer surfaces reach the yield point. However, the stresses will┬Āno longer vary with distance from the neutral axis, so the flexure formula [Eq.┬Ā(5.54)] no longer holds. However, if simplifying assumptions are made, approximating┬Āthe stress-strain relationship beyond the elastic limit, the load-carrying capacity┬Āof the beam can be computed with satisfactory accuracy.
Modulus of rupture is defined as┬Āthe stress computed from the flexure┬Āformula for the maximum bending moment┬Āa beam sustains at failure. This is┬Ānot a true stress but it is sometimes used┬Āto compare the strength of beams.
For a ductile material, the idealized┬Āstress-strain relationship in Fig. 5.79b┬Āmay be assumed. Stress is proportional┬Āto strain until the yield-point stress ŲÆy is┬Āreached, after which strain increases at
a constant stress.
For a beam of this material, the following┬Āassumptions will also be made:
1. Plane sections remain plane, strains┬Āthus being proportional to distance┬Āfrom the neutral axis.
2. Properties of the material in tension┬Āare the same as those in compression.
3. Its fibers behave the same in flexure┬Āas in tension.
4. Deformations remain small.
Strain distribution across the cross┬Āsection of a rectangular beam, based on┬Āthese assumptions, is shown in Fig. 5.80a. At the yield point, the unit strain is y┬Āand the curvature y, as indicated in (1). In (2), the strain has increased several┬Ātimes, but the section still remains plane. Finally, at failure, (3), the strains are very┬Ālarge and nearly constant across upper and lower halves of the section.
Corresponding stress distributions are shown in Fig. 5.80b. At the yield point,┬Ā(1), stresses vary linearly and the maximum if ŲÆy . With increase in load, more and┬Āmore fibers reach the yield point, and the stress distribution becomes nearly constant,┬Āas indicated in (2). Finally, at failure, (3), the stresses are constant across the┬Ātop and bottom parts of the section and equal to the yield-point stress.
The resisting moment at failure for a rectangular beam can be computed from┬Āthe stress diagram for stage 3. If b is the width of the member and d its depth, then┬Āthe ultimate moment for a rectangular beam is
Since the resisting moment at stage 1 is My ŲÆybd2 / 6, the beam carries 50% more┬Āmoment before failure than when the yield-point stress is first reached at the outer┬Āsurfaces.


text:
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text: United States Government Publishing Office publisher pbl distributor dst United States National Archives and Records Administration Office of the Federal Register author aut Government Organization text government publication eng STATUTE Bills and Statutes legislative 2012-11-15 Statue of Esther Morris--Temporary Placement Part 1 Concurrent Resolutions D09002ee1837e62d6 https://www.gpo.gov/fdsys/granule/STATUTE-73/STATUTE-73-PgB15-3 STATUTE-073-1-4.pdf 73 Stat. B15 73 Stat. B15 https://www.gpo.gov/fdsys/granule/STATUTE-73/STATUTE-73-PgB15-3/content-detail.html https://www.gpo.gov/fdsys/pkg/STATUTE-73/pdf/STATUTE-73-PgB15-3.pdf 1 p. B15 B15 73 Stat. B15; United States Statutes at Large, Volume 73, 86th Congress, 1st Session; Statue of Esther Morris--Temporary Placement; S. Con. Res. 38 SCONRES STATUTE-73-PgB15-3 1959-08-18 86 38 1 1959 73 1 1 false 3 SENATE 1959-073-SCONRES-B15.pdf S. Con. Res. 55 United States National Archives and Records Administration Senate author aut Government Organization S. Con. Res. 38, 86th Congress United States Senate Concurrent Resolution 55 (86th Congress) S. Con. Res. 55 86 United States Statutes at Large Volume 73 Page B15 73 Stat. B15 U.S. Government Printing Office 1959-09-15 continuing annual deposited born digital AE 2.111: https://www.gpo.gov/fdsys/pkg/STATUTE-73 P0b002ee1837e5dcf STATUTE-73.pdf DGPO 2012-11-15 2012-10-02 STATUTE-73 machine generated eng fdlp STATUTE STATUTE-73 86 1 1959 73 1959-01-07 1 United States Statutes at Large, Volume 73, 86th Congress, 1st Session Vol. 73 https://www.gpo.gov/fdsys/pkg/STATUTE-73/content-detail.html https://www.gpo.gov/fdsys/pkg/STATUTE-73/pdf/STATUTE-73.pdf Statutes at Large, Vol. 73, September 15, 1959


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