Truss

For other uses, see Truss (disambiguation).

Double chorded heavy timber truss with 80ft clear span.

Truss bridge for a single track railway, converted to pedestrian use and pipeline support

In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either tensile or compressive forces. Moments (torsional forces) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes.

A planar truss is one where all the members and nodes lie within a two dimensional plane, while a space truss has members and nodes extending into three dimensions.

Characteristics of trusses

A truss is composed of triangles because of the structural stability of that shape and design. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed.^[1] In comparison, both the angles and the lengths of a square must be fixed for it to retain its shape.

The simplest form of a truss is one single triangle. This type of truss is seen in a framed roof consisting of rafters and a ceiling joist.^[2] Because of the stability of this shape and the methods of analysis used to calculate the forces within it, a truss composed entirely of triangles is known as a simple truss.^[3]

A planar truss lies in a single plane.^[3] Planar trusses are typically used in parallel to form roofs and bridges. A space truss is a three-dimensional framework of members pinned at their ends. A tetrahedron shape is the simplest space truss, consisting of six members which meet at four joints.^[3]

The depth of a truss, or the height between the upper and lower chords, is what makes it an efficient structural form. A solid girder or beam of equal strength would have substantial weight and material cost as compared to a truss. For a given span length, a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.^[4]

Truss types

Pre fabricated steel bow string roof trusses built 1942 for war department properties in Northern Australia.

Roof truss in a side building of Cluny Abbey, France.

A large timber Howe truss in a commercial building

There are two basic types of truss:

• The pitched truss, or common truss, is characterized by its triangular shape. It is most often used for roof construction. Some common trusses are named according to their web configuration. The chord size and web configuration are determined by span, load and spacing.
• The parallel chord truss, or flat truss, gets its name from its parallel top and bottom chords. It is often used for floor construction.

A combination of the two is a truncated truss, used in hip roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with metal connector plates.

  Pratt truss

The Pratt truss was patented in 1844 by two Boston railway engineers^[5]; Caleb Pratt and his son Thomas Willis Pratt^[6]. The design uses vertical beams for compression and horizontal beams to respond to tension. What is remarkable about this style is that it remained popular even as wood gave way to iron, and even still as iron gave way to steel.^[7]

The Southern Pacific Railroad bridge in Tempe, Arizona is a 393 meter (1291 foot) long truss bridge built in 1912^[8]. The structure is composed of nine Pratt truss spans of varying lengths. The bridge is still in use today.

Bow string roof truss

Named for its vicissitudal shape, thousands of bow strings were used during World War II for aircraft hangars and other military buildings.

King post truss

Main article: King post

One of the simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support.

The queen post truss, sometimes queenpost or queenspost, is similar to a king post truss in that the outer supports are angled towards the center of the structure. The primary difference is the horizontal extension at the centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans. ^[9]

Lenticular Truss

American Lenticular Truss Bridges have the top and bottom chords of the truss arched forming a lens shape. Patented in 1878 by William Douglas.

Town's lattice truss

Main article: Lattice truss bridge

American architect Ithiel Town designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, patented in 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them.

Vierendeel truss

A Vierendeel bridge; note the lack of diagonal elements in the primary structure and the way bending loads are carried between elements

Further information: Vierendeel Bridge

The Vierendeel truss is a truss where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. Regular trusses comprise members that are commonly assumed to have pinned joints with the implication that no moments exist at the jointed ends. This style of truss was named after the Belgian engineer Arthur Vierendeel^[10], who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss.

The utility of this type of truss in buildings is that there is no diagonal bracing, the creation of rectangular openings for windows and doors is simplified and in cases the need for compensating shear walls is reduced or eliminated.

After being damaged by the impact of a plane hitting the building, parts of the framed curtain walls of the Twin Towers of the World Trade Center resisted collapse by Vierendeel action displayed by the remaining portions of the frame.

Statics of trusses

Support structure under the Auckland Harbour Bridge.

A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints or rollers, is described as being statically determinate. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all horizontal forces, all vertical forces, as well as all moments acting about the node equal zero. Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.

Trusses that are supported at more than two positions are said to be statically indeterminate, and the application of Newton's Laws alone is not sufficient to determine the member forces.

In order for a truss with pin-connected members to be stable, it must be entirely composed of triangles. In mathematical terms, we have the following necessary condition for stability:

where m is the total number of truss members, j is the total number of joints and r is the number of reactions (equal to 3 generally) in a 2-dimensional structure.

When m = 2j − 3, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members.

Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. They are called statically indeterminate structures, because their member forces depend on the relative stiffness of the members, in addition to the equilibrium condition described.

Analysis of trusses

Cremona diagram for a plane truss

Because the forces in each of its two main girders are essentially planar, a truss is usually modelled as a two-dimensional plane frame. If there are significant out-of-plane forces, the structure must be modelled as a three-dimensional space.

The analysis of trusses often assumes that loads are applied to joints only and not at intermediate points along the members. The weight of the members is often insignificant compared to the applied loads and so is often omitted. If required, half of the weight of each member may be applied to its two end joints. Provided the members are long and slender, the moments transmitted through the joints are negligible and they can be treated as "hinges" or 'pin-joints'. Every member of the truss is then in pure compression or pure tension – shear, bending moment, and other more complex stresses are all practically zero. This makes trusses easier to analyze. This also makes trusses physically stronger than other ways of arranging material – because nearly every material can hold a much larger load in tension and compression than in shear, bending, torsion, or other kinds of force.

Structural analysis of trusses of any type can readily be carried out using a matrix method such as the direct stiffness method, the flexibility method or the finite element

Forces in members

On the right is a simple, statically determinate flat truss with 9 joints and (2 x 9) − 3 = 15 members. External loads are concentrated in the outer joints. Since this is a symmetrical truss with symmetrical vertical loads, it is clear to see that the reactions at A and B are equal, vertical and half the total load.

The internal forces in the members of the truss can be calculated in a variety of ways including the graphical methods:

• Cremona diagram
• Culmann diagram
• the analytical Ritter method (method of sections).

Design of members

The Auckland Harbour Bridge from Watchman Island, west of it.

A truss can be thought of as a beam where the web consists of a series of separate members instead of a continuous plate. In the truss, the lower horizontal member (the bottom chord) and the upper horizontal member (the top chord) carry tension and compression, fulfilling the same function as the flanges of an I-beam. Which chord carries tension and which carries compression depends on the overall direction of bending. In the truss pictured above right, the bottom chord is in tension, and the top chord in compression.

The diagonal and vertical members form the truss web, and carry the shear force. Individually, they are also in tension and compression, the exact arrangement of forces depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression.

In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the picture, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members.

A building under construction in Shanghai. The truss sections stabilize the building and will house mechanical floors.

The inclusion of the elements shown is largely an engineering decision based upon economics, being a balance between the costs of raw materials, off-site fabrication, component transportation, on-site erection, the availability of machinery and the cost of labor. In other cases the appearance of the structure may take on greater importance and so influence the design decisions beyond mere matters of economics. Modern materials such as prestressed concrete and fabrication methods, such as automated welding, have significantly influenced the design of modern bridges.

Once the force on each member is known, the next step is to determine the cross section of the individual truss members. For members under tension the cross-sectional area A can be found using A = F × γ / σ_y, where F is the force in the member, γ is a safety factor (typically 1.5 but depending on building codes) and σ_y is the yield tensile strength of the steel used.
The members under compression also have to be designed to be safe against buckling.

The weight of a truss member depends directly on its cross section -- that weight partially determines how strong the other members of the truss need to be. Giving one member a larger cross section than on a previous iteration requires giving other members a larger cross section as well, to hold the greater weight of the first member -- one needs to go through another iteration to find exactly how much greater the other members need to be. Sometimes the designer goes through several iterations of the design process to converge on the "right" cross section for each member. On the other hand, reducing the size of one member from the previous iteration merely makes the other members have a larger (and more expensive) safety factor than is technically necessary, but doesn't require another iteration to find a buildable truss.

The effect of the weight of the individual truss members in a large truss, such as a bridge, is usually insignificant compared to the force of the external loads.

Design of joints

After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the bolted joints, e.g., involving shear of the bolt connections used in the joints, see also shear stress.

Little Belt: a truss bridge in Denmark

خرپا

استفاده ها از خرپا

جذب دو برابر ریسمان توسط خرپا با اندازه واضح 80 فوت

خرپا پلی برای یک راه آهن تک شیار برای استفاده ، پیاده سازی و حمایت کردن خط لوله است. خرپاها کابرد های زیادی در پل ها و سقف ها و... دارند و خوبی انها این است که سبک هستند و معمولا در مقابل بار وارده از وزنشان صرف نظر می شود.در اکثر موارد خرپاها بصورت اعضای مثلثی که در کنار هم طوری جوش داده میشود که اتصالات که گره (Joint) نامیده میشوند بصورت لولایی عمل کنند.

قرار داد ما در خرپاها بدین صورت است که نیروها در گره ها وارد میشوند و اگر نیرویی بر غیر گره یعنی عضو وارد شد بحث از خرپا خارج و به سمت قاب می رود .

در معماری و مهندسی ساختمان خرپا شامل یک یا چند ساختمان واحد به وسیله یک عضو مستقیم از انتخاب محل اتصال گره است .سطح نیرو های مسطح و واکنش به آن نیرو ها با اندیشه عمل صحیح فقط از گره ها و نتیجه این نیروها در هر یک ازب خش ها انبساط یا نیروی فشرده است .

در هر لحظه مجموعه نیرو های زمینی مانع آشکار شدن هستند زیرا تمام محل های اتصال در خرپا مانند لب برگشته است .

مشخصات خرپا

خرپا ترکیبی از ساختمان های مثلثی شکل ثابتی است که تغییر شکل نمی دهد و طول آن ثابت است. در هر دو مقایسه گوشه های بلند از چهار گوش باید برای حفظ کردن شکل ثابت باشد.

خرپا از اجزایی به وجود می آید که همگی در یک صفحه قرار داشته و ترکیب آن یک شبکه مثلثی ایجاد می کند . چون در خرپا ها فرض می شود که اعضا در انتهای خود به اعضای دیگر لولا شده اند بتابراین شکل مثلثی شکل پایدار خواهد بود.

خرپاها از جملهٔ ساده‌ترین اعضاء باربر سازه‌ها هستند که در کل به عنوان اعضاء خمشی عمل نموده و در سقف ها ، پلها ، و سازه های هوا وفضا مورد استفاده قرار می گیرند. در این گونه سازه ها به علت عدم وجود نیروی پرشی و لنگر خمشی در تک تک اعضا متشکله مثلث ها اتصالات باید به صورت مفصلی شود .

عمق خرپا یا بلندی ریسمان در ساختن یک ساختمان موثر است . تیر آهن جامد یا میله شبیه نیروی جسمی سنگین و مقاسیه کردن هزینه مصالح در خرپا است . برای تعیین محدوده طول و عمق یک خرپا نیاز کمتر داشتن به مصالح ریسمان و مصالح بزرگ در عمودی ها م مورب هاست . عمق بهینه از خرپا بیشترین بازده را دارد .

انواع خرپا

در قدیم برای ساختن عبور  وسایل نقلیه با فولاد از خرپای چوبی در سال 1942برای جنگ دایره در شمال استرالیا ا نجام گرفت.

استفاده یک خرپا در پهلوی ساختمان از کلیسا در فرانسه

فرو رفتگی چوب بزرگ خرپا در یک ساختمان تجاری

دونوع خرپای اساسی وجود دارد :

نصب خرپا یا خرپای معمولی به وسیله شکل مثلث سه گوش مشخص می شود .خیلی مواقع  برای سقف های ساختمانی استفاده می شوند . برخی خرپای معمولی نام موا فق در ترکیب بافت هستند . ا ندازه ریسمان و تر کیب بافت  محدود و فاصله مصمم هستند .

ریسمان موازی خرپا یا خرپاهای پهن بدست آمده از نام موازی و پایین ریسمان هاست . خیلی مواقع  برای کف اتاق ساختمان خودمان استفاده می کنیم .

ترکیبی از دو نوع خرپای در جنس سقف ساختمان ها استفاده می شود . یک صفحه فلزی متصل به چوب خر پا در سقف یا خر پای کف اتاق بخشی از چوب مفصل با اتصال صفحه فلزی است .

پارت خرپا

خرپای پارت در سال 1844 توسط دو بوستن مهندسان خط راه آهن بود.

کالیب پرا تر و ویلندر توماس است. طرح عمودی میله  برای ساختمات ها و تیر های ا فقی برای پاسخ کشش استفاده می شود . موارد قابل توجه درباره این سبک باقی ماننده مجموع چوب از راه آهن وحتی راهی به سوی فولاد است .

پل راه آهن اقیانوس جنوبی در اریزونا 393 ( 1291 فوت ) متر پل خرپای دراز در سال 1912 بود. ساختمان ها ترکیبی از محدوده 9  پل خرپا در عوض کردن بلندی هاست . پل ها حرکتی در استفاده امروز است.

خم شدن ریسمان سقف خرپا

نام ها برای شکل تحول هزاران ریسمان درمدت جنگ جهانی دوم برای حفظ هواپیما ودیگر ساختمات های نظامی بود .

پست پادشاه خرپا

کالا نیرومند : پست پادشاه

یک خرپای ساده ا بزاری سبک شامل پست پادشاه از دو تکه آنالوگ بین یک حمایت کننده مشترک عمومی است.

پست ملکه خرپا : گاهی  پست ملکه یا پست های ملکه مشابه به یک پست خرپای پادشاه در حمایت کننده نزدیک زاویه بیرونی مرکز از ساختمان هستند . فرق ابتدایی میله مرکز اضافی افقی در اعتماد کردن  حرکت میله وتهیه کردن پایداری میکانیکی است . این سقف خرپا فقط مناسب برای محدود نسبی کوتاهی است .

خرپای ذره بینی

پل خرپای ذره بینی در آمریکا نوک و تهه ریسمان فرم وقوس خرپا یک سکل عدسی است .

ا متیاز آن در سال 1818 توسط ولیام دونگلاس داده شد.

شهرک شبکه بندی خرپا تعریف نیرومند : پل خرپای شبکه بندی شده

آفیل معمار آمریکایی با طرح سفارش شهرک خرپای شبکه بندی شده یک پل چوبی به طرف هاوایی این طرح آزاد در سال 1835 به صورت آسان با چبدن قطعه هایی مرب با فضایی کم در بین آن ها.

خرپا ویرندل

پل ویرندل : روی دریاچه از عناصر مورب در ساخت مقدمات اولیه و راه بار کردن خمیدگی و حمل ونقل میان محیط طبیعی نبوده.

اطلاعات بیشتر در مورد پل ویرندل : بخشی از یک خرپا از سه گوش نیست  اما از دهانه های مستطیل و خمیدگی و پایداری است .

خرپای منظم شامل عضو هایی به طور عادی که با یکدیگر فرق می کنند هستند و محل اتصال ایجاد می کنند و به وسیله اتصال دادن آجر اهمیت داده می شود . این سبک از خرپا علامتی       بعد از مهندسان  پل ویرندل بود که طرح در سال 1896 توسعه داده شد . پل در کم بودن حقوق و در مقایسه با هزینه های یک خرپای سه گوش استفاده می شود.

سودمندی از این نوع خرپا در ساختمان ها جایی در بخش های مورد ایجاد دهانه های مستطیلی برای پنجره ها و در ها در ساده سازی و نیاز قالب برای جبران کردن در کم کردن یا رفع کردن بود .بعد از این زمانخسارت هایی توسط فشارهایی از صفحه ثابت ساختمان بخش هایی از دیوار ها از برج های جفت در جهان در پایداری مر کزی و فروریختن توسط ویرندل حرکتی توسط مانده  بخش هلیی از قاب نمایش داده شده .

In the name of god

Parviz khosravi    :  supplier

Number student: 860737013

Lofty professor: gentlewoman Sara fotovat

Symposium: Truss

Junior college: Sama khorasgan

Spring 1388