REVIEWER-FOR-MIDTERM-CE-423-Steel-and-Timber-Designedn PDF

Equilibrium A body is said to be in equilibrium if no net force acts on it. This means all the forces acting on the body add up to zero. There are two cases in which a body can be in equilibrium: When the body is at rest and when the body is moving at a constant speed without changing direction Th...

Equilibrium A body is said to be in equilibrium if no net force acts on it. This means all the forces acting on the body add up to zero. There are two cases in which a body can be in equilibrium: When the body is at rest and when the body is moving at a constant speed without changing direction These two conditions must be simultaneously (existing or occurring at the same time: exactly coincident.) Satisfied in equilibrium. If one of them is not satisfied, the body is not in equilibrium. Structures are subjected to forces external to themselves, such as weights placed on them, the dead weight of the structure itself, wind or water pressure, and reactions exerted by the ground on which the structure rests; to name but a few of those most met in civil engineering. If the structure is at rest or not being accelerated, for example a structure attached to the ground, what are the two forces formed to be called that the structure is in equilibrium? If the structure is at rest, or to be more precise, not being accelerated, which is usually the case with structures attached to the ground, discounting vibrational and earthquake movements, the loads and reactions form a system of forces in equilibrium satisfying the laws of statics. Reactions at support are just as many forces acting on the structure helping to maintain it in equilibrium as are the loads. They differ from the latter only by loads are those forces applied to the structure by active agents, such as gravity, wind or mechanical means; whereas reactions are those forces applied to the structure due to the resistance of a supporting medium, such as the ground. Example, of a piece of cast iron resting on the floor. The lump of cast iron is in equilibrium under the action of two equal and opposite forces. One is the load, which is the weight of the piece of cast iron; that is the mutual gravitational attraction existing between it and the earth; and the other force is the reaction provided by the floor. The load is under direct control in the sense that a larger or a smaller piece of iron can be substituted, whereas the reaction of the floor adjusts itself to variations in the load, so that equilibrium is maintained. STRESS When we apply force on a body, the body tends to resist the applied force. So, stress is the resistive force developed in a body per unit area OR The quantity that describes the magnitude of forces that cause deformation. It is defined as force per unit. OR Stress is the measure of the force required to cause deformation. SHEAR What is shear in the world of construction? In the world of construction, shear can refer to several things. To engineers it's a certain type of stress inside a structural member due to some applied load. Shear can also mean a lateral load from earthquake or wind. Shear can refer to a construction method of resisting wind and earthquake loads. What is the difference between shear stress and shear strength? Shear stress is a resistive force developed per unit area in a body due to the applied Shear force. Shear force causes shape changes without changing the volume of the body. Strength is the ability of a material to resist external load against failure. Strength is property and fixed for a particular material. And strength is the primary design factor. Shear strength is the ability of the material to resist shear load until failure. The main difference between these two terms is Shear strength is a property and is constant for material. Shear stress varies according to the load applied. Shear strength is the maximum shear stress developed at the time of failure MOMENTS MOMENT in construction? A moment is the turning effect of a force. Forces that create a moment act around a point called the pivot. The pivot is the point around which the object can rotate or turn. On a see- saw the pivot is the point in the middle. A moment (also sometimes called a torque) is defined as the "tendency of a force to rotate a body". The Principle of Moment The principle of moments, also known as Varignon's theorem, is a fundamental concept in physics and engineering that describes the equilibrium of a rigid body under the influence of external forces. The principle states that the moment of a force about a point is equal to the sum of the moments of the components of the force about the same point. The moment is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of application to the point about which the moment is being calculated. What is Varignon's Theorem? Varignon’s theorem, also known as the Varignon’s principle or the theorem of moments, is a fundamental concept in the field of statics and engineering. Named after the French mathematician and physicist Pierre Varignon, this theorem provides a powerful tool for analyzing and simplifying complex force systems. It allows us to understand how forces act and interact in a two-dimensional plane, making it an essential principle in the study of equilibrium and structural analysis. Varignon’s Theorem Equation The equation for Varignon’s theorem, which relates the sum of moments to the moment of the resultant force, is as follows: ΣM = Mr In this equation: ΣM represents the sum of the moments of the individual forces about a point. Mr represents the moment of the resultant force about the same point. Essentially, the equation states that the sum of the moments of the forces (ΣM) is equal to the moment of the resultant force (Mr) about a specific point. The moments are calculated by multiplying the magnitude of each force by its perpendicular distance from the reference point or axis. By applying this equation, engineers and physicists can analyze the distribution of forces and determine the overall rotational effect of a system. This simplifies the analysis of complex force systems, as it allows for the replacement of multiple forces with a single resultant force located at a specific point, without altering the overall moment. Applications of Varignon’s Theorem Varignon’s theorem finds numerous applications in various fields, particularly in statics and engineering. Some of the notable applications of Varignon’s theorem are: Structural Analysis: Varignon’s theorem is extensively used in analyzing the equilibrium and stability of structures. It allows engineers to simplify complex force systems acting on structural elements such as beams, trusses, and frames. By replacing the distributed forces with an equivalent resultant force, engineers can determine the overall moment and its effect on the structure, aiding in the design and optimization process. Mechanical Engineering: In mechanical engineering, Varignon’s theorem is applied to analyze the forces and moments acting on mechanical systems, such as linkages, levers, and pulleys. By using the theorem, engineers can determine the resultant forces and moments at specific points, helping in the calculation of required torques, balancing systems, and optimizing mechanical designs. Robotics and Biomechanics: Varignon’s theorem is relevant in the analysis of robotic systems and human movements. By applying the theorem, researchers can calculate the net moments acting on joints and linkages, facilitating the design and control of robotic manipulators. In biomechanics, the theorem helps in understanding the distribution of forces and moments in human skeletal systems, providing insights into the mechanics of human movement and facilitating the development of assistive devices and ergonomic designs. Civil Engineering: In civil engineering, Varignon’s theorem is used in analyzing the forces and moments in structures such as bridges, buildings, and dams. By simplifying the force systems acting on various structural components, engineers can assess the stability, load distribution, and overall structural integrity, ensuring that the design can withstand the anticipated forces and moments. Aerospace Engineering: Varignon’s theorem finds applications in aerospace engineering for analyzing and designing aircraft and spacecraft structures. By simplifying the complex force systems acting on wings, fuselages, and other components, engineers can determine the overall moments and their impact on structural stability, performance, and safety. What is Beam? A beam is basically defined as one structural member used to bear the different loads. In structure, beam helps to bear the load and we must have to note it here that there will not be any structure without beams and therefore we must have to understand the various types of beams in strength of materials. Beam is usually subjected with vertical load, shear load and also sometimes with horizontal load. We must have to note it here that cross section of a beam will be quite smaller as compared to its length. TYPES OF BEAM Simply supported beams A simply supported beam is one that rests on two supports and is free to move horizontally or we may say that simply supported beams are defined as having two supports at either end – one pinned and one roller. This is generally considered as being the simplest type of beam. Application: The most common use of a roller support is in a bridge. In civil engineering, a bridge will typically contain a roller support at one end to account for vertical displacement and expansion from changes in temperature. This is required to prevent the expansion causing damage to a pinned support. A roller (sometimes called rocker in real life) only transmits loads in one direction, typically Y axis. They too are used in real life to support girders for large bridges Pinned supports are commonly used in residential or light commercial applications for joining multiple members together, such as in trusses, three-hinged arched bridges, and simply supported beams. They are also used in other structures where rotation is needed, such as in cranes, towers, and other similar structures. Connections on a steel bridge may appear to be fixed connections as we observe them. However they are designed to experience large loads that will exceed their moment capacity. Thus they are modelled as pin connection on paper. The proper approach in structural engineering is to consider the orders of magnitude of the loads and the capacity of the connection to determine whether the connection should be modelled as fixed, pinned or as a roller. Cantilevered beams Cantilever beams are supported from one end, using a fixed support. A cantilever beam is a rigid structural element supported at one end and free at the other, as shown in Figure-1. The cantilever beam can be either made of concrete or steel whose one end is cast or anchored to a vertical support. It is a horizontal beam structure whose free end is exposed to vertical loads. In a building, a cantilever is constructed as an extension of a continuous beam, and in bridges, it is a segment of a cantilever girder. Cantilever construction allows overhanging structures without additional supports and bracing. This structural element is widely used in the construction of bridges, towers, and buildings, and can add a unique beauty to the structure. Fixed Beam Fixed beams have fixed supports at either end – offering moment resistance at either end. This type of beam may be used when the designer wants to control the deflection at the mid- span because the two fixed supports prevent rotation. Continuous Beam Continuous beams are multi-spanned beams that have multiple supports across the length of the beam. An example of a continuous beam would be a single beam that is supported by a number of columns along its length. Overhanging Beam Overhanging beams are those with two supports, but unlike simply supported beams, one of the supports is not at the end of the member. A typical example of this is a balcony that is being extended from a frame structure. The frame offers the two supports, yet no support exists at the end of the member – allowing it to ‘overhang’ as the name suggests. DIFFERENT TYPES OF LOAD ACTING ON BEAM Beam is usually subjected with vertical load, shear load and also sometimes with horizontal load. We must have to note it here that cross section of a beam will be quite smaller as compared to its length. Various types of loads on beams A beam is usually horizontal member and load which will be acting over the beam will be usually vertical loads. There are following types of loads as mentioned here and we will discuss each type of load in detail.  Point load or concentrated load  Uniformly distributed load  Uniformly varying load Point load or concentrated load Point load or concentrated load, as name suggest, acts at a point on the beam. If we will see practically, point load or concentrated load also distributed over a small area but we can consider such type of loading as point loading and hence such type of load could be considered as point load or concentrated load. Following figure displayed here indicates the beam AB of length L which will be loaded with point load W at the midpoint of the beam. Load W will be considered here as the point load. Uniformly distributed load Uniformly distributed load is the load which will be distributed over the length of the beam in such a way that rate of loading will be uniform throughout the distribution length of the beam. Uniformly distributed load is also expressed as U.D.L and with value as w N/m. During determination of the total load, total uniformly distributed load will be converted in to point load by multiplying the rate of loading i.e. w (N/m) with the span of load distribution i.e. L and will be acting over the midpoint of the length of the uniformly load distribution. Let us consider the following figure, a beam AB of length L is loaded with uniformly distributed load and rate of loading is w (N/m). Total uniformly distributed load, P = w*L Uniformly varying load Uniformly varying load is the load which will be distributed over the length of the beam in such a way that rate of loading will not be uniform but also vary from point to point throughout the distribution length of the beam. Uniformly varying load is also termed as triangular load. Let us see the following figure, a beam AB of length L is loaded with uniformly varying load. We can see from figure that load is zero at one end and increases uniformly to the other end. During determination of the total load, we will determine the area of the triangle and the result i.e. area of the triangle will be total load and this total load will be assumed to act at the C.G of the triangle. Total load, P = w*L/2 BENDING MOMENT AND SHEAR FORCE Bending moment at a section is defined as the algebraic sum of the moments about the section of all the forces (including the reaction) acting on the beam, either to the left or to the right of the section. Shear force at a section in a beam is defined as the algebraic sum of all the forces including the reactions acting normal to the axis of the beam either to the left or to the right of the section. Shear And Moment Diagrams of Simply Supported Beams Due To Different Loads 1. Simply Supported Beam with Uniformly Distributed Load Shear Force and Bending Moment Diagram Formulas for finding moments and reactions 2. Simply Supported Beam with Uniformly Distributed Load at both ends Shear Force and Bending Moment Diagram Formulas for finding moments and reactions 3. Simply Supported Beam with Uniformly Distributed Load at its mid span Shear Force and Bending Moment Diagram Formulas for finding moments and reactions 4. Simply Supported with Uniformly distributed Load at the left support Shear Force and Bending Moment Diagram Formulas for finding moments and reactions 5. Simply supported Beam having UVL along its span Shear Force and Bending Moment Diagram , Formulas for finding moments and reactions 6. Simply supported beam having UVL from the midspan to both ends Shear Force and Bending Moment Diagram Formulas for calculating Moments and reactions Reference https://www.aboutcivil.org/simply-supported-UDL-beam-formulas-bending-moment- equations.html Shear and Moment Diagrams of Cantilever Beams Due To Different Loads 1. Cantilever Beam with Uniformly Distributed Load Shear Force and Bending Moment Diagram Formulas for finding Shear Shear force at section XX FX = w*x Shear force at free end At point B, x=0 FB = 0 Similarly, Shear force at fixed end at point A, x=L FA = w*L FA = W Where, W = w*L Formulas for finding Moment Bending moment at section XX MX = - (Total uniformly distributed load) x (distance between section XX and point of action of total uniformly distributed load) MX = - (w*x) * (x/2) MX = - w*x2/2 Bending moment at free end at B, value of distance x = 0 MB= 0 Bending moment at fixed end at A, value of distance x = L MB= - w.L2/2 MB= - W.L/2 Where, W = w*L 2. Cantilever beam with point load Shear Force and Bending Moment Diagram Formulas for finding Shear Shear force at section XX FX = W Shear force at section XX is equal to the resultant force acting to the right portion of the section. Resultant force acting to the right portion of the section will be W and it will be positive. F=W Formulas for finding moments Bending moment at section XX MX = - W. x Bending moment at section XX Bending moment at free end at B, value of distance x = 0 MB= 0 Bending moment at fixed end at A, value of distance x = L MB= - W.L is negative. 2. CANTILEVER BEAM WITH carrying a gradually varying load or UVL ( uniform Varying load) Shear Force and Bending Moment Diagram Formulas for finding shear The rate of loading or intensity of the load at section XX and it can be written as (w/L)*x or w*x/L Shear force at section XX will be equal to the resultant force acting to the right portion of the section. Therefore, shear force at section XX FX = Area of triangle BCX FX = (w*x/L)*x/2 FX = w*x2/2L Shear force at free end i.e. at point B, x=0 FB = 0 Similarly, Shear force at fixed end at point A, x=L FA = w*L/2 Formulas for finding Moment Bending moment at section XX will be written as MX = - (Total load for length of x) * (distance between section XX and point of action of total load for length of x) MX = - (Total load for length of x) * (distance between section XX and C.G of the triangle ) MX = - (w*x2/2L) * (x/3) MX = - w*x3/6L Bending moment at section XX is negative. SIGN CONVENTION FOR SHEAR FORCE AND BENDING MOMENT DIAGRAM Sign conventions for shear force Let us consider that we have one beam AB and we have assumed one section XX as displayed in following figure. Now we will understand here that what sign conventions will be used here for shear force. Shear force at a section will be positive Shear force at a section will be considered as positive if resultant of the forces to the left of the section is in upward direction. Shear force at a section will be considered as positive if resultant of the forces to the right of the section is in downward direction. Shear force at a section will be negative Shear force at a section will be considered as negative if resultant of the forces to the left of the section is in downward direction. Shear force at a section will be considered as negative if resultant of the forces to the right of the section is in upward direction. Sign conventions for bending Let us consider that we have one beam AB and we have assumed one section XX as displayed in following figure. Now we will understand here that what sign conventions will be used here for bending moment. Bending moment at a section will be positive Bending moment at a section will be considered as positive if bending moment to the left of the section is in clockwise direction and bending moment to the right of the section is in anti- clockwise direction. Such type of bending moment will also termed as sagging bending moment. In other words, we can also say that bending moment at a section will be considered as positive if the bending moment at that section will tend to bend the beam in a curvature having concavity at the top. Bending moment at a section will be negative Bending moment at a section will be considered as negative if bending moment to the left of the section is in anti-clockwise direction and bending moment to the right of the section is in clockwise direction. Such type of bending moment will also termed as hogging bending moment. Similarly, we can also say that bending moment at a section will be considered as negative if the bending moment at that section will tend to bend the beam in a curvature having convexity at the top. Above figure indicates the condition of positive bending moment and negative bending moment. We can easily see that in case of positive bending moment, beam will be bent in a curvature with concavity at the top. We can also see that that in case of negative bending moment beam will be bent in a curvature with convexity at the top. What is structural analysis? When new structures are conceptualised there are a whole host of factors that need to be considered from the outset. A structure’s ‘ability to operate under applied loads’, or more simply, how it will cope under strain and stress, is a key one. Guided by mechanical theory and obeying physical laws, structural analysis sets out to predict the behaviour of a structure vs. load. Structural analysis is commonly used on structures that are judged on their ability to bear loads. As a practice, it aims to assess the integrity of a conceptual structure by computing stresses and potential deformations. In a structural analysis problem, the following properties may be given: Cross-sectional dimensions Number of reinforcement members Reinforcement diameter Location of the reinforcement Material mechanical properties Structural analysis is a hugely important step in a construction or review process. Without undertaking this work there will be no proof of structural soundness, meaning buildings would be constructed without key load bearing points scrutinised for effectiveness. It confirms the resistance, strength, and adequacy of a structure What is structural design? While structural analysis deals with the calculations and observations of load and stress, structural design decides the dimensions of the structural members by using those structural analysis findings. Once the above has been confirmed, projects can then move into the phase of structural design. The objective of structural design is to produce a structure capable of resisting all applied loads without failure. Structural engineers aim to find out the safest and most cost-effective structure specifications, accounting for the use of materials, geometry, technology, and structural member size – all whilst maintaining that the structure remains strong, stable, and rigid enough to carry loads of structure during its life period. Structural design requires a balanced mixture of imagination and critical thinking, combining a sound knowledge of basic mechanics, physics, material chemistry, and knowledge of modern design standards and codes of practice. What are the criteria in designing structures? Strength, beauty and economy But the ESSENTIAL requirement of any structure is that it must be capable of resisting a variety of loadings without changing its shape, other than by the tiny deformations due to straining of the material of which it is made. Before an engineer can design a structure, he must be able to determine all the forces acting on it at any one time. (i)Loads (ii)Reactions at points of support, as shown diagrammatically in Fig. 1.1. What are the types of loads that the structural designer should consider before designing the structure? Gravity Loads like dead load and live loads (moving and movable loads) Lateral loads like wind load, seismic load, hydrostatic pressure and soil pressure As the loads and reactions together form a system of forces in equilibrium, the resultant of the loads will be equal and opposite to, and act along the same line of action as the resultant of the support reactions. Loads may be subdivided into (a)Dead loads, due to the self-weight of the structure, and which are always present, (b) Live loads or imposed loads, which embrace all loads not included in (a), for example, weight of machinery, stores, vehicles, cranes, and people, as well as loading due to wind or water pressure. Unlike dead loads, imposed loads may, or may not, be present. Loading on Structures Arriving at the design loading involves considering quite a large number of factors. Structures are designed to withstand, without developing excessive stresses or deflections, loadings specified by Building Regulations and Codes of Practice or by the person or Authority for whom the structure is being erected. Example of live load / imposed load to the following structures. BRIDGE - the loading may be due to moving vehicles. At steel girder bridges, there are lists of forces which shall be considered when calculating the stresses developed and gives standard loadings for both highway and railway bridges. FLATS, CONDOMINIUM FLOORING - when you are to design the flooring, the loading may be due to people and furniture that the occupant will intend to put. The recommended loads should be considered in the design of buildings and other structures. Specifies the minimum imposed loads for floors according to the use to which the building is put whether floor is part of an office block and relatively lightly loaded, or a heavily loaded warehouse floor. DAM OR WATER TANK - water pressure In each case the engineer will have to estimate as accurately as he can the most severe form of loading to which the structure may be subjected. Live loads / imposed loads which is recommended should be considered in the design of buildings and other structures using standard specifications and codes of practice, but of course standard specifications and codes of practice, is not part of the law of the land, but are drawn up to simplify design and construction, eliminate waste of time and material, and yet ensure a safe structure. It only becomes obligatory to comply with them where a contract for the construction of a structure insists on it. What the designer must ensure is that his structure satisfies the local building by-laws and relevant regulations like ASEP Handbook of Structural Steel Shapes & Sections and NSCP - National Structural Code of the Philippines. In addition to imposed loads a structure must also carry its own weight. The dead load of a structure can only be roughly estimated in the first place, because the required size of the members is not known until the final design is arrived at. Because considerable judgement is needed to estimate the dead load of a structure in the early stages of design, there is a tendency to by-pass dead load calculations in questions of an academic nature, but this should not blind students to the importance of taking dead loads into account in any real design. To calculate the dead load of a building By calculating the volume of each member and multiplying it by the unit weight of the materials from which it is composed, an accurate dead load can be determined for each component. Importance of Proper Building Design Effective building design transcends mere aesthetics; it lays the groundwork for sustainable, safe, and harmonious environments. A well-designed building not only enhances the quality of life for its occupants but also contributes to the broader fabric of communities, fostering social interaction and economic vitality. Conversely, overlooking key aspects of design can lead to inefficiencies, safety hazards, and missed opportunities for innovation. Complexity and Considerations Involved However, embarking on a building design project entails navigating a labyrinth of complexities and considerations. From conceptualization to construction, architects, engineers, and stakeholders must grapple with diverse factors, including site constraints, budgetary limitations, regulatory frameworks, and user needs. Balancing these competing interests while striving for design excellence demands meticulous planning, interdisciplinary collaboration, and creative problem-solving. A Step-By-Step Guide for Structural Design of Building 1. Conceptual Design A structural design engineer will analyze the drawings created by the architects first to create a structural design of building plan. The engineer will analyze the various spaces in the residential, commercial, or industrial building to create structure engineering design. Conditions at the site are evaluated, including the soil report, the exposure category, the wind load, and the seismic load for the design of steel structures, and design of concrete structures. Engineers perform preliminary designs of architectural components after environmental factors have been established, including roof, wall, and floor plans according to architectural drawings for structural steel building design. Footings, slabs, load bearing walls, beams, and columns are designed after finding and coordinating mechanical, electrical, and plumbing clashes. 2. Load Analysis All potential live and dead loads experienced by a building over its lifetime should be analyzed by a structure engineer. Thus, you need to think about the varying loads based on the location of your structure. You can find the values of these loads by consulting the relevant structural design codes and references. There are a variety of loads acting on the building at the same time in the real world. It is important to assess the whole load for the design and drawing of steel structures. Part of performing a loads analysis is determining which load combinations are the worst for your structure. Autodesk Revit and Tekla, are two examples of BIM structural engineering software that can be set to generate all possible loads automatically. 3. Structural Analysis Structural engineers are the ones responsible for doing structural analysis on the structural members. Shear, bending moment, normal, and torsion stress diagrams, as well as responses and deformations or deflections caused by the various load combinations, are all included in the structural analysis. Software for Building Information Modeling (BIM) structural analysis, such as Autodesk Revit and Tekla, is used for both basic and advanced structural analysis. 4. System Design When the preliminary design of the structure has been finished, the structure engineer will shift their focus to the design of the system using a top-down approach. It is absolutely necessary to have a good grasp of the load path of the structure, with particular attention paid to the effects of gravity loads, lateral loads, and uplift on the various parts contained within the structure. When the engineer has a general concept of the load path of the structure, they will start initial designs of the various structural systems. 5. Element Detailing The specific design of structural elements is detailed with accurate dimensions. The structure engineer will perform detailed member analysis for certain spans, such as estimating the loads that will be placed on the roof. It is possible to significantly cut down on the cost of constructing structures by planning the details of steel connections carefully in advance. 6. Iterative Design and Drafting The iterative approach is utilized by structural engineers in order to fine-tune the structural design. Revit helps project teams uncover insights and drive outcomes with data by providing integrated analysis tools and interoperability support for a broad range of CAD and BIM applications. Because of the modification of the structural analysis model, it now incorporates load routes that are more accurate. 7. Construction Administration Structural contractors should ensure that the building structure design and construction are carried out as per the construction shop drawings. So, proper construction administration is required for a structurally sound building. In the later stages of the building process, the engineer is frequently asked to perform tasks such as review requests for information (RFI) and deferred submittal, acquire code approvals, or develop construction schedules. In addition to ensuring that the building is built in accordance with the structural design, engineers will also monitor the progress of construction on the client’s behalf. They will also frequently conduct site inspections to ensure that the building process is moving forward and that there are no errors in the installation of products. STEEL What Is Steel? Steel, in its simplest form, is iron metal that’s been alloyed with less than 2% carbon. However, many other elements can be added as well to create multiple grades of steel alloys with varying properties. Common alloying elements include chromium, manganese, and nickel. What Is the History of Steel? The history of steel begins with the history of iron. Iron’s discovery and rise to prominence in what we now call the Iron Age began in about the 12th century BCE (though it varies depending on geographical location). What Is Steel Made of? Fundamentally, steel is made of iron and carbon, but many other alloying elements also get added to create thousands of different grades of steel. How Are Steels Made? Steel is made via one of two main smelting processes — either a blast furnace or an electric arc furnace. What Are the Characteristics of Steel? 1. Strength: Steel is a high-strength material, particularly in tension, and can be used for structural loads. 2. Durability: Steel is highly durable with a potential lifespan of over 100 years. It does not swell or creep, instead remaining very rigid. 3. Versatility: Steel is an incredibly versatile material. Its many grades can be applied to thousands of uses. 4. Machinability: Most steel is easily machinable, depending on the grade. Some specific grades of steel (free-cutting steels) are highly machinable. 5. Weldability: Most grades of steel are easily weldable, although some need specialized welding procedures. 6. Corrosion Resistance: Steel can be alloyed with other elements such as chromium, nickel, and molybdenum to better resist corrosion. 7. Conductivity: Steel generally has lower thermal and electrical conductivity compared to other metals. It can be employed as a strong and heat-resistant shielding material. 8. Recycling: Steel can be completely recycled, and due to its value, a large portion (>60%) of steel globally is recycled. What Are the Applications of Steel? Steel is an incredibly versatile metal and has a wide variety of types and grades. Listed below are some of its applications: 1. Transportation Steel is used in transportation in several ways. Infrastructure such as bridges and rails are built with steel. It also forms the frames of train cars, motor vehicles, and large ships. It is the incredible strength of steel that makes it a good fit for these applications. 2. Construction Steel is used widely in construction, primarily in the form of structural, load-bearing members. This is because of its high strength and rigidity. 3. Manufacturing Manufacturing industries employ plenty of steel, particularly for machine components and tools. Its strength makes it a popular choice for heavy-duty applications. 4. Packaging Steel is used in cans for food and beverages. It can be ideal because it is durable and recyclable. 5. Medical Equipment Stainless steels are used extensively in medical equipment because they resist corrosion. They don’t naturally promote microbial growth and can easily be cleaned and even heat- sterilized. Surgical tools and medical instruments are commonly made from stainless steel. 6. Sports Equipment Steel is used for sports equipment such as bicycles and golf clubs. It appears in items that experience heavy loads, so its strength and durability are valuable. Why Use Steel? Steel is an incredibly versatile and durable material. Because so many variations are available, there’s a grade of steel to match nearly any application. Steel’s strength makes it ideal for large structures and demanding applications. With the correct grade or coating, it can even resist corrosion. Steel also has excellent dimensional stability. It does not swell, shrink, or easily warp or creep. Is Steel a Metal? Yes, steel is metal. The major component of steel is iron (which itself is a metallic element), and aside from carbon, the vast majority of alloying elements in steel grades are metals. Steel is a shiny, hard, malleable metal and has good thermal and electrical conductivity. Can Steel Rust? Yes, steel can rust. Rust occurs when the iron in steel reacts with oxygen in the air (in the presence of water) to form iron oxide. Stainless steels, however, have alloying elements such as chromium and nickel that prevent or severely inhibit iron oxide formation. Is Steel Stronger Than Iron? Yes, steel is stronger than iron due to the carbon contained within its molecular structure. Generally, steel’s toughness increases with the carbon content. Is Anything Harder Than Steel? Yes, several materials are harder than steel. Diamond is the hardest natural material known (though it is more brittle). Silicon carbide is a manufactured material that is harder than steel. Other metals such as tungsten are also harder than steel. What Is the Difference Between Steel and Metal? Steel is a type of metal but not all metals are steel. Steel’s properties differ from those of other metals. Depending on the grade of steel, it can be much stronger and may corrode or resist corrosion differently. What Is the Difference Between Steel and Aluminum? Steel is a metal alloy of the elements iron and carbon whereas aluminum is a single metal element. This results in very different properties between the two materials: steel is strong but heavy, and aluminum has lower strength but is much lighter. ANALYSIS OF INDETERMINATE STRUCTURAL by MOMENT DISTRIBUTION METHOD What is the difference between statically determinate and indeterminate? Statically determinate structures have reaction forces that can be analyzed using the equilibrium equations. By contrast, statically indeterminate structures have unknown reaction forces that cannot be analyzed using the equilibrium equations What are statically indeterminate structures? Statically indeterminate structures include beams and trusses that have one or more unknown reaction forces. Analyzing these structures depends upon the identification of the materials involved in their construction, as well as the use of analytical methods such as the force method (or flexibility method), the stiffness method (or matrix method), and the moment distribution method. When a body in a selected inertial frame of reference neither rotates nor moves in translational motion, we say the body is in static equilibrium in this frame of reference. Moment Distribution Method Moment distribution is based on the method of successive approximation developed by Hardy Cross (1885–1959) a structural engineering professor at the University of Illinois at Urbana Hardy Cross In 1930, Hardy Cross published a paper called "Analysis of Continuous Frames by Distributing Fixed-End Moments" in which he described the moment distribution method, commonly called the Hardy Cross Method. It changed the way engineers in the field performed structural analysis. The moment distribution method was used to determine the forces in statically indeterminate structures and allowed for engineers to safely design structures from the 1930s through the 1960s, until the development of computer oriented methods. His work includes developing simplified methods of analysis by means of converging approximations. The most significant of these, the fixed-end moment distribution for analysis of continuous structures, greatly simplified the way stresses could be calculated. This method was published in 1930. This method is applicable to all types of rigid frame analysis. Moment Distribution is an iterative method of solving an indeterminate Structure. Moment distribution is suitable for analysis of all types of indeterminate beams and rigid frames. It is also called a ‘relaxation method’ and it consists of successive approximations using a series of cycles, each converging towards final result. It is comparatively easier than slope deflection method. It involves solving number of simultaneous equations with several unknowns, but in this method does not involve any simultaneous equations. It is very easily remembered and extremely useful for checking computer output of highly indeterminate structures. It is widely used in the analysis of all types of indeterminate beams and rigid frames. The moment-distribution method was very popular among engineers. It is very simple and is being used even today for preliminary analysis of small structures. The primary concept used in this methods are, Fixed End Moments Relative or Beam Stiffness or Stiffness factor Distribution factor Carry over moment or Carry over factor Basic Concepts In moment-distribution method, counter-clockwise beam end moments are taken as positive.The counter-clockwise beam end moments produce clockwise moments on the joint. Note the sign convention: Anti-clockwise is positive Clockwise is negative Procedure for Analysis of Indeterminate Beams by the Moment Distribution Method 1. Calculate the fixed-end moments for members, assuming that the joints are clamped against rotation. 2. Calculate the distribution factor for each of the members connected at the joint 3. Calculate the unbalanced moment at each joint and distribute the same to the ends of members connected at that joint. 4. Carry over one-half of the distributed moment to the other ends of members. 5. Add or subtract these latter moments (moments obtained in steps three and four) to or from the original fixed-end moments. 6. Apply the determined end moments at the joints of the given structure. 7. Draw the free-body diagram of each span of the given beam, showing the loads and moments at the joints obtained by the moment distribution method. 8. Determine the support reactions for each span. 9. Compute and construct the shearing force and bending moment diagrams for each span. 10. Draw one bending moment and one shearing force diagram for the given beam by combining the diagrams in step 9. Assumptions in moment distribution method  All the members of the structures are assumed to be fixed and fixed end moments due to external loads are obtained.  All the hinged joints are released by applying an equal and opposite moment.  The joints are allowed to deflect (rotate) one after the other by releasing them successively.  The unbalanced moment at the joint is shared by the members connected at the joint when it is released.  The unbalanced moment at a joint is distributed in to the two spans with their distribution factor. FIXED END MOMENT  Moment develop at each end of a member when that member is ASSUMED FIXED or CLAMPED  All members of a given frame are initially assumed fixed at both ends.  The loads acting on these fixed beams produce fixed end moments at the ends.FEM are the moments exerted by the supports on the beam ends.These (non-existent) moments keep the rotations at the ends of each member zero. UNBALANCE MOMENT The difference between the summation of the fixed end moment and zero at joints DISTRIBUTED MOMENT The product of the unbalance moment at a joint and the distribution factor of the members meeting at that joint DISTRIBUTION FACTOR  Proportionate value of the stiffness of the members meeting at a joint  When several members meet at a joint and a moment is applied at the joint to produce rotation without translation of the members, the moment is distributed among all the members meeting at that joint proportionate to their stiffness. Distribution factor = Relative stiffness / Sum of relative stiffness at the joint If there is 3 members, Distribution factors = k1 / (k1+k2+k3), k2/ (k1+k2+k3), k3/ (k1+k2+k3) CARRY OVER MOMENT  The effect of the distributed moment of the other end of a member due to continuous reaction  The moment induced at the fixed end of the beam by the action of the moment applied at the other end.  Carry over moment: It is defined as the moment induced at the fixed end of the beam by the action of a moment applied at the other end, which is hinged.  Carry over moment is the same nature of the applied moment. Carry over factor (C.O) A moment applied at the hinged end B “carries over” to the fixed end „A‟, a moment equal to half the amount of applied moment and of the same rotational sense. C.O =0.5 RELATIVE OR BEAM STIFFNESS OR STIFFNESS FACTOR  Is the moment required to produce unit rotation at the simply supported end of a beam, the other end being rigid fixed  When a structural member of uniform section is subjected to a moment at one end, then the moment required so as to rotate that end to produce unit slope is called the stiffness of the member.  Stiffness is the member of force required to produce unit deflection.  It is also the moment required to produce unit rotation at a specified joint in a beam or a structure. It can be extended to denote the torque needed to produce unit twist.  It is the moment required to rotate the end while acting on it through a unit rotation, without translation of the far end being Beam is hinged or simply supported at both ends k = 3 EI / L Beam is hinged or simply supported at one end and fixed at other end k = 4 EI / L Stiffness of members in continuous beams and rigid frames Stiffness of all intermediate members k = 4 EI / L Stiffness of edge members, If edge support is fixed k = 4 EI / L If edge support is hinged or roller k = 3 EI / L Where: E = Young‟s modulus of the beam material I = Moment of inertia of the beam L = Beam‟s span length FIXED END MOMENTS Example Using the moment distribution method, determine the end moments and the reactions at the supports of the beam shown in Figure 12.6a. Draw the shearing force and the bending mo- ment diagrams. EI = constant. Fig. 12.6. Beam. Solution Fixed end moment. Stiffness factor. Distribution factor. Table 12.1. Distribution table. Shear force and bending moment diagrams. Example 12.2 Using the moment distribution method, determine the end moments and the reactions at the supports of the beam shown in Figure 12.7a. Draw the shearing force and the bending mo- ment diagrams. Fig. 12.7. Beam. Solution Fixed end moment. Stiffness factor. Distribution factor. Table 12.2. Distribution table. Shear force and bending moment diagrams. SUMMARY Moment distribution method of analysis of indeterminate structures: The moment distribution method of analysis is an approximate method of analysis. Its degree of accuracy is dependent on the number of iterations. In this method, it is assumed that all joints in a structure are tem- porarily locked or clamped and, thus, are prevented from possible rotation. Loads are applied to the members, and the moments developed at the member ends due to fixity are determined. Joints in the structure are then unlocked successively, and the unbalanced moment at each joint is distributed to members meeting at that joint. Carry over moments at members’ far ends are determined, and the process of balancing is continued until the desired level of accu- racy. Members’ end moments are determined by adding up the fixed-end moment, the dis- tributed moment, and the carry over moment. Once members’ end moments are determined, the structure becomes determinate.