Strength of Materials book. Read reviews from world's largest community for readers. This is a comprehensive guide for Mechanics Of Materials in the subject of Mechanical Engineering. A Textbook of Strength Of Materials Mechanics of Solids By Dr. R.K. Tags: Mechanics Of Materials by B C Punmia Ashok Kumar Jain And Arun Kumar Jain Mechanical Engineering Mechanical. Departmentof Civil Engineering 1 Code No. Subject Name Credit CE CE CE CE CE CE CE CE CE CE CE CE
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Strength Of Materials Standard Books – PDF Free Download Strength Of MECHANICS OF MATERIALS BY B.C. PUNMIA, ASHOK KUMAR JAIN, ARUN. Unit1 From Mechanics of Materials by b c Punmia - Download as PDF File .pdf), Text File .txt) or read online. Unit1 From Mechanics of Materials by b c. Mechanics of materials by Bc Punia - Ebook download as PDF File .pdf), Text File .txt) or read book online. Mechanics of materials by bc punia.
Under the action of the pulls P, the two plates will press against the rivet in bearing, and contact stresses, called bearing stresses will be developed against the rivet. A free-body diagram of the rivet Fig. This free body diagram shows that there is a tendency to shear the rivet along cross section mn. From the free body diagram of the section mn of the rivet Fig.
In this particular case known as the case of single shear , the shear force V is equal to P. This shear force is, infact, the resultant of the shear stresses distributed over the cross-sectional area of the rivet, shown in Fig.
Under the action of pulls P, the bar and the clevis will press against the bolt in bearing, resulting in the development of bearing stresses against the bolt, as shown in Fig.
The bolt will have the tendency to get sheared across sections mini and m2n2. Fig 2.
These shear forces are in fact the resultants of the shear stresses distributed over the cross-sectional area of the bolt, at sections mini and m2n2 Fig. Such direct stresses arise in bolted, pinned, riveted, welded or glued joints, wherein the shear stresses are caused by a direct action of the force trying to act through the material. Shear stresses are also developed in an indirect manner when members are subjected to bending or torsion.
Bending stresses, torsional stresses and bearing stresses have been discussed in later chapters. Units of stress i SI system: Since normal stress p is obtained by dividing the axial force by the cross-sectional area, it has units of force per unit of area.
However, newton is such a small unit of stress that it becomes necessary to work with large multiples. Due to this, force is generally expressed in terms of kilo-newton and meganewton, where: N Similarly, the stress unit Pascal le.
Taking Also. This change in length is usually called deformation. If the axial force is tensile, the length of the bar is increased, while if the axial force is compressive, there is shortening of the length of the bar. This elongation or shortening , as the case may be, is the cumulative result of the stretching or compressing of the material throughout the length L of the bar. The deformation Le. In general, strain is the measure of the deformation caused due to external loading. If the bar is in tension, the resulting strain is known as tensile strain.
Similarly, the strain resulting from a compressive force is known as compressive strain. In general, strains associated with normal stresses are known as normal strains.
Similarly, - the strain associated with shear stress is known as shear strain. Since strain is the deformation per unit length, it is a dimensionless quantity. Thus, it has no units, and therefore, it is expressed as pure number. For example, if the deformation of a bar of 1. Thus, strain of the above example is 0.
Example 2. A prismatic bar has a cross-section of 25 mm x 50 mm and a length of 2 m. Under an axial tensile force of 90 kN, the measured elongation of the bar is 1. Compute the tensile stress and strain in the bar. The most common materials test is the tension test performed on a cylindrical specimen of the material. The loads arc measured on the main dial of the machine while the elongations arc measured with the help of extensometers. The cylindrical specimen has en- larged ends so that they can fit in the grips of the machine.
This ensures that failure will occur ir. In investigating the mechanical properties of the material beyond this limit, the relationship between the strain and the corresponding stress is usually represented graphically by a tensile test diagram or stress strain diagram.
A stress-strain diagram for a typical structural steel in tension is shown in Fig. The diagram begins with a straight line O to Ay in which the stress strain relationship is linear, ue. Point A marks the limit of proportionality beyond which the curve becomes slightly curved, until point B, the elastic limit of the material, is reached. Region AB is the non-linear region in which the stress is not proportional to strain.
However, upto the point By the removal of load would result in complete recovery by the specimen of its original dimensions. If the load is increased further, yielding takes place; point C is the point of sudden large extension, known as the yield point.
After the yield point stress is reached, the ductile extensions take place, the strains increasing at an accelerating rate as represented by C to D. In this region, there is no noticeable increase in the tensile force. The material becomes perfectly plastic in this region C to Z , which means that it can deform without an in- crease in the applied load.
For mild steel, the elongation in this region is 10 to 15 times the elon- gation that occurs between O and A.
If the load is further increased, the steel begins to strain harden. During strain hardening region, the material appears to regain some of its strength and offers more resistance, thus requiring increased tensile load for further deformation. This is so because the material undergoes changes in its atomic and crystalline structure in the strain hardening region. After D, with further increases in loads and extensions, the point E of the maximum load or ultimate stress commonly known as the ultimate strength is reached.
Up to the maximum load, the bar extends uniformly over its parallel length but. It is customary to base all the stress calculations on the original cross-sectional area of the specimen, and since the latter is not constant, the stresses so calculated arc known as nominal stresses. The nominal stress is less at rupture load than at the maximum load, as indicated by points F and E respectively. The diagram of real stresses Le. The breaking load divided by the reduced area of section Le.
The strains that occur from C to Z are 15 times more than the strains that occur from O to A, and further the strains from D to F are many times greater than those from C to D. Hence, in this diagram, the linear part of the diagram appears to be vertical, with the points A, B and C over lapping.
Stress-strain curves for other materials Fig. From these curves, we notice that with increasing carbon content, the curves approach the form characteristic of brittle materials such as cast iron, though the ultimate stress is many times greater. However, for copper, cast aluminium and high alloys, no clearly defined limit of proportionality, elastic limit or yield point are exhibited. Cast iron behaves like a brittle material which fails without any visible elongation or reduction in area.
The curve for rubber is linear upto very large strains in the vicinity of 0. Soft rubber usually continue to stretch enormously without failure, and after that if offers increasing resistance to the load with the result that the curve turns markedly upward prior to failure. Typical stress-strain curve for brittle material is shown in Fig.
Examples of brittle materials are concrete, stone, cast iron, glass, ceramic materials and many common metallic alloys. Limit of proportionality Limit of proportionality is the stress at which the stress-strain curve ceases to be a straight line; it is the stress at which extensions cease to be proportional to strain. Robert Hooke,s famous law "Ut tensio sic vis", Le. The proportional limit is important because all subsequent theory involving the behaviour of elastic bodies is based on stress-strain proportionality.
Elastic limit It is that point in the stress-strain curve upto which the material remains elastic, Le. Thus, elastic limit represents the maximum stress that may be developed during a simple tension test such that there is no permanent or residual deformation after the removal of the load. Its value can be approximately determined by loading and unloading the test specimen till permanent set is found on complete removal of the load.
This point is represented by point B in stress-strain curve of Fig. However, for many materials, elastic limit and proportional limit are almost numerically the same, and the terms are sometimes used synonymously. In cases such as in Fig. Elastic range This is the region of the stress-strain curve between the origin and the elastic limit. Thus in Fig. These deformations disappear on the removal of the load. Plastic range This is the region of the stress-strain curve between the elastic limit B and point of rupture F.
Thus, in Fig. These deformations are permanent deformations which do not disappear even after the removal of the load. The plastic range consists of three regions: Region bd and de taken together mark the uniformly distributed plastic deformation. Yield point Yield point is the point just beyond the elastic limit, at which the specimen undergoes an appreciable increase in length without further increase in the load.
The phenomenon of yielding is more peculiar to structural steel; other materials do not possess well defined yield point. Careful testing of more ductile materials like annealed low carbon steel indicates that there is, in reality, a slight load reduction giving two yield points C and C' Fig.
In a tensile test, it is usual to remove the extensometer from the specimen at this stage le. Yield strength The yield strength of a material is closely associated with the yield point. Yield strength is defined as the lowest stress at which extension of the test piece increases without further increase in load. It is indicated by careful testing of the specimen. Many maierials do not have well defined yield point. For such cases, yield strength is determined by off-set method.
As illustrated in Fig. Where there is no specific straight line portion the diagram being continuously curved , the 0. In both the cases, the intersection of the offset line with the curve i. At this highest point, con- centrated plastic deformation takes place, resulting in the for- mation of neck or waist in the specimen, resulting in decrease in the load.
For structural steel, it is some what lower than the ultimate strength. This is so because the rupture stress is computed by dividing the rupture load by the original cross-sectional area, while the actual area is very much less because of necking.
Although actual rupture strength is considerably higher than the ultimate strength, the ultimate strength is commonly taken as the maximum stress of the material. Proof stress Proof stress is the stress necessary to cause a non-proportional or permanent extension equal to a defined percentage say 0. Alternatively, proof stress can be expressed as the stress at which the stress-strain diagram departs by a specified percentage of the gauge length from the produced straight line of proportionality.
If a certain value for proof stress is specified for a material, and, after loading to that stress and then unloading, the permanent extension is less than the specified percentage of the gauge length, then the material is considered in respect of the minimum proof stress requirement. It should be clear! The proof stress for a maierial is determined Fig. The in- tersection of this line with the stress-strain curve represents the 0. Estimation of ductility of the material The study of stress-strain diagram indicates that from the yield point to the ultimate strength, the elongation is practically distributed uniformly over the length of the specimen.
This region of uniformly dis- tributed plastic deformation is typical of ductile material. An advantage of duc- tility is that visible distortions may occur if ihe loads become two large, thus ' providing an opportunity to take remedial measures before an actual frac- ture lakes place.
Also, ductile materials are capable of absorbing large amounts of energy prior to fracture. The presence of a pronounced yield point followed by large plastic strains is an important characteristic of mild steel that is some times used in practical design.
Other due- fig. Ductility of a material is estimated by two methods. Percentage elongation The percentage elongation is the percentage increase in the length of the gauge length. If Lo is the original gauge length and Lf the final length between the gauge marks, measured after fracture. Hence it is always essential to mention the gauge length over which percentage elongation is computed Percentage reduction in area or percentage contraction Ductility of the material can also be estimated in terms of percentage reduction in the area in the waist at fracture.
Gauge length: Barba,s law From the study of the tensile test diagram Fig.
It is found that the uniform extension, taking place during the clastic and the plastic range, is proportional to the gauge length, while the local extension is independent of the gauge length.
Due to this, it becomes essential to specify the gauge length in a tension test; otherwise, if the gauge length is increased, the effect of local extension would decrease the percentage elongation. Unvin verified that the local extension is proportional to the square root of the cross-sectional area.
He gave the following expression for the total extension Ar: Check your Email after Joining and Confirm your mail id to get updates alerts. Other Useful Links. Your Comments About This Post. Is our service is satisfied, Anything want to say?
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