mechanics of solids power-point presentation

Subject: Mechanics of Solids-I CE-104

Instructor: Prof. Dr. Akhtar Naeem Lecturer: Engr. Muhammad Nissar

Instructor: Prof: Dr.Akhtar Naeem Lecturer: Engr Muhammad

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N-W.F.P University of Engineering & Technology Peshawar

Lecture # 1: Basic Concepts

Basic Concepts

• What is Civil Engineering ?1) Civil 2) Engg

• What is Strength of Materials or Mechanics of Solids?

1) Strength of Material2) Mechanics of Solids


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IntroductionIntroduction•Mechanics of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading.

•This field of study is known by several names, including "Strength of materials" and "mechanics of deformable bodies.".


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40 ft span

IntroductionIntroduction


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• Suspension bridges are good example of structures that carry these stresses. The weight of the vehicle is carried by the bridge deck and passes the force to the stringers (vertical cables), which in turn, supported by the main suspension cables. The suspension cables then transferred the force into bridge towers.


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IntroductionIntroduction•The solid bodies considered include axially loaded members, shafts in torsion, thin shells, beams, and columns, as well as structures that are assemblies of these components.


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IntroductionIntroduction Axial Force. Shear Force Transverse Force

• Torsion


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Deflection due to Load

P

• Usually the objectives of our analysis will be the determination of the stresses, strains, and deflections produced by the loads.


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IntroductionIntroduction•Theoretical analyses and experimental results have equally important roles in the study of mechanics of materials.

•These properties are available to us only after suitable experiments have been carried out in the laboratory.

Also, because many practical problems of great importance in engineering cannot be handled efficiently by theoretical means, experimental measurements become a necessity.

• Theoretical Analysis (Equilibrium and Compatibility Equations).

• Experimental Analysis (Constitutive)


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500 N 5000 N

Steel Bar

Equilibrium Equation

Simply Supported Beam


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Compatibility Problems


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IntroductionIntroductionConstitutive Problems


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IntroductionIntroductionTypes of Failure:


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IntroductionIntroductionFailure Pattern:


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Beam with Reinforcement

Reinforcement

Beam

Longitudinal Section

Composite Section


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Normal Stress Formula Normal Stress Formula DerivationDerivation

The fundamental concepts of stress can be illustrated by considering a prismatic bar that is loaded by axial forces P at the ends, as shown in Figure 1 prismatic bar having constant cross section throughout its length. The axial forces produce a uniform stretching of the bar; hence, the bar is said to be in tension.


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Area 1Area 2

Area 1>Area 2

Non prismatic X-Section

Prismatic and Non Prismatic Bar


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Prismatic X-Section


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• To investigate the internal stresses produced in the bar by the axial forces, we make an imaginary cut at section aa (Figure 1).

• The intensity of force (that is, the force per unit area) is called the stress and is commonly denoted by the Greek letter s (sigma).


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• The intensity of force (that is, the force per unit area) is called the stress and is commonly denoted by the Greek letter s (sigma).

• Assuming that the stress has a uniform distribution over the cross section (see Figure 1), we can readily see that its resultant is equal to the intensity s times the cross-sectional area A of the bar.


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• Furthermore, from the equilibrium (balancing of forces) of the body shown in Figure 1, it is also evident that this resultant must be equal in magnitude and opposite in direction to the applied load P. Hence, we obtain

A

P


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• When a sign convention for normal stresses is required, it is customary to define tensile stresses as positive (+) and compressive stresses as negative (-).


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Tensile Normal StressTensile Normal Force

mechanics of solids power-point presentation

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