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Chapter IV Torsion
1. Torsion of Prismatic Bars
a) Circular Cross Sections
In this chapter we will consider the deformation and stresses in prismatic
members subject to torque. First consider a torsional moment

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2. Torsion of Thin-Walled Cross Sections
a) Open Thin-Walled Cross Sections
Now consider open, thin-walled cross section composed of several
rectangular subsections. The distribution of the shear flow due to a t

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4. Governing Differential Equations
At this point, we will take some time to present derivations of the six
equations of static equilibrium. These equations are all based on the principle
that objects at rest ar

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Chapter III. Shear Stresses and Shear Centers
a) Shear Stresses due to Beam Bending
When a beam is bent by transverse loads (let us assume a symmetrical
bending temporarily), usually both a bending moment and a

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3. Cross Sectional Properties of Composite Beams
a) Effective Stiffness and Effective Flexural Rigidities
Let the effective axial stiffness be defined by:
EA = EdA
(1.24)
Similarly, let the effective flexural ri

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2. Virtual Work Methods
a) Equilibrium
In the application of virtual work methods, we often imagine
displacements to occur with actual loads acting on a structure. These
displacements are called virtual displace

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Chapter II Energy Methods
1. Work and Energy
a) Definition of Work
As it is known, energy is equal to the capacity to do work. The work done
on a particle is equal to the displacement times the component of the

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2. Equilibrium and Deflections of Straight Beams
a) Beam Deformation Geometry
We now consider a structural member, the beam under unsymmetrical
bending and axial extension, wherein we will develop the governing

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3. Castiglianos Theorems
a) Castiglianos First Theorem
Application of the virtual work method includes the use of Castiglianos
theorem. We write the strain energy of the structure in terms of generalized
displac

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Chapter I Unsymmetrical Beam Bending and Extension
1. Basic Concepts and Definitions
a) Displacements
The displacements experienced by a ship or offshore structure are due to
external forces. In order to understa