Essentials in the Theory of Framed Structures

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McGraw-Hill Book Company, Incorporated, 1922 - Structural analysis (Engineering) - 330 pages
 

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Page 83 - The manner of working out the stresses of such trusses by the analytical method, will be given below. In all statically determined structures, there are three equations which must be true in order that the structure shall remain in equilibrium : 1. The algebraic sum of the moments, about any point, of all the external forces acting on the structure, must be zero. If this is not the case, there will be a rotation of the structure about this point. 2. The algebraic sum of all the external vertical...
Page 177 - Fig. 54. are twisted when it is transmitting power; and by the twisting moment at any cross-section .of .the shaft is meant the algebraic sum of the moments of all the forces acting on the shaft on either *NoTE.
Page 218 - E is the modulus of elasticity in pounds per square inch, and 7 is the moment of inertia of the constant cross-section of the beam about the neutral axis, measured in inches4.
Page 8 - If a moving point possess simultaneously velocities which are represented in magnitude and direction by the two sides of a parallelogram drawn from a point, they are equivalent to a velocity which is represented in magnitude and direction by the diagonal of the parallelogram passing through the point.
Page 8 - The Parallelogram of Forces. — If two forces acting at a point be represented in magnitude and direction by the adjacent sides of a parallelogram, the resultant...
Page 83 - In order to evaluate the shear at any section, the following definition may be formulated: The Shear at Any Right Section of a Beam is the Algebraic Sum of All the Transverse Forces on One Side of the Section.
Page 92 - F2 = kX (1) where X and Y are variables and k is a constant. The...
Page 11 - Now the product of a force into its perpendicular distance from a point is called the moment of the force about the point; the product is taken with the positive or negative sign according as the force tends to turn counterclockwise or clockwise about the point.
Page 132 - The bending moment at any normal section of a beam is the algebraic sum of the moments of all the forces acting on one side (either side) of the section, taken about the center of gravity of the section as an axis.
Page 9 - The law of the triangle of forces may be stated as follows: Three concurrent coplanar forces in equilibrium may be represented in magnitude, direction and sense by the three sides of a triangle taken in continuous order. Any one of the three forces may be made to represent the resultant of the other two by reversing its sense. 8. Magnitude-direction Diagram.— When the resultant of several concurrent forces is required, the resultant of any two may be found from the force triangle; and this resultant...

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