Theory of Structure

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New York, 1918 - Structural analysis (Engineering) - 584 pages
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give the books like stability and determinate of structures also live load and dead load structures

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Page 95 - ... moment. The balancing moment' which B exerts on A is called the moment of resistance of the beam at that section. The statical conditions of equilibrium show that the moment of resistance and the bending moment are numerically equal.
Page 81 - Theorem (2). — The sum of the moments of inertia of any plane figure about two perpendicular axes in its plane is equal to the moment of inertia of the figure about an axis perpendicular to its plane passing through the intersection of the other two axes. Or, if...
Page 80 - ... or k is that value of y at which, if the area A were concentrated, the moment of inertia would be the same as that of the actual figure. Two simple theorems are very useful in calculating moments of inertia of plane figures made up of a combination of a number of parts of simple figures such as rectangles and circles. Theorem (1). — The moment of inertia of any plane area about any axis in its plane exceeds that about a parallel line through its centre of gravity (or centroid) by an amount...
Page 121 - The total moment of resistance of the horizontal forces across the section is equal to the algebraic sum of the moments of the external forces to either side of the section, /'.#. to the bending moment M.
Page 9 - Direct stress produces a strain in its own direction and an opposite kind of strain in every direction perpendicular to its own. Thus a tie-bar under tensile stress extends longitudinally and contracts laterally. Within the elastic limits the ratio lateral strain longitudinal strain generally denoted by , is a constant for a given material. The value ni of m is usually from 3 to 4, the ratio T being about \ for many metals.
Page 118 - Theory of Simple Bending. — It may be well to recall the assumptions made in the above theory of " simple bending," under the conditions stated — (1) That plane transverse sections remain plane and normal after bending. (2) That the material is homogeneous, isotropic, and obeys Hooke's law, and the limits of elasticity are not exceeded. (3) That every layer of material is free to expand or contract longitudinally and laterally under stress, as if separate from other layers. Otherwise, E in the...
Page 204 - EXAMPLE i. — A cantilever carries a concentrated load W at ; of its length from the fixed end, and is propped at the free end to the level of the fixed end. Find what proportion of the load is carried on the prop. Let W be the load, and P the pressure on the prop. Then 1VP_lWgr_ WQP 3 El ~3 El '"'• 2EI IP = wfcjL + _) = EXAMPLE 2.
Page 297 - Using the values from Table II. in the Appendix without the plates, from (2), the moment of inertia about the central axis parallel to the plates is (2 x 190-7) = 381-4 (inches)4 and for the two plates add Jj x 14(13...
Page 67 - P a line (BO) drawn across the space B parallel to bo to meet the line of action of BC in Q, and from Q a line is drawn across the space C parallel to oc to meet CD in R, and this process is continued until finally a line EO is drawn from the intersection S parallel to oe across the space E to meet the line AO in T. Then T is a point in the line of action of the resultant, the direction of which is given by ae in the vector diagram. Hence the equilibrant EA or the resultant AE is completely determined....
Page 95 - Shearing Force. — The resultant vertical force exerted by B on A is then equal to the algebraic sum of the vertical forces on either side of the plane of section X ; the action of A on B is equal and opposite. This total vertical component is the shearing force on the section in question. (3) If the distances of...

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