The stresses in framed structures; Including the strength of materials and theory of flexure - Softcover
Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...At Both Ends--ConStant Cross Sections--With Two Equal And SymMetrically Placed Loads.--Let the beam, Fig. 180, support two weights P, P, placed at equal distances z from each end. The reaction at each support is then P, and the greatest moment is evidently at the centre and equal to Pt. For change of shape, we have, from (VIII.),-Pr dx dx If the loads are uniformly distributed, instead of being concentrated as shown in Fig. 181, we F,B-181 can put pdz in the place of P. Equation (22) then becomes If we integrate this between the limits z, and „ we have for the deflection at the centre, (23) J=/4(V-0-6/'(V-«.') When the load covers the whole beam, z, = l, and 2, = o, and 384/' as already found. Case 8.--Beam Supported At One End And Fixed At The Other--Constant CrossSection--Concentrated Load.--Let the beam be fixed horizontally at the right end, Fig. 182. At this end, then, we have not only a vertical reaction /?„ but R Fig.rsa also a negative moment M, which causes the beam to "f be horizontal. At the left end we have only the re-/ action Hr Let the weight P be distant from the left j end by a distance s,, and from the right end by a dis-1 tance sv Then from (VIII.), taking „r from the fixed end, When x = o, in the second equation is zero, and hence C, = o. When x = za, is the same in both. Hence Cl =. Inserting these values of C, and C,, and integrating again, we have If we put the value of-j-in (24a) equal to zero, and insert the values of C,, C,, and JPlt we have for the point at which the deflection is a maximum, 2/2,(2/--2,),,v when x „ = 'v (25) 2A + 2,(2/--2,) When.v = 2, in these equations the maximum deflection will be at the load and will be the greatest possible. Placing therefore x = 2, we obtain from both thes...
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