Solutions for certain rectangular slabs continuous over flexible ...

More documents

Recommendations

Info

ILLINOIS ENGINEERING EXPERIMENT STATION due to loads distributed along the lines y = b/2 and y = -b/2, respectively. The boundary condition, from which k is to be determined, is q=EEi = V'4 - V d= L I =b/2+ Ldx] yb/2-e = - 2N - (2w') L y-y b/2+e where q is the load on the beam, positive downward, El and I, are the modulus of elasticity and moment of inertia of the beam, respectively, z is the downward deflection of either beam, and e is an infinitesimally small positive distance. From this boundary condition one finds ab 1 +-- 2 k = (52) (1+ab)e 2 + 1+- en 2 The deflection of each beam is SPa 2 1 4 z = w = - - k- sin au sin ax, (53) vy=b/2 21rN ,,...- n nnrH 1 and the bending moment in each beam is d 2 z 2Pa 1 Mbeam = -EiI 1 - = - ,.- k sin au sin ax. (54) dX 2 r 2 1,23- n2 If M( ) ) and M( 0) designate the bending moments due to the load P on the infinitely long slab without cross beams, the resultant bending moments under the load are - a Mj =MF -- -- (1+p)+(1-p)- sin 2 a, M -u M -) u 7 1,2,3. n 2J S(55) Sh Pr ke r abe M, =M -- - (1+U) -(l-M)- sin 2 au, -u r-u i,- n 2 -0 vy-0 the terms given by the series being the effects of the cross beams.
SOLUTIONS FOR CERTAIN RECTANGULAR SLABS The solution may be modified for rigid beams by letting Hi = oo. This special case is treated more fully in Section 39 for a central position of the load on the panel. 11. The Infinitely Long Slab Having Three Uniformly Spaced Flexible Cross Beams and Supporting a Concentrated Load Over the Center Beam.-The slab is shown in Fig. 13. Using the same method FIG. 13 as was used in the previous examples with flexible beams, one finds the deflection of the slab for b > y > 0 to be 2Pa 3 an wi = - - (b. cosh ay - sinh ay 7 4 E, 1 1,, n 4 where + ay cosh ay - Cn ay sinh ay) sin au sin ax (56) an - 4 --- 4 nirHj n SbrH bn = nirH 2 [1 - (1 + 2ab + 2a 2 b 2 ) e- 2 "b + 4 n 7 rH 2 [1 + (1 + 2ab) e- 2 ab] + 4 nrH 2 (1 - e- 2 ab) + 4 n7rH 2 [1 + (1 + 2ab) e - 2 ab] + 4 . (57)
Page 1: H ILL I N 0 I S UNIVERSITY OF ILLIN
Page 4 and 5: 3000-5-38-14400 pEssF II
Page 6 and 7: CONTENTS (CONTINUED) V. THE RECTANG
Page 8 and 9: CONTENTS (CONCLUDED) PAGE 36. Recta
Page 11 and 12: SOLUTIONS FOR CERTAIN RECTANGULAR S
Page 29 and 30: - SOLUTIONS FOR CERTAIN RECTANGULAR
Page 41: SOLUTIONS FOR CERTAIN RECTANGULAR S
Page 93 and 94:
SOLUTIONS FOR CERTAIN RECTANGULAR S
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
RECENT PUBLICATIONS OF THE ENGINEER
show all

Solutions for certain rectangular slabs continuous over flexible ...

Create successful ePaper yourself

Delete template?

Save as template?