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T-BEAMS WITH TENSION REINFORCEMENT 111. Flexure Formulas.—In a rectangular reinforced concrete beam, in which the steel carries all the tension, the area of concrete below the neutral axis does not affect the resisting moment of the beam. The office of this concrete is to hold the steel in place and carry the shear, thus connecting the steel with the compression area of concrete.

In a '1'-beam, the flange carrying the compression is connected with a narrow web which holds the steel, as shown in Fig. 52. When the neutral axis is in the flange, such a beam may be computed by the formula_ and tables used for a rectangular beam, using the width of the flange, b, as the width of the beam.

When the neutral axis is below the bottom of the flange of the T-beam, the compression area is less than that of the rectangular beam, and special formulas are necessary. Fig. .52 represents a beam of this kind. The amount of compression on the web is usually very small and may be neglected without material thus greatly simplifying the formulas.

The same notation will be employed as in the rectangular beam, letting b =width of flange; b'= width of web; t =thichmess of flange.

The position of the neutral axis in terms of the unit stresses may be found as in the rectangular beam, giving (22) f k ' and (23) The average unit compression on the flange is the half sum of the compressions at the top and bottom of the flange, or 1kd—t kd .

The total compression on the concrete is C= f ` 2kd (24)This is the equal to the total tension on the steel, T =f,A=f,pbd (25) From the equality of (24) and (25) we find (2k—t d) t 26p_ 2n(1-k) d' (26) and (t!d)2 (27) pn+t!cl • The distance of the centroid of compression from the upper face of the beam is t 2k—t: d therefore jd=d-3k.-2t'd t (28) 3 The resisting moment of the beam is 11I = Tjcl = = (29) or 31= Cjd = f, 3k • btjd. (30) Examples.—The use of these formulas in the solution of problems arising in the design or investigation of T-beams are illustrated in the following examples: 9. A T-beam has the following dimensions, b=48 inches, t=4

inches, d=22 inches, inches. The steel reinforcement con sists of six .-,-inch round rods. If the safe unit stresses of steel and concrete are 15,000 and 600 lb., respectively, and n=15, what is the safe resisting moment of the beam? Solution.—From Table X, A =2.65 and formula (27) gives _ . 0025X 15-} Using (28) we find 2X.247— ' From (22), 15(1—.247) =-l5.7. If f,= 600 X45.7 =27,420 lb. This is greater than the safe unit stress on steel, and the safe moment will be that which causes a stress of 15,000 lbs., on the steel, or from (29), M = 2.65 X 15000X 20.39 = 810000 in.-11).

10. The flange of the T-beam is 26 inches wide and 4 inches thick. The beam is to carry a bending moment of 520,000 in.-lb. The safe unit stresses for concrete and steel are 600 and 16,000 lb. in." respectively. What area of steel and depth of beans are needed.

(23) l:'XGO0 —.360. We must now X 600 find d by assuming values and testing their suitability. Try d= 18; from (28) we have ) 2X.360— 3 (9) gives C = /,' jd = 520000/16.3 = 31900.

From (24) fc= C 2kd — t lb. in.'- This is a safe value, but 2kd a less depth will answer. Trying 15 inches, we find C=38,000 pounds, and f =580 lb., in."; 15 inches is, therefore, approximately the minimum value for d. For this value of d, Formula (25) gives, Width of without lateral reinforcement in the flanges should have a width of flange not more than three times the width of web, b = 3b'. When the flange is reinforced at right angles to the length of beam, as in a slab floor with T-beams support, experi ence indicates that the flange may overhang the web on each side to a distance equal to five or six times the thickness of flange, and still act satisfactorily as compression area for the beam. If the width of flange be greater than this, the extra width is of little value and should not be considered in estimating the strength of the beam.

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