CIVL 1112 Reinforced Concrete Beam - Example 3 1/5

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Clinton Horn
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1 CIVL Reinfored Conrete Beam - Example /5 Let s use the failure models to predit the ultimate strength-toweight (SWR) of one of our reinfored onrete eams from la Reinforing ars are denoted y the ar numer. The diameter and area of standard rears are shown elow. Consider a eam with the following harateristis: Conrete strength f = 4,000 psi Steel strength f y = 0,000 psi The tension reinforement will e rears The shear reinforement will e rears, U-shaped, spaing Use the minimum width to aommodate the reinforement d Bar Diameter () As ( ) Based on the hoie of reinforement we an ompute an estimate of and d rear diameter Minimum over rear diameter If we allow a minimum over under the rears were an estimate d Half of ar diameter Minimum over d (0.75 in) (0.75 in) (0.75 in).0 d 0.75 d d 4.5 rear diameter We now have values for, d, and A s d Asf y M Asfyd 0.59 f ' The A s for one rears is: A 0.44 s Compute the moment apaity Af s y M Asfyd 0.59 f ' 0.44 (0 ksi) (0 ksi) 4 ksi() M 84.5 kin tension.kips 4

2 CIVL Reinfored Conrete Beam - Example /5 Let s hek the shear model Afd v y shear f ' d s Area of a rears psi 0. 0, ,000 psi 4.5 Shear reinforement spaing 4,05l. 4.0kips Sine tension < shear therefore tension ontrols Let s hek the reinforement ratio A s d f ' 0.85 d f To ompute, first we need to estimate y as funtion of /d The height of the stress ox, a, is defined as a perentage of the depth to the neural axis f ' 4000 psi 0.85 f ' 4000 psi f ' ,000 4, ,000 Chek the reinforement ratio for the maximum steel allowed tension ompression (0.85)0.75 d fy f ' 4ksi ksi f ' 4ksi ksi (0.85)0.00 d fy Chek the reinforement ratio for the maximum steel allowed A 0.44 s 0.0 d (4.5) ompression Lets onsider ompression failure in over-reinfored onrete eam. steel when onrete reahes its ultimate strain d a 87,000 psi Let s ompute values for a and A f a 0.85f a s y ' ksi 0.854ksi.59

3 CIVL Reinfored Conrete Beam - Example /5 steel when onrete reahes its ultimate strain d 87,000 psi ,000 psi 4,0 psi.05 If f steel < f y then and 0.00 d As d a 4 87,000 ompression d psi steel when onrete reahes its ultimate strain d 87,000 psi ,000 psi 4,0 psi.05 If f steel < f y then and 0.00 d ompression ,000 psi kips The minimum fore ontrols tension shear ompression.kips 4.0kips 4.58kips 4.58kips An estimate of the weight of the eam an e made as: W Size of onrete eam ()()(0) 45l. 78 ft. ft. Additional weight of rears Unit weight of onrete Unit weight of steel (0.44 )(0) 490l. -45l. 78 ft. ft. 45.l..4l l. In summary, this reinfored onrete eam will fail in tension The ost of steel may e estimated as follows: kips 4,580l SWR l AL s 490 l. $700 ton Cost of steel, 78 ft. ton,000 l. ft. where A s is the ross-setional area of steel rears, L is the length of the steel rears, and 490 l./ft. is the unit weight of steel. This eam should fail in ompression!

4 CIVL Reinfored Conrete Beam - Example 4/5 For example, if one rear in plaed in the eam the steel ost is estimated as: Consider the following mix for a yd. of onrete developed using the ACI mix design proedure. Bar Diameter () As ( ) Cost of steel (0.44 )(0) l. $700 ton 490,78 ft. ft. ton,000 l. Component Water Cement Coarse aggregate Fine aggregate Amount (l) 5 55,4,4 $. The ost of the onrete required for a y y 0 eam is estimated as:.0()0 55 l. $ ton Cost of ement,78 ft. 7 ft. ton,000 l. $0.7.0()0,4l. $8 ton Cost of oarse aggregate,78 7.,000 l. ft. ft ton $0.7 The ost of the onrete required for a y y 0 eam is estimated as:.0()0,4l. $0 ton Cost of fine aggregate,78 7.,000 l. ft. ft ton $0.08 The ost onrete is estimated as: $0. The ost reinfored onrete eam is estimated as: $.9 The ost adjustment for the reinfored onrete eam is : If the unadjusted SWR for a eam is 04 and the ost is $.9, then the ost adjusted SWR is: If ost < $.00 then: Cost Fator = If ost > $.00 then: SWR Adjusted 04 Cost Fator $.00 Cost

5 CIVL Reinfored Conrete Beam - Example 5/5 Questions?

Example 24.3 Flexural Strength of Prestressed Member Using Approximate Value for f ps

Example 24.3 Flexural Strength of Prestressed Member Using Approximate Value for f ps Calulate the nominal moment strength of the prestressed member shown. f = 5000 psi f pu = 270,000 psi (low-relaxation