Train: 6 Kips/Ft Each Track Including Impact

CE 572 Homework 7 Spring 2005

Due: April 4th, 2005

Name: ______

1. Shear(6)- It is proposed to build a new railway bridge across a river valley as a series of simply supported box girders each spanning 140 ft center to center of the bearings. The bearings are 24 in. long. As shown in the figure below, the post-tensioned box girder supports two railway tracks, two walkways, and a substantial quantity of ballast in addition to its own weight. The loadings are as follows:

Live loads: Train: 6 kips/ft each track including impact Walkway: 0.3 kips/ft each walkway Dead Loads: Superimposed ballast and hardware: 9.5 kips/ft Self-weight of box girder 19.7 kips/ft

A preliminary design has resulted in a choice of 18 tendons each containing twelve 0.6 in. diameter, 270 ksi low relaxation strands with the strands post-tensioned to an effective prestress level of 0.6fpu. Ten of the tendons are located at mid-depth of the bottom flange and are straight from end to end. Eight of the tendons are located in the webs of the girder and have parabolic profiles. At mid-span the centroid of the of these eight tendons is located 7 in. from the bottom face, while at the supports, the centroid of these eight tendons is 24 in. from the top face of the girder. Design the spacing of shear reinforcement required, in the form of two vertical layers of #5 Gr. 60 steel in each web, at the following sections: h/2 form the face of the support and ¼ of the span using the ACI 318-05 approach with Vci and Vcw. Repeat problem using Eq. (11-9) for Vc. Use a load factor of 1.6 for live loads and 1.2 for dead load with a ϕ factor of 0.75, and a simplified straight line factored shear envelope consisting of the maximum shear at the centerline of the support and at midspan. The design concrete compressive strength is 5000 psi. Tendons are 2 fully grouted after stressing. Additional data are: Ag = 18,540 in ,ybot = 99.6 in, and Ig = 68,330,480 in4. CE 572 Homework 7 Spring 2005

Due: April 4th, 2005

Name: ______

A design aid is provided below for parabolic tendon profile:

2. Losses (4 points) - The concrete beam cross section below spans 60 ft simply supported. It is prestressed with 14fully bonded - 0.5 in. diameter, Gr. 270 Low-Lax strands. Six of the strands are draped at the 1/3 point of the span to have zero eccentricity at the supports; the rest remain straight. The midspan eccentricity is 14 in. The prestressing prior to elastic shortening is estimated at 350 kips. Compute losses at midspan and express them as a percentage of the prestressing force prior to transfer. Use the lump sum estimate of separate losses presented in the PCI Handbook. The normal weight concrete compressive strength at transfer is 4000 psi and the 28-day design strength is 6000 psi. The sustained load consists of the self-weight of 546 plf and 2 4 additional dead load of 200 plf. Other design data are: Ag =524 in , Ig = 22,040 in , ybottom = 18.23 in, R.H. = 75%, V/S = 2.