248 BRIDGE ABUTMENTS AND PIERS. CHAP. VI. 



M = i(5.74 + 4.690)4 X 2.1 X 12 

 = 525,672 in-lb. 



The tension on the concrete at the bottom of the footing will be 



_ M-c _ M-d _ 525,672 X 27 



/ 2! 157,464 



= 92 Ib. per sq. in. 



The footing is safe, but f in. D rods were placed 18 in. centers and 3 in. from the bottom of 

 the foundation. 



Case (b). The solution is the same as for (a) except that the live load from the girder = 9,980 

 Ib., and the surcharge load 1-2-5-6 = Wa = 6,620 Ib. were omitted. The wall is safe for over- 

 turning. The factor of safety against sliding is from equation (27) Chapter V, /, = 41,500 

 X 0.57/14,700 = 1.6, which is safe. The pressure on the foundation is safe. 



The back wall was placed after the bridge seats were finished. To bond the back wall to 

 the abutment, \ in. D rods 4 ft. long, spaced 18 in. centers, were placed in two rows 3 in. from 

 the back and front face, one-half of the length of the rod being imbedded in the main wall. 



PRINCIPLES OF DESIGN. To prevent tension on the back side of the footing and to 

 make sure that the maximum compression on the front side of the footing shall not be greater 

 than twice the average pressure, the resultant of the thrust of the filling, the weight of the masonry, 

 the weight of the bridge and the live load must strike within the middle third of the base. Where 

 the abutment rests on rock or solid material where settlement will not occur, it will not be serious 

 if the resultant strikes a little outside of the middle third, providing the allowable pressure on the 

 foundation is not exceeded. When the abutment is on compressible material where settlement 

 will take place, the resultant of the pressures should strike at or back of the center of the base, so 

 that the abutment will not tip forward in settling. It is standard practice to use piles in the 

 foundation for abutments resting on compressible soil. 



For the design of wing walls see the design of Retaining Walls, Chapter V. 



In addition to the requirements for stability abutments should satisfy the following additional 

 requirements. 



(a) The abutment should protect the bank from scour, (b) The abutment should prevent 

 the embankment drainage from washing away the bank, (c) The abutment should be easily 

 drained. 



Empirical Design. A common rule is to make the minimum thickness of the main part of 

 the abutment not less than -fa the height above any section; and project the footings on each 

 side as may be required. Empirical methods of design often give unsatisfactory results and are 

 not to be recommended. 



DESIGN OF BRIDGE PIERS. Bridge piers must be designed (i) for the total vertical 

 load due to the dead load of the span and the live load on the span, and the weight of the pier; 

 (2) for wind pressure on the pier and the bridge; (3) to withstand floating drift and ice; and (4) 

 to take the longitudinal thrust due to stopping a car or train on the bridge, and due to temperature 

 when the rollers do not move freely. The wind pressures are calculated as specified in speci- 

 fications for bridges, and are assumed to act in the vertical line of the center of the pier; on the 

 top chord of the truss; the bottom chord of the truss; 6 or 7 feet above the base of the rail; and at 

 the center of gravity of the exposed part of the pier. The total wind moment is then calculated 

 about the leeward edge of the base of the pier, and the maximum stresses on the foundation due 

 to direct load and wind are calculated in the same manner as the calculation of the pressures of 

 abutments. 



The effect of the current of the stream and of floating ice and drift are difficult to calculate. 

 The pressure of a flowing stream on an obstruction is given by the formula 



F 2 

 P = m-w-a- 



