DESIGN OF FIXED ENDED ARCHES BY THE ELASTIC THEORY 151 



stresses. Hence the steel of structures like these is never highly 

 stressed since the greatest stresses in the metal cannot exceed about 

 twenty times the greatest allowable concrete stresses; in this case 

 20x450=9,000 lbs. 



By substituting in equation (23), the greatest stresses of com- 

 pression and tension, without steel, are found in the concrete for the 

 different points of the rib. The results are given in pounds per 

 square inch in columns 24 and 25 of Table II. It is seen, therefore, 

 that tension occurs only at and near the springing points with a max- 

 imum of 189 pounds per square inch at Y and V. "With the excep- 

 tion of points 1 and 2, the maximum compression exceeds the 

 allowable value of 450 pounds per square inch at all points, the 

 greatest intensities being found at the springing points and at the 

 crown. Steel must therefore be introduced to reduce the compression 

 throughout the rib and to relieve the excessive tension at the spring- 

 ing joints. 



The arch, 89 feet in total width, is built of ribs 8 feet wide 

 separated by false ribs or coiffures. It is proposed to insert three 

 steel ribs in each 8-foot concrete rib, making the steel rib spacing 

 32 inches center to center. Across the crown of the arch from point 

 1 to point 18 the steel flanges will be 8' 'x^' ' bars located as shown in 

 figure 1. From points 1 and 18 respectively, to the springing points 

 and continued well into the abutments, the three steel ribs will have 

 flanges like that shown in figure 2. For figure 1, 20A2=8.75 square 

 inches; for figure 2, 20A2 = 38.8 square inches. 



By substituting in equations (21) and (22), the greatest stresses 

 of compression and tension, with steel are found, the results being 

 given in columns 26 and 27 of Table II. The greatest compression, 

 therefore, now occurs at the crown, sections 9 and 10, while the great- 

 est tension occurs at the springing joints, V and V. The greatest 

 compression in the arch concrete is 428 pounds and the greatest tension 

 55 pounds per square inch. In columns 26 and 27, the positive sign 

 indicates tension, the negative, compression. An examination of 

 column 19 shows that the shears are very small; the greatest shearing 

 intensity being about 19 pounds per square inch (neglecting the steel) 

 and found at the springing joints. 



