DESIGN OP FIXED ENDED ARCHES BY THE ELASTIC THEORY 149 



arch ring sections V and V. Thus in the force diagram, for section 

 V, DL is the normal thrust and LB the shear. 



The normal thrust, the shear and the resultant thrust for each 

 point of the arch rib are found respectively in columns 18, 19 and 

 20. 



To find these quantities for any point of the rib other than the 

 springing points a slight modification in the above procedure is nec- 

 essary. For example, take the point F; — draw the ray DN parallel 

 to the chord EG of the true frame and decompose it into components 

 DM and MN parallel and perpendicular respectively to the tangent 

 to the neutral curve of the rib at the point 18. Then DN is the 

 resultant and DM the normal thrust while MN is the shear at section 

 18. The same method is used for all other points, 17 to 1 inclusive. 



We now have completely obtained the stresses in the rib, columns 

 17, 18, 19 and 20 giving everything. It is next in order to inquire 

 whether the assumed rib is too strong or too weak. 



Column 23 gives the moments of inertia of all rib sections in 

 inch dimensions per inch width of rib. The allowable intensity of 

 compression in concrete will be taken at 450 fes. per square inch and 

 the allowable tension at 60 fcs. per square inch. 20,000 lbs. per 

 square inch for both tension and compression might be allowed in 

 the steel work. It will be found, however, that the steel from the 

 nature of the combination of steel and concrete cannot be stressed 

 above about one-half this allowable amount. 



The stresses in the extreme fibres of the concrete and the steel of 

 con Crete -steel ribs of symmetrical section are found by the formulas: — 



S,=-^— ^^^, (21) 



' A,+20A2""Ii+20I, 



20T ^120^^ 

 ' A,+20A,~I,+20I, ^ 



In these equations: — 



S,=maximum intensities of tension and compression in the con- 

 crete of the rib, in pounds per square inch. 



