474 PROFESSOR MOSELEY, ON THE THEORY OF 



6. The Straight Arch, or Plate Bande. 



Let e be now assumed = ^, the sections will then be vertical (Fig. 3), 



the line of resistance will coincide with the line of pressure (Art. 2), and 

 the equation common to botli will be 



_ gS P sin <!> - //'(y, - y.) r/s' + S ± P^ cos ^^ 



y~ ' sp'cosO) ^ '• 



In the case of a trapezoidal mass (Fig. 9), this formula gives by 

 equation (7) 



- Irjtana, - tan osl - Aff«'' + J82Psinfl) + 2 + P^cosO , , 



V = — — — ^"D s: = •••(25), 



•' 2Pcos4) ^ ' 



and the points of rupture are determined by the equation 



8,^ tan a, — tan oj} + 3as; + 6jtan «,2Pcos <I)-2P fincl)|i!j 



+ |«2Pcos<I>- 2+ Pk co%^\ =0....(26). 



If a, = a-i (Fig. 10), the equation to the line of resistance and to 

 the line of pressure becomes 



_ — ^«»^ +zSPsin<I) + 2 + P^cos<I> 



y " 27^7* <-^'')- 



The equation to a parabola whose axis is vertical, whose parameter 



is , and the co-ordinates of whose vertex are 



a 



2Psin<l) «2 + P^ cos t^ + 1 (2P sin 4>)' 



a «2Pcos<l> 



The elements of this parabola are thus independent of the position 

 of the mass. 



Let us suppose the impressed forces P to be placed symmetrically 

 (Fig. 11), then will the vertex of the parabola manifestly be situated 

 midway between the extremities of the mass. Let the length of it 

 be 2A; 



2Psin(I) , ,„„, 



••• =* (28). 



