STRESSES IN BRIDGE TRUSSES. 



loaded. The shear in the panel is $\P, or V P> and the stress in i-X sl-P-sec 9 -f 125,400 

 Ih., while the stress in 1-2 ^P-accO 125,400 Ib. The minimum stresses in i-X and 

 1-2 are zero. The maximum stresses in 2-3 and 3-4 occur when 6 loads are on the right of the 

 1 1. m. 1 .uxl i IHTC an- no loads on the left of the panel. The shear in the panel will then be equal 

 to th.- li-ft reaction, - RI - (6 X 3$ X P)/8 - >j P. The stress in 2-3 - ^-P-eec $ - 

 + 94,080 Ib., while the stress in 3-4 V-P-sccd = 94,080 Ib. The minimum stresses 

 in 2-3 ami 3 4 will occur when there is one load on the shorter segment. In the corresponding 

 panel on the right of the truss, if the shorter segment is loaded, the left reaction \P the 

 slu-.ir in the panel. The minimum stress in 2-3 = \P-sec0 = 4,480 Ib., while the 

 minimum stress in 3-4 = + 4,480 Ib. The stresses in the remaining panels are calculated in the 

 ^iiiu- m.imier. The maximum chord stresses are equal to the sum of the dead and live load chord 

 The minimum chord stresses are the dead load chord stresses. The maximum web 

 M roses are equal to the sum of the dead and the maximum live load web stresses. The minimum 

 web stresses are equal to the algebraic sum of the dead load stresses and the minimum live load 

 stresses. 



(c) Results. The web members 7-6 and 7-8 have a reversal of stress from tension to com- 

 pression, or the reverse. These members must be counterbraced to take both kinds of stress. 



PROBLEM 4. MAXIMUM AND MINIMUM STRESSES IN A PRATT TRUSS BY ALGEBRAIC 



RESOLUTION. 



(a) Problem. Given a Pratt truss, span 140' o", panel length 20' o", depth 24' o", dead 

 load 800 Ib. per lineal foot per truss, live load 1, 600 Ib. per lineal foot per truss. Calculate the 

 maximum and minimum stresses due to dead and live loads by algebraic resolution. Scale of 

 truss, i" = 20' o". 



(6) Methods. Construct three truss diagrams as shown. On the first place the dead load 

 coefficients and the dead load stresses. On the second place the live load coefficients and the 

 live load stresses. On the third place the maximum and minimum stresses due to dead and live 

 loads. The maximum chord stresses are the sums of the dead and live load chord stresses, while 

 the minimum chord stresses are those due to dead load alone. The hip vertical is simply a hanger 

 and has a minimum stress of one dead load and a maximum stress of one live and one dead load. 

 The conditions for maximum and minimum stresses in the webs are the same as for the Warren 

 truss, the vertical posts having stresses equal to the vertical components of the stresses in the 

 inclined web members meeting them on the unloaded (top) chord. 



(c) Results. There is no dead load shear in the middle panel, but it is seen that there are 

 stresses in the counters for live loads. Only one of the counters will be in action at one time 

 Whenever the center of gravity of the loads is not in the center line of the truss, that counter 

 will be acting that extends downward toward the center of gravity. The numerators of the 

 maximum and minimum live load web coefficients are o, I, 3, 6, 10, 15, 21, as for the Warren 

 truss. This shows that the maximum and minimum web stresses are proportional to the ordinates 

 to a parabola. 



PROBLEM 5. MAXIMUM AND MINIMUM STRESSES IN A DECK BALTIMORE TRUSS BY ALGEBRAIC 



RESOLUTION. 



(a) Problem. Given a deck Baltimore truss, span 280' o", panel length 20' o", depth 

 40' o", dead load 0.375 tons per lineal foot per truss, live load 0.625 tons per lineal foot per truss. 

 Calculate the maximum and minimum stresses due to dead and live loads by algebraic resolution. 



(b) Methods. Construct three truss diagrams and use them as shown. 



Dead Load Stresses. The auxiliary struts 1-2, 5-6, 9-10, etc., carry a full dead load com- 

 pression, while the auxiliary web members 2-3, 6-7, 10-11, etc., have a tensile stress of $W-sec 0. 

 The stress in l-F equals the shear in the panel multiplied by sec = 6|W-sec 0. The stress 

 in 3-F equals the shear in the panel multiplied by sec 0, plus the inclined component of the one- 

 half load that is carried toward the center by the auxiliary member 2-3, = (si + i)W-sec 6 

 = 6W-sec0. The stress in 3-4 is the vertical component of the stress in 3~F = + 6W. 

 The stress in $-Y is the horizontal component of the stress in J,-Y = 6W-ta.n 6. The stress 

 in l-X and 2-X = + 6%W-tan 6. The stress in 4-5 is the inclined component of the shear in 

 the panel = - $\W- sec 0. The stress in 5-^" = - (- 6 - tf)W-tan = + loJW-tan 9. 

 The remaining dead load stresses are calculated in a similar manner. 



Live Load Web Stresses. The maximum shears in the different panels occur when the longer 

 segment of the truss is loaded, while the minimum shears occur when the shorter segment of the 

 truss is loaded. The maximum stresses in the webs in the first and second panels occur for a 

 full live load on the bridge. The maximum shear in the third panel occurs with all loads to the 

 right of the panel and no loads to the left. The shear in the panel will then be equal to the left 

 reaction = n X J(" + 1)^/14 = fJP. The maximum live load stress in 4-5 will be = 



