+34.4 X2 X20— (11.47+5.73)20+ U,U, X 24.28 = 0 U,U, = —42.51.
The stress in is determined by passing a vertical section in the 3d panel, and taking the sum of the horizontal forces. As there is no dead-load stress in the members and their compo nents will be zero. Therefore (see Fig. 60) it is evident that must be equal and opposite to and will be equal to —41.26.
By reference to Fig. 55, the stress in L,U, is seen to be tensile and equal to +11.47.
Pass a circular section around and take the sum of the vertical components, assuming that the stress in acts away from the section. The length of is + = 20.6, and therefore the vertical component of will be (42.51 - 20.6) X 5 = 10.32, which acts upward. The stress equation of (see Fig. 61) is: +10.32 - 5.73 - = 0 .-. U,L, = +4.59, showing that a tensile stress occurs in when all panel points are loaded.
The simplest method of ascertaining the stress in is to pass a vertical section cutting members as shown in Fig. 62, and to equate the horizontal forces and stresses. The horizontal component of is: All the dead-load stresses being computed, the next operation will be to determine the live-load chord stresses. These are pro portional to the dead-load stresses in the same ratio as the live panel load is to the dead panel load. This ratio is 50 _ 17.2 = 2.907, and the chord and end-post live-load stresses are: Also, the stress in when the live load covers the entire bridge is not 2.907 X 4.59, as it must be remembered that part of the dead
load is at the panel points of the upper chord. Taking a circular section around (see Fig. 61), and noting that there is no load at it is seen that the stress in due to live load is simply equal to the vertical component of the live-load stress of and will be tensile. It is: • The maximum live-load stress in U,L, is tensile, and equal to the live panel load at L, (see Fig. 55).
To obtain the maximum sfress in load L and L,. The shear will then be + 2) _ +30.0. The section will cut the members as shown in Fig. 63, and the equation of stress will be: 25 + 30.0— U,L, cos 0= 0; but cos 0 _ =0.782; 25' U,L, = +38.4.
If panel points L, and were loaded, it is evident that the stress in would be +38.4.
To obtain the maximum live-load stress in a section is passed cutting and (Fig. 64). The center of moments will be at the intersection of and and this point lies some place to the left of the support The lever arm of will be the perpendicular distance from this point to the line extended. The panel points and L, are loaded. The left reaction is then (1 + 2 + 3) _ + 60.0. The lever arms are easily computed, and these, together with the members cut, are shown in Fig. 64. The equation of stress is: