Page 88 - Handbook of Civil Engineering Calculations, Second Edition

STATICS, STRESS AND STRAIN, AND FLEXURAL ANALYSIS 1.71

4. Construct a diagram representing the shear associated
with every position of the unit load
Apply the foregoing equations to represent the value of V cd associated with every position
of the unit load. This diagram, Fig. 48c, is termed an influence line. The point j at which
this line intersects the base is referred to as the neutral point.
5. Compute the slope of each segment of the influence line
Line a, dV cd /dx 1/120; line b, dV cd /dx 1/120; line c, dV cd /dx 1/24. Lines a and b
are therefore parallel because they have the same slope.

FORCE IN TRUSS DIAGONAL CAUSED
BY A MOVING UNIFORM LOAD

The bridge floor in Fig. 48a carries a moving uniformly distributed load. The portion of
the load transmitted to the given truss is 2.3 kips/lin ft (33.57 kN/m). Determine the limit-
ing values of the force induced in member Cd by this load.

Calculation Procedure:

1. Locate the neutral point, and compute dh
The force in Cd is a function of V cd . Locate the neutral point j in Fig. 48c and compute dh.
From Eq. c of the previous calculation procedure, V cd jg/24 S 0; jg 72 ft (21.9
m). From Eq. a of the previous procedure, dh 60/120 0.5.
2. Determine the maximum shear
To secure the maximum value of V cd , apply uniform load continuously in the interval jg.
Compute V cd by multiplying the area under the influence line by the intensity of the ap-
1
plied load. Thus, V cd /2(72)(0.5)(2.3) 41.4 kips (184.15 kN).
3. Determine the maximum force in the member
2
2
2 0.5
Use the relation Cd max V cd (csc ), where csc [(20 25 )/25 ] 1.28. Then
Cd max 41.4(1.28) 53.0-kip (235.74-kN) tension.
4. Determine the minimum force in the member
To secure the minimum value of V cd , apply uniform load continuously in the interval aj.
Perform the final calculation by proportion. Thus, Cd min /Cd max area aij/area jhg
2
(2/3) 9. Then Cd min (4/9)(53.0) 23.6-kip (104.97-kN) compression.
FORCE IN TRUSS DIAGONAL CAUSED BY
MOVING CONCENTRATED LOADS

The truss in Fig. 49a supports a bridge that transmits the moving-load system shown in
Fig. 49b to its bottom chord. Determine the maximum tensile force in De.

Calculation Procedure:
1. Locate the resultant of the load system
The force in De (Fig. 49) is a function of the shear in panel de. This shear is calculated
without recourse to a set rule in order to show the principles involved in designing for
moving loads.