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In the following equations for load constants, D, and D, values are divided into two terms. The first represents the effect of bending, and the second represents the effect of rib-shortening and shear detrusion.

94. Uniform Radial Load.-Moments, thrusts, and shears due to a uniform radial load at the upstream face, as shown in figure 33-a, may be computed by the following equations.

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By substituting these values in equations 131, 132, and 133, the following formulas are obtained.

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D2,1st term =

D2, 2nd term =

Ec T3

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Ec I

Hsin
HL sinds

Ec A

(137)

(138)

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The evaluation of these and succeeding integrals is discussed in chapter IX. It should be noted that the D2 and D, temperature terms are omitted in equations 137 to 141, since the formulas are for uniform radial loads which do not include temperature effects.

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95. Triangular Radial Load.-Moments, thrusts, and shears due to a triangular radial load at the upstream face, as shown in figure 33-b, may be computed by the following equations.

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to a uniform tangential load applied along the center line of an arch, as shown in figure 34-a, may be computed by the following equations.

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Equations for load constants, derived by substituting equations for ML, HL, and VL in equations 131, 132, and 133, are given below.

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97. Triangular Tangential Load.-Moments, thrusts, and shears due to a triangular tangential load, as shown in figure 34-b, are calculated by the following formulas:

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98. Uniform Twist Load. Twist loads are horizontal couples causing pure bending of the arches. Consequently, they do not produce thrusts or shears, and terms involving these quantities do not appear in the following formulas. The moment due to a uniform twist load applied along the center line, as shown in figure 35-a, is

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Load constants for a uniform twist load involving this internal moment are

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