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Surcharge Formula Das and AASHTO for strip load adjacent to wall

Surcharge Formula Das and AASHTO for strip load adjacent to wall

Surcharge Formula Das and AASHTO for strip load adjacent to wall

(OP)

In the two referenced formulas for the stress at any depth resulting from a strip surcharge loading I have a formula question.

Das Principles of Foundation Engineering Second Edition formula 5.38, stress=2*q*( b-sinb*cos(2a))/pi
In the formula in the Das text, is the cos2a term just the angle a times two, say a=.7 radians then cos(2*.7) = cos(1.4) or is the cos2a term intended to be a double angle identity = cos^2a-sin^2a = 1-2sin^2a ?

Similarly in the AASSHTO LRFD Bridge Design formula 5.11.6.2-1, stress = 2*p*( d-sind*cos(d+2a))/ pi is the cos(d+2a) intended to be a double angle identity or just a simple addition and product,say a=.7 and d=.2 radians then = cos(.2+2*.7) = cos(1.6)

In the solved example I found, they used the angles as numeric values.

Does anyone know the correct interpretation of the cos2a term ?

Thank You,

PEVT2

RE: Surcharge Formula Das and AASHTO for strip load adjacent to wall

It's just a straight plug and chug. (With β, δ, etc input as radians.)

You get the same thing in the AASHTO example that you would in Das's equation. The difference is: it is taking different angles in each sketch. (Das's way is how I am use to seeing it.)

RE: Surcharge Formula Das and AASHTO for strip load adjacent to wall

(OP)
Hello WARose, thank you for your answer, it really helped to clarify the intent of the formulas for me. I appreciate it.

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