For the load group and influence line shown, P₁ = 32 kips, P2 = 32 kips, P3 = 8 kips, a = 14', and b = 14'. The influence line is for V40 = shear just left of 40'. Determine V40 in kips to two decimal places when the force P₁ is at 8! Use the correct sign. 16 0.5 15 20 30 -1 P₁ P₂ a b P3

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Influence Lines

The graphs that show the variation of a function at a specific point on a beam or truss due to a unit load placed at any point along the structure are known as influence lines in engineering. Some common functions that are studied with influence lines are shear, moment, and deflection. In designing beams and trusses, it is important to use influence lines in structures where loads would move along their span such as bridges, crane rails, conveyor belts, floor girders, etc. The influence lines help to study where a load will create the maximum effect for any of the functions.