Question
A 3-span continuous beam has span lengths of 20 ft, 30 ft, and 20 ft. The beam carries a uniform dead load of 1.2 kips/ft and a movable uniform live load of 2.5 kips/ft. Using ASCE 7 load combinations and influence lines, what is the maximum possible negative bending moment at the first interior support due to the combination 1.2D + 1.6L?
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-350.7 kip-ft
Explanation: To maximize negative moment at the first interior support, the live load must be placed on the two adjacent spans (Span 1 and Span 2). Using structural analysis coefficients or three-moment equations for this loading configuration: MD = -0.100 w_D L²ₐvg (or exact analysis: M_D = -103.2 kip-ft). ML = -226.9 kip-ft. Factored Moment M_u = 1.2(-103.2) + 1.6(-226.9) = -350.7 kip-ft.
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