A millionaire is building a palatial (big. big .big) house in Alaska and has a 1

Question

A millionaire is building a palatial (big. big .big) house in Alaska and has a 16 ft long 8" times 8" cross-section beam that weighs 800 lb dropped off near a river's edge. There is a rain storm and the beam rolls into the river and is floating weightlessly in the water (i.e. supported completely by the water). a) What is omega the weight/ft of this beam? b) What direction does the distributed force (of the water) supporting the beam act? c) What is the magnitude of the supporting force? d) An enterprising mammal that weights 200 lb decides to climb onto the exact middle of this beam and hops a ride down the river. Now, what is the magnitude of the force supporting the beam and mammal? c) Assume the mammal is on the beam. What is the supporting force per unit length? f) Assume the mammal can be treated as a concentrated force of 200 lb, and draw the free-body force diagram for the beam and mammal floating at rest on water. Note there are two distributed forces. g) Draw load, shear and moment diagrams for this case. Include numbers as appropriate.

Explanation / Answer

a) weight per unit length w = 800/16 = 50 lb/feet

b) upward direction, in order to cancel force due to weight.

c) magnitude of supporting force = 800 lb,

d) magnitude of supporting force =200+800 = 1000 lb

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