Hinge's effect on uniform load on beam?
Hinge's effect on uniform load on beam?
(OP)
While studying for the SE I came across problem 109 in the first attached document. The solution is added in the second post. My question is, how did they determine the 0.2 factor for the load due to the uniform load on the right side of support B? Does the hinge affect it; I thought hinges only affect moment transfer.






RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
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RE: Hinge's effect on uniform load on beam?
All I did was solve this non-redundant system and created the shear diagram after solving for the reactions.
The portion left of the hinge is a simple span which results in a point load on the end of the cantilever.
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RE: Hinge's effect on uniform load on beam?
The triangle on the left span is the influence line for shear just to the right of Point B resulting from a unit load placed anywhere between points A and B. If the unit load is placed at A or B, it contributes nothing to moment in span A-B or shear at B.
If the unit load, say 1k is placed at the hinge, it produces a moment of 1*12 = 12'k at point B. This in turn produces equal and opposite reactions of 12/60 = 0.2 kips at B and C, upward at B and downward at C. The influence line is linear between the hinge and either A or B.
To find the effect of a uniform load between points A and B, you need to take the area under the influence line and multiply it by w, the uniform load.
BA
RE: Hinge's effect on uniform load on beam?
But if you want to use the influence line, calculate the shear force at B due to a unit point force at the hinge.
The span A-Hinge is simply supported, so a point load at the hinge will not transfer any load to A.
Take moments about C: 1 x 72
Reaction at B = 72/60 = 1.2
Shear force to right of B = 1.2 - 1 = 0.2
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
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RE: Hinge's effect on uniform load on beam?
EMc=o: 24kip(72ft)+10kip(60ft)-Rb(60ft)+72kip(36ft), Rb=82kip
Clearly this is the wrong approach?
RE: Hinge's effect on uniform load on beam?
That gives you a shear of 46 kips to the right of the support.
Coming from the left, your shear starts at -24 kips from the point load and is driven to -36 kips by the distributed load by the time you reach the support. The support is 82 kips in the opposite direction, which means that immediately to the right of the support your beam shear switches direction and is 46kips for a very short distance before the moving point load shows up.
RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
Showing solution using influence line is interesting..........but way too confusing to just arrive at solution!
John F Mann, PE
www.structural101.com
RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
RE: Hinge's effect on uniform load on beam?
Lion06 is correct. A point load just left of support B produces zero shear just right of B as shown on the influence line in the left span. If that is not clear, think about Span B-C with a 12' cantilever and a concentrated to the left of Point B but very close to it. The shear to the left of B will be 10k but the shear to the right of B will be close to zero.
BA