Horizontal reactions for a simple span, inclined beam with vertical loads
Horizontal reactions for a simple span, inclined beam with vertical loads
(OP)
Dear All:
My colleagues and I are having difficulty understanding if an inclined, simple span beam with vertical loads requires a horizontal reaction for static equilibrium. Our software tells us there is no reaction, which makes sense from a statics perspective since there are no horizontal external loads, however, this doesn't make intuitive sense when one considers a simple ladder example. Without a horizontal reaction at the base of the ladder, it would just fall over. Could someone help us clear this up please?
Thank you,
jochav5280
My colleagues and I are having difficulty understanding if an inclined, simple span beam with vertical loads requires a horizontal reaction for static equilibrium. Our software tells us there is no reaction, which makes sense from a statics perspective since there are no horizontal external loads, however, this doesn't make intuitive sense when one considers a simple ladder example. Without a horizontal reaction at the base of the ladder, it would just fall over. Could someone help us clear this up please?
Thank you,
jochav5280






RE: Horizontal reactions for a simple span, inclined beam with vertical loads
thread507-326814: Structural Ridge Rafter Thrust
thread507-189340: wood rafter thrust problem
thread507-280567: Roof Live Load
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
In the case of a simple ladder, assuming no friction between the ladder and the wall, the upper reaction is horizontal. The lower reaction must have a vertical component equal to the total vertical load on the ladder and a horizontal component to match the upper reaction.
BA
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Sounds like you and your colleagues better brush up on your statics and free body diagrams before you design anything else
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
If the upper connection is a perfect pin that cannot itself move, then the pin cannot go down, and the bottom of the ladder has no horizontal component, only a vertical component.
If the top connection is a real-world (sliding) connection, then bottom of the ladder (its feet) MUST have enough friction force (horizontal component force) with the pavement to equal the force against the wall at the top of the ladder.
Hint: Redo your calculation with the ladder sloped only 15 degrees from the horizontal. Now, put a ladder on the floor and try to leave it leaned over at 15 degrees.
MODELS AND TEXTBOOKS ARE NOT THE REAL WORLD. (But "sometimes" they approximate it close enough to use under limited circumstances.)
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
The internal statics work out, but it is not as intuitive as a beam parallel to the ground.
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Thank you for your posts.
We obviously needed to brush up on our free body diagrams as it became quite clear once we did so.
With an inclined, simple-span beam that supports vertical loads, it becomes apparent that since there are no applied horizontal loads as well as only (1) pin-support, there's no way for a horizontal reaction at the pin-support to be balanced.
Many thanks again,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Not true. If one support is a pin and the other support is a roller permitting translation in any direction other than horizontal, there will be equal and opposite horizontal reactions at each end of the beam.
BA
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Agreed, that is why I wrote "simple span", which I believe normally implies that the roller support is a horizontal roller, unless specifically noted that the support is an inclined roller.
Thank you,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Because the upper point is not pinned with a friction-free roller nor restrained vertically , there is both a horizontal and a vertical force on the lower end of the ladder.
http://content4.viralnova.com/wp-content/uploads/2...
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Agreed! The vertical reaction resists the vertically applied load and the horizontal reaction balances the stability reaction at the vertical roller support.
Thank you,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
BA
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
Summing the moments about the pinned support yields a horizontal reaction of (Pa)/H.
Best regards,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
BA
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
My apologies, forgot the second part. Yep, I totally agree. Thank you for your help!
Best regards,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
BA
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
That doesn't really make sense to me. I think picturing the extremes helps illustrate the point. As the ladder inclination approaches vertical, there will be less and less bending in the member and more axial load, which suggests that the bending moment is not the same as the simple span beam bending moment. As the ladder nears vertical, nearly all of the applied gravity loads will be resisted axially, not via bending. That said, the bending moment in the member would be proportional to the ladder inclination, which would always be less than that of a level simple span beam.
Did I miss something or misinterpret your response? Thanks for the follow-up.
Best regards,
jochav5280
RE: Horizontal reactions for a simple span, inclined beam with vertical loads
The bending moment on an inclined beam will be the same as that of a simple beam whose span is equal to the horizontal span of the inclined beam. This is true for any combination of gravity load and for any inclination of the roller support.
BA