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    Engineering Plastic Analysis: Upper Bound Theorem

    In your initial sketch, allegedly without sway, you have included some sway of the left hand column, but not of the right hand column. The line AF produced meets the line DC produced at a point 4 m above C. This is the instantaneous centre of rotation of the beam segment FC, say call it point...
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    Simple Question - Preloading of a Cantilever Beam

    Could this be an axial load in the direction -ve x in order to prevent tension developing at top left corner?
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    Frame Deflection homework

    You seem to be ignoring the deflection of E in the y direction. That will increase the deflection at C.
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    Force members

    In order for there to be a vertical component of reaction at C, member CD would have to be inclined rather than horizontal..
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    Shear force in influence line of beam

    There are at least two ways of learning about influence lines. The first way is algebraic, as given in the solution quoted. If you have learned about shear force diagrams before coming to influence lines, it is easy to get the two things confused. It is necessary to keep returning to the...
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    Evenly distributed beam with overhang and multiple supports

    I think you seem intent on using elastic analysis, which is fine at working loads, if can do it. However, plastic analysis is easier, and arguably safer, whilst admittedly not giving you deflections.
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    Statics problem. Cable with distributed load

    You know the forces at the ends of the cable. You know those forces are tangential to the cable ends. You know the drag. That makes 3 forces. If they are in equilibrium they must all meet at one point. You don't have enough information about the cable self-weight to take account of that. Can you...
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    Stress in steel and concrete

    Still looks funny. I am struggling to visualise 3.174 mm2. You haven't declared your units. Can you explain the 10^6 and the 10^3 in your corrected equation?
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    Stress in steel and concrete

    Your answer of 0.52 mm2 seems improbable, if not impractical, and so, without looking at your working, I am inclined to try a different approach. The usual problem here is often the units; so stick to, say N and mm. Try a concrete area of say 50 mm x 50 mm. At 14 MPa (ie N/mm2) , its resistance...
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    Force Couple on Frame

    The assumption that a point of zero moment occurs half-way up the columns is unconvincing, because the conditions at the top and the bottom of the columns are not the same; at the bottom it is encastre and no rotation is assumed to occur, but at the top of the columns, the fixity is provided by...
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    Moments in beam

    The diagram is quite a good representation of what I mean, although I am struggling to understand your language: "800Nm is the diffrence in length of the triangle"
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    Moments in beam

    You are right to recognise that the 2400 has a different orientation to the -2000. But, just as you can add a positive number (say, +6) to a negative number (say, -2) to give a result of +4, so you can add areas on a graph. At a point just to the right of C, the result is +2400 -2000= +400 (the...
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    Beam deflection

    Because the expression for M is the summation of moments to the LEFT of section X, but the 12 kN load is to the right. If you were to write down an expression for the moment to the RIGHT of x, you would get an expression that may at first sight look different, but, if correctly drawn up, will be...
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    Moments in beam

    Unfortunately the M diagram you gave us is not drawn to scale. I suggest you redraw it to scale on graph paper. Let's call C the point of application of the 400 Nm moment, and point D the point of application of the 1000 N load. If you redraw the 2000 Nm triangle above the horizontal axis, as if...
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    Moments in beam

    The so-called 'missing' 400 Nm is the difference between 2400 and -2000. This is a graph preparing for gaphical summation. If you like, you can imagine folding the lower triangle about the horizontal axis, to cancel a good bit of the right hand upper triangle. The zero line would then, in that...
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    Beam deflection

    The figure does not include the variable 'x'. But, wherever you put it in the range 0 to 9 m, what contribution to Mx do you think the 12 kN force would make? Recall one definition of moment that it is the algebraic sum of moments on ONE side of a section.
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    Is it normal to keep forgetting?

    I am surprised that, so far in this thread, responders have not suggested that you learn more by teaching a subject to a class that will ask awkward questions. Therefore get a group of critical friends together and teach yourselves something you really want to know and retain.
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    Distributed load

    I don't know what the author assumed. I am just indicating that you have made an assumption that the distributed load is acting vertically, when it might just be acting horizontally if you regard the diagram (a) given as a plan., rather than as an elevation. All this doesn't affect the...
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    Distributed load

    You may be assuming that the distributed load is against gravity. This problem could be a model of a structural member such as a window mullion carrying a distributed wind load, where gravity is a force along the axis of the member.
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    Sign convention of shear force and moment on beam

    This is similar to another post of yours, to which I replied: What definition of Moment are you using? There are two possible definitions, each of which can be derived from the other. The one I prefer is that the bending moment at a section is the algebraic sum of the moments on ONE SIDE of the...
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    Moments in beam

    "First , 1st solution, the author taking moment about 2m from A?" The author is taking moments about EVERY point in the beam and then plotting the result as a graph. That is what a bending moment diagram is. "secondly, the 800Nm is clockwise moment, so it is positive? why the 2400Nm on the...
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    Maximum moment at the center

    That is the definition of bending moment. It's useful.
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    Moment diagram

    I think the confusion might be that the hinge at B is drawn to hide the fact that the beam is moment-continuous over it. Thinking of the beam as a continuous, some rotation can occur there, but not the complete rotation as in a mechanism, that I suspect the op is thinking about.
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    Maximum moment at the center

    When you 'take moments about a point', you will get a zero answer for a body in static equilibrium. If you take moments on ONE side of the section, you will get a non-zero answer which should be numerically the same as that algebraic sum on the OTHER side of the section - in this case w(l^2) /8...
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    Moment of beam

    That is not a definition. see my reply to another of your questions
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    Maximum moment at the center

    This is similar to another post of yours, to which I replied: What definition of Moment are you using? There are two possible definitions, each of which can be derived from the other. The one I prefer is that the bending moment at a section is the algebraic sum of the moments on ONE SIDE of the...
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    Moment of beam

    What definition of moment are you using?
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    Forces in truss

    You don't need dimensions in a statically determinate frame - just the proportions. Guessing that the left hand triangle is in a 3/4/5/ proportion, the figures 6 and 8 make sense. The choices of forces as multiples of 14 suggest the question is looking for an answer that can be achieved without...
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    Best bridge type

    Think of winding the string around something that won't slip. There are hazards in all designs but you will best learn from the experience itself.
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    Best bridge type

    A cable-stayed bridge would need to use the deck as a compression anchor, and it would be difficult to load. A better solution is to use a tied beam with the cables going below the deck. Cables still need to be anchored to the deck, but it's easier to load. You need to know the dimensions of the...