Solve Mechanics Problem: Carrier Loads, F=50kN, M=20kNm, g=10kN/m, a=1m

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Discussion Overview

The discussion revolves around a mechanics problem involving a carrier loaded with specific forces and moments. Participants are tasked with finding the reactions at supports, analyzing static dimensions at a specific section, determining the greatest moment of flexion, and graphically representing various forces and moments. The scope includes analytical calculations and graphical representations related to static equilibrium.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The initial poster presents calculations for the reactions at supports A and B, along with moments and forces acting on the carrier.
  • Some participants question the clarity of the provided diagram, suggesting that a clearer image or separate sketch is necessary for proper evaluation.
  • There is a query about the angle of the applied force with respect to the beam, which is answered with a proposed angle of 30 degrees.
  • One participant checks the calculations of the reactions at supports, noting an assumption about the beam's constraints and indicating a potential error in the moment equation used for calculating vertical reactions.
  • Another participant emphasizes the importance of self-checking calculations by applying equilibrium conditions and sign conventions, suggesting that the poster should verify their own work rather than relying on others for confirmation.

Areas of Agreement / Disagreement

Participants express differing views on the accuracy of the calculations presented, with some agreeing on certain aspects while others point out potential errors and the need for clearer diagrams. The discussion remains unresolved regarding the correctness of the calculations and the assumptions made.

Contextual Notes

There are indications of missing annotations in the diagram, which may affect the clarity of the problem setup. Additionally, the discussion highlights the importance of understanding sign conventions and equilibrium conditions in static analysis.

ulo_minje
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Homework Statement


For carrier loaded the way it's shown in the picture and whose load-values are:
F=50kN, M=20kNm, g= 10kN/m and a=1m
a) find analytically resistances of supporters
b) find analytically intensities of elementary static dimensions for section(cut) at the point C on the carrier
c)find the greatest moment of flexion
d)graphically represent the check of axial forces, transversal forces and moments of flexion

Homework Equations

The Attempt at a Solution


a) resistance of supporters:
##\sum _{i=1} ^n X_i = 0 \\ X_A + X = 0 \\ X_A = -X \\ X_A = -43.25kN \\ \\ \sum _{i=1} ^n Y_i = 0 \\ Y_A - F_g + F_B - Y = 0 \\ \\ \sum _{i=1} ^n M_A = \\ -Y6a + F_B5a - M - F_ga = 0 \\ F_B = \frac{Y6a + M + F_ga}{5a} \\ F_B=\frac{25*6*1 + 20 + 40*1}{5*1} \\ F_B = 42kN \\ \\ Y_A = F_g - F_B + Y \\ Y_A = 40 - 42 + 25 \\ Y_A = 23kN \\ \\ F_A = \sqrt{x_A^2 + Y_A^2} \\ F_A = 48.98kN \\ \\ tan\alpha_A = \frac{Y_A}{X_A} \\ tan\alpha_A = -o.531 \\ \alpha_{A'} = 62\degree 60'##

b)
## F_A= - X_A = 43.25kN \\ F_t = Y_A - g3a = -7kN \\ M_X = Y_A2a - g3a = 16kNm##

c) ##D: M_X = 0 \\ E: M_X = g\frac{a}{2}3a^4 = 15kNm \\ A: M_X = 9*3a^4 = 30kNm \\ F: M_X = 92a^2 + Y_A3a = 89kNm \\ C: M_X = Y_A2a - g3a = 16kNm \\ G: Y_Aa^3 = 23kNm \\ H':\frac{a}{2}a^2 + M = 10kNm \\ H'': M_X = a^2 + M = 20kNm \\ B: M_X = a + M = 21kNm \\ J: M_X = 0 ##

and now graphically (picture of carrier is also shown here) :
ova slika.jpg


Now, i would like to know if i made any mistakes here.
 
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This image is so blurry as to be useless for checking your work. Please post a better image or make a separate sketch of the problem.
 
upload_2015-12-21_15-9-32.png

Is it ok?
 
ulo_minje said:
View attachment 93549
Is it ok?
What's the angle of the 50 kN force with respect to the beam?
 
30 degrees
 
ulo_minje said:

Homework Statement


For carrier loaded the way it's shown in the picture and whose load-values are:
F=50kN, M=20kNm, g= 10kN/m and a=1m
a) find analytically resistances of supporters
b) find analytically intensities of elementary static dimensions for section(cut) at the point C on the carrier
c)find the greatest moment of flexion
d)graphically represent the check of axial forces, transversal forces and moments of flexion

Homework Equations

The Attempt at a Solution


a) resistance of supporters:
##\sum _{i=1} ^n X_i = 0 \\ X_A + X = 0 \\ X_A = -X \\ X_A = -43.25kN \\ \\ \sum _{i=1} ^n Y_i = 0 \\ Y_A - F_g + F_B - Y = 0 \\ \\ \sum _{i=1} ^n M_A = \\ -Y6a + F_B5a - M - F_ga = 0 \\ F_B = \frac{Y6a + M + F_ga}{5a} \\ F_B=\frac{25*6*1 + 20 + 40*1}{5*1} \\ F_B = 42kN \\ \\ Y_A = F_g - F_B + Y \\ Y_A = 40 - 42 + 25 \\ Y_A = 23kN \\ \\ F_A = \sqrt{x_A^2 + Y_A^2} \\ F_A = 48.98kN \\ \\ tan\alpha_A = \frac{Y_A}{X_A} \\ tan\alpha_A = -o.531 \\ \alpha_{A'} = 62\degree 60'##
I've checked your calculations of the reactions at A and B.

It's not clear from the diagram, but I'm assuming that the beam is pinned at A and free to move horizontally at B, which means that A can resist a force applied axially.
In that case, the horizontal reaction at A would be -43.25 kN as you indicated.

For the vertical reactions, it seems you have written in incorrect moment equation about point A. Therefore, the vertical reactions you have calculated are incorrect.

Remember, the distributed load w and the vertical component of the concentrated load F are working in opposite directions from one another, that is, the vertical component of the concentrated load F is tending to support the beam and reduce the reactions at A and B.
 
You ask us to tell you if there are mistakes. As far as the reactions are concerned this is something that you could check yourself. In this case, having obtained the reactions, by summing forces in x and y directions, plus taking moments about A (wherever that is - not annoted), you do the check by taking moments about any point other than A, and if there is equilibrium, then either you are correct or you have self-cancelling errors. The same is true for functions such as bending moment. If you use the definition of bending moment that it is the algebraic sum of moments on one side of a section, then this should be precisely the same as the algebraic sum of the moments on the other side of the section; and that is your check. errors are usually caused by mis-applying sign conventions. The same applies to shear force or axial force. So you don't need US to check your work when you could do it yourself, and this is what people in industry have to do when they are analyzing real world problems not found in textbooks.