- #1
ulo_minje
- 3
- 0
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) :
Now, i would like to know if i made any mistakes here.