The 3D rigid truss structure is supported by three connections to the ground in the ry plane at D, E, andF. None of these connections can resist rotation. The connection at D can resist translation in alldirections. The connection at F can only resist translation in the +z direction. The connection at E canresist translation in the +x direction and the +z direciton. A force of F = 250 ĝ kN is applied at B. Asecond force F2 = - 225 î + 140 ĵ - 60.0 k kN is applied at point C.Determine the reactions at connections D, E and F. Enter your answers in Cartesian components.F2BFEValues for dimensions on the figure are given in the table below. Note the figure may not be to scale.TEVariable Valuea1.84 m2.13 m2.76 mThe reaction at D is D -k kN.The reaction at E is Ek kN.The reaction at F is Fk kN.++II

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The 3D rigid truss structure is supported by three connections to the ground in the ry plane at D, E, and
F. None of these connections can resist rotation. The connection at D can resist translation in all
directions. The connection at F can only resist translation in the +z direction. The connection at E can
resist translation in the +x direction and the +z direciton. A force of F = 250 ĝ kN is applied at B. A
second force F2 = - 225 î + 140 ĵ - 60.0 k kN is applied at point C.
Determine the reactions at connections D, E and F. Enter your answers in Cartesian components.
F2
B
F
E
Values for dimensions on the figure are given in the table below. Note the figure may not be to scale.
TE
Variable Value
a
1.84 m
2.13 m
2.76 m
The reaction at D is D -
k kN.
The reaction at E is E
k kN.
The reaction at F is F
k kN.
+
+
II

Expert Solution

Step 1

Given data,

Important point:- If a point/joint /support, resisting any rotation motion or translation motion. Then in that particular point/joint/support have that particular reaction of rotation or translation.

In the given case, none of the supports resisting the rotation motion. So, summation of moments in all the supports will be zero.
The support D resisting all the translation motion.
So, reaction at D is ${\vec{R}}_{D}$ = $R_{D x} \hat{i} + R_{D y} \hat{j} + R_{D z} \hat{k}$
The support F can resist only in +Z direction.
So, reaction at F is ${\vec{R}}_{F}$ = R_Fz $\hat{k}$
The support E can resist in only +x and +z direction translation.
So, reaction at E is ${\vec{R}}_{E}$ = $R_{E x} \hat{i} + R_{E z} \hat{k}$

The force ${\vec{F}}_{1}$ = 250 $\hat{j}$ KN

The force ${\vec{F}}_{2}$ = $- 225 \hat{i} + 140 \hat{j} - 60 \hat{k}$ KN

Values of

a =1.84 m

b = 2.13 m

c =2.76 m

Coordinates of F = (0, 0, 0)

Coordinates of D = (b, 0, 0) = (2.13, 0, 0)

Coordinates of E = (0, a, 0) = (0, 1.84, 0)

Coordinates of C = (0, 0, c) = (0, 0, 2.76)

Coordinates of B = (b, a, c) = (2.13, 1.84, 2.76)

To determine, the reaction at D, E and F

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