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A load W=2 kN is applied vertically to joint C of truss ABCDE as indicated. You will use the method of joints to obtain the axial forces in the bars and reactions at the supports A, E .

E4_1?

All the bars in truss ABC have constant cross section and are made of a homogeneous linear elastic material. Under the effect of a 1 kN horizontal load applied at B , the pin at A is observed to displace to the right by 6 cm.

Use the method of joints to obtain the numerical value (in kN) of the axial forces in the bars.

NAB=

kN

unanswered

NBC=

kN

unanswered

NCA=

kN

unanswered

E4_1B

Obtain the numerical value (in kN) of the reactions at the supports.

RAy=

kN

unanswered

RCx=

kN

unanswered

RCy=

kN

unanswered

E4_1C

Obtain the numerical value (in kN/m) of the stiffness of bar CA .

KCA=

kN/m

unanswered

E4_2: SOLVING TRUSSES WITH MATLAB PART 1: SELECT DEGRESS OF FREEDOM

All the bars of the truss in the figure below have a cross-sectional area of 10 mm2 . We want to determine the axial forces in each of the bars and the Cartesian components of the reactions at supports C and D using the method of joints.

We will soon use MATLAB to solve this problem, but first we need to identify the "free" and the "constrained" degrees of freedom (DOFs) of the joints of the truss. Because this is a 2D problem in the x-y plane, each joint of the truss can only have two (Cartesian) DOFs (i.e., the joint can move only along x and along y). Some joints are hinges directly attached to the wall. These joint/hinges (like joint C in the example above) cannot freely move when the truss is loaded, because the wall prevents it: these DOFs are "constrained". In contrast, a joint like A is not attached directly to the wall, so it is free to move in both Cartesian directions: its DOFs are unconstrained or "free".

For each component below, select "Free" if it is unconstrained and "Fixed" if it is constrained.

Joint A , x component

FreeFixed

Joint A , y component

FreeFixed

Joint B , x component

FreeFixed

Joint B , y component

FreeFixed

Joint C , x component

FreeFixed

Joint C , y component

FreeFixed

Joint D , x component

FreeFixed

Joint D , y component

FreeFixed

Joint E , x component

FreeFixed

Joint E , y component

FreeFixed

A load W=2 kN is applied vertically to joint C of truss ABCDE as indicated. You will use the method of joints to obtain the axial forces in the bars and reactions at the supports A, E .

We start with the classification of the degrees of freedom as "free" or "constrained".

From the geometry of the truss, we see that we have:

Free DOF x and y at B, C, and D.

Constrained DOF x and y at A and E .

Question 1: Use MATLAB to find the axial forces in the bar.

Order the vector {X} of unknown axial forces in the bars as:

I obtained,

X =

4.00

2.00

-2.82

2.00

-2.82

-2.00

but is incorrect, can someone help me please?