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
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NCA=
kN
unanswered
E4_1B
Obtain the numerical value (in kN) of the reactions at the supports.
RAy=
kN
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RCx=
kN
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RCy=
kN
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E4_1C
Obtain the numerical value (in kN/m) of the stiffness of bar CA .
KCA=
kN/m
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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:
To obtain the axial forces in the bars and reactions at the supports using the method of joints, follow these steps:
Step 1: Draw the free body diagram of the entire truss ABCDE, including all the external forces and reactions at the supports. Label the known forces and distances on the diagram.
Step 2: Choose a joint where only two non-collinear members are connected. In this case, joint A meets this criterion.
Step 3: Isolate the selected joint A and draw the free body diagram of the joint. Show all the forces acting on the joint, including the forces in the members and the reactions at the supports.
Step 4: Resolve all the forces acting on the joint into horizontal and vertical components. Assign unknown forces in the members as positive or negative vectors, depending on the assumed direction of force.
Step 5: Apply the equations of equilibrium to the joint. Sum up the horizontal and vertical forces separately and set them equal to zero.
Step 6: Solve the resulting equations to find the unknown forces in the members and the reactions at the supports.
Step 7: Repeat steps 2 to 6 for each joint in the truss until all the member forces and reactions at the supports are determined.
Step 8: Verify the results by checking the equilibrium of each joint and ensuring that the forces in the members meet the assumptions made during the analysis.
Following these steps will enable you to obtain the axial forces in the bars and reactions at the supports using the method of joints for the given truss.