How can I calculate a bar structure

Calculate beam structures with the FEM system MEANS V10. Homepage: Telephone:

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1 Calculate beam structures with the FEM system MEANS V10 Homepage: Telephone:

2 Chapter 14: Calculating beam structures with MEANS V10 1 Chapter 14: Calculating beam structures with MEANS V10 Example 1: Three-hinged frame A three-hinged frame cannot transfer any bending moments at nodes 1, 3 and 6 and is loaded with 10 kn in the Z direction. Calculate the internal forces with the bending, shear force and normal force curve. Entering the nodes Select the menu Switch on line mode or Switch on node mode to enter the nodes and bar elements interactively.

3 Chapter 14: Calculating beam structures with MEANS V10 2 Switching between line and node mode You can switch back and forth between node and line mode at any time by clicking on the node or lines tab. Entering the node points Now enter the following 6 node points in line mode, first set the 2D and XZ level for beam structures with the menu: Node 1: Click on New to create node 1, enter the coordinates x = 0 and z = 0 and choose Create Node. Node 2: Click on New to create node 2, enter the coordinates x = 2 and z = 4 and select Create node. Node 3: Click on New to create node 3, enter the coordinates x = 4 and z = 4 and select Create node.

4 Chapter 14: Calculating beam structures with MEANS V10 3 Node 4: Click on New to create node 4, enter the coordinates x = 6 and z = 4 and select Create node. Node 5: Click on New to create node 5, enter the coordinates x = 4 and z = 0 and select Create node. Node 6: Click on New to create node 6, enter the coordinates x = 4 and z = 4 and select Create node. Node display After the entry, the 6 nodes are displayed. If the nodes are displayed too small or too large, you can set them precisely with the Nodes tab and the Size menu. The overall view can be zoomed in or out with the wheel.

5 Chapter 14: Calculating beam structures with MEANS V10 4 Entering the beam elements Now connect the 6 nodes to 5 beam elements in line mode: Create beam element 1-2: Move the mouse pointer over node 1 so that it changes from black to red, select Starting point line SP to create the starting point. Then move the mouse over node 2 and use the end point line LP1 to create bar element 1.Create bar elements 2-3, 3-4, 4-5 and 5-6: Create the next 4 bar elements 2-3, 3 -4, 4-5 and 5-6 as described.

6 Chapter 14: Calculating beam structures with MEANS V10 5 Refine the beam model In Line mode, select the Refine side menu to create a beam model that is 8 times finer. The beam model now consists of 41 nodes and 40 beam elements

7 Chapter 14: Calculating beam structures with MEANS V10 6 Entering the load The frame is loaded at node 4 with -10 kn in the z-direction. Select the Create Nodal Load menu and Step 2: Create Nodal Load. In the next dialog box, enter the load value -10 in the z-direction with the node selection Click on individual nodes. Click on node 4, this is displayed in the select box. Select Generate there to generate the nodal load.

8 Chapter 14: Calculating beam structures with MEANS V10 7 Entering the boundary conditions The frame is supported at nodes 1 and 6 with an articulated fixed bearing. Select the Create Boundary Conditions menu and Step 2: Create Boundary Conditions. In the next dialog box, lock the degrees of freedom in the x, y and z directions and select the node selection Stretch rectangle and stretch a rectangle over nodes 1 and 6, these are displayed in the select box, there with Create the 6 boundary conditions produce.

9 Chapter 14: Calculating beam structures with MEANS V10 8

10 Chapter 14: Calculating beam structures with MEANS V10 9 Entering the beam joint At node 3 there is a bending joint that cannot transfer any bending moment there. Select the menu Create Boundary Conditions as well as Edit Beam Hinge and Create Beam Hinge. Select the joint at the first node for the beam element 3 and create a new and very short beam element 41 with the nodes 3-42 without bending stiffness.

11 Chapter 14: Calculating beam structures with MEANS V10 10 Enter material data Select the menu Edit FEM project and material data and select the material steel with material transfer from the menu material database. In line 1, change the modulus of elasticity from 2.1E + 11 N / m² to 2.1E + 8 kn / m². Since steel is preset, this menu can also be skipped if only internal forces are sought. Then select Generate bar profiles and select the profile IPE270 with generate bar profile for element group 1 from the profile database that can be expanded by yourself

12 Chapter 14: Calculating beam structures with MEANS V10 11 FEM analysis Select the menu FEM analysis and FEM analysis and use the MEANS solver to calculate the deformations, support reactions, the local M, V and N internal forces as well as the v .mises equivalent stresses.

13 Chapter 14: Calculating beam structures with MEANS V10 12 Result evaluation Select the menu Result evaluation with dialog box to graphically evaluate the internal forces and support forces. Select the following settings:

14 Chapter 14: Calculating beam structures with MEANS V10 13 Bending moment M BY Shear force Vz

15 Chapter 14: Calculating beam structures with MEANS V10 14 Normal force N Support forces in the z-direction

16 Chapter 14: Calculating beam structures with MEANS V10 15 Example 2: Rafters with wind load Calculate the M, V and N internal forces as well as deformations, support reactions and the equivalent stresses for the rafters under wind load. Calculation of the line loads in the x and z directions W 1 = 0.64 kn / m W 1X = W 1 * SIN 60 = kn / m W 1Z = - W 1 * COS 60 = kn / m (downwards) W 2 = 0.48 kn / m W 2X = W 2 * SIN 60 = kn / m W 2Z = - W 2 * COS 60 = kn / m (up)

17 Chapter 14: Calculating beam structures with MEANS V10 16 Entering the nodes Now enter the following 3 nodes in line mode, first set the XZ level for beam structures with the 2D and XZ level menu: Node 1: Click on New to create node 1, enter the coordinates x = 0 and z = 0 and choose Create node. Node 2: Click on New to create node 2, enter the coordinates x = 2 and z = 3.46 and select Create node. Node 3: Click on New to create node 3, enter the coordinates x = 4 and z = 0 and select Create node.

18 Chapter 14: Calculating beam structures with MEANS V10 17 Entering the beam elements Now create the following 2 beam elements in line mode: Beam element 1: Move the mouse pointer over node 1 so that it changes from black to red, select start point line SP to to generate the starting point. Then move the mouse over node 2 and create bar element 1 with the end point line LP1. Beam element 2: Move the mouse pointer over node 1 so that it is displayed in red, select start point line SP to create the start point . Then move the mouse over node 3 and create the beam element 2 with the end point line LP1.

19 Chapter 14: Calculating beam structures with MEANS V10 18 Refining the beam model In Line mode, select the Refine side menu to create a beam model that is 16x finer. The beam model now consists of 33 nodes and 32 beam elements:

20 Chapter 14: Calculating beam structures with MEANS V10 19 Entering the wind load The line loads W 1 and W 2 must first be converted into their x and z components. 4 load cases and a load case superposition with load case 5 are generated by adding up: load case 1 with W 1X = kn / m load case 2 with W 1Z = kn / m load case 3 with W 2X = 0.41 kn / m load case 4 with W 2Z = 0.24 kn / m load case 5 with W 1X + W 1Y + W 2X + W 2Y

21 Chapter 14: Calculating Beam Structures with MEANS V10 20 Create Load Case 1 In the node mode, select the Create node area menu and span a rectangle over the left half of the rafter. Create line load Select the menu Create line load and Step 3: Create line load and

22 Chapter 14: Calculate beam structures with MEANS V10 21 enter load case 1 with the load value in X-direction with the node selection all nodes displayed: The following node load with 17 node loads is generated:

23 Chapter 14: Calculating beam structures with MEANS V10 22 Displaying load values ​​With the icon, the loads with load values ​​can be optimally displayed on the screen. In addition, the color for the background or the model can be changed.

24 Chapter 14: Calculating beam structures with MEANS V10 23 Generate load case 2 Select the menu Generate line load and Step 3: Generate line load and output load case 2 with the load value in the Z direction with the node selection, all nodes displayed for the same node area Load case 1. The following nodal point load with 17 nodal loads is generated:

25 Chapter 14: Calculating beam structures with MEANS V10 24 Create load case 3 In the node mode, select the menu Create node area and create a new node area. Spread a rectangle over the right half of the rafter. Select the menu Generate line load and Step 3: Generate line load and enter load case 3 with the load value 0.41 in the X direction with the node selection all nodes displayed:

26 Chapter 14: Calculating Beam Structures with MEANS V10 25 Generate Load Case 4 Select the menu Generate Line Load and Step 3: Generate Line Load and enter Load Case 4 with the load value 0.41 in the Z direction with the node selection all nodes displayed for the same node area from load case 3:

27 Chapter 14: Calculating beam structures with MEANS V10 26 Create load case 5 Select the menu Edit FEM project and Loads, here you can display and edit the 4 load cases individually. To create load case 5, select the menu Add and copy load cases for load cases 1 4 and add each load case to the new load case 5 as shown below. Each load case can be multiplied by a factor before adding up using the Load case factor menu. After adding up the load cases, a node load with 66 load values ​​is obtained:

28 Chapter 14: Calculate beam structures with MEANS V10 27 Create boundary conditions Select menu Create boundary conditions and Step 2: Create boundary conditions to enter the floating support at node 1 and the fixed support at node 3. Select in the Z-direction and the node selection Rectangle as well as the button Create Rbs and stretch a rectangle over nodes 1 and 3 to enter a floating bearing in the Z-direction at this node.

29 Chapter 14: Calculating beam structures with MEANS V10 28 Enter fixed support with editor Select Edit FEM project and boundary conditions and set the number of boundary conditions to 4 and lock the FHGs in the X and Y directions in the new line 3 and line 4 with 1 and 2 to expand the floating bearing into a fixed bearing at node 3: The floating bearing at node 1 and fixed bearing at node 3 are displayed as follows: Enter material data and FEM analysis See previous example as the same entry.

30 Chapter 14: Calculating beam structures with MEANS V10 29 Result evaluation Select the menu Result evaluation with dialog box to graphically evaluate the internal forces, support forces, deformations and stresses.

31 Chapter 14: Calculating beam structures with MEANS V10 30 Bending moment M BZ Shear force V Z

32 Chapter 14: Calculating beam structures with MEANS V10 31 Normal force N deformations

33 Chapter 14: Calculating beam structures with MEANS V10 32 V-Mises node stresses Support forces in the Z-direction