Mode Shapes
Modal Time History Analysis (Periodic)
Click the File menu > New Model command to access the New Model form.
Click the drop-down list to set the units to 
.
Click the 2D Frame button 
to access the 2D Frames form. In that form:
Select Portal in the 2D Frame Type drop-down list.
Type 1 in the Number of Stories edit box.
Type 1 in the Number of Bays edit box.
Type 15 in the Bay Width edit box.
Click the + (plus) symbol beside the Beams or Columns drop-down list to access the Frame Properties form.
Click the Import New Property button to access the Import Frame Section Property form. Select Steel in the Frame Section Property Type drop-down list and click the I/Wide Flange button to access the Section Property File form.
Select the SECTIONS.PRO file and click the Open button to display a database form of available sections.
On the database form, click the + (plus) symbol beside the drop-down list to access the Define Materials form.
Highlight the A992Fy50 definition in the Materials display list and click the Modify/Show Material button to access the Material Property Data form.
Change the Units to 
.
Verify that the Modulus of Elasticity is 29000 and Poisson’s Ratio is 0.3.
Click the OK buttons on the Material Property Data and Define Materials forms to close the forms and return to the database form.
Ensure that the A992Fy50 definition is selected in the Materials drop-down list.
Scroll down the list of sections, and while holding down the Ctrl key, click on W8X48 and W12X26 to select them.
Click the OK button to close the database form and display the I/Wide Flange Section form.
Click the OK buttons on the I/Wide Flange Section and Frame Properties forms to return to the 2D Frames form.
Select the W12X26 section in the Beams drop-down list.
Select the W8X48 section in the Columns drop-down list.
Click the OK button on the Frame Properties form to close the form and display the template model in the program windows.
Click the “X” in the top right-hand corner of the 3-D View window to close it.
Select the joints labeled C and D in the problem statement.
Click the Assign menu > Joint > Masses command to access the Joint Masses form. In that form:
Type .02 in the Direction 1 edit box.
Type .02 in the Direction 3 edit box.
Click the OK button.
Click the Show Undeformed Shape button 
to remove the displayed joint mass assignments.
Select the joint labeled C in the problem statement.
Click the Assign menu > Joint Loads > Forces command to access the Joint Forces form. In that form:
Type 1 in the Force Global X edit box.
Click the OK button.
Click the Show Undeformed Shape button to remove the displayed joint force assignments.
Click the Define menu > Functions > Time History command to access the Define Time History Functions form. In that form:
In the Choose Function Type to Add area, click the drop-down list that reads Sine Function and then click on the User Function item.
Click the Add New Function button to access the Time History Function Definition form. In that form:
Accept the default FUNC1 Function Name.
Type .0 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .0625 in the Time edit box, type 10 in the Value edit box, and click the Add button.
Type .125 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .1875 in the Time edit box, type -10 in the Value edit box, and click the Add button.
Type .25 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Click the OK button to return to the Define Time History Functions form.
Click the Add New Function button to access the Time History Function Definition form. In that form:
Accept the default FUNC2 Function Name.
Type .0 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .125 in the Time edit box, type 10 in the Value edit box, and click the Add button.
Type .25 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .375 in the Time edit box, type -10 in the Value edit box, and click the Add button.
Type .5 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Click the OK button to return to the Define Time History Functions form.
Click the Add New Function button to access the Time History Function Definition form. In that form:
Accept the default FUNC3 Function Name.
Type .0 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .25 in the Time edit box, type 10 in the Value edit box, and click the Add button.
Type .5 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Type .75 in the Time edit box, type -10 in the Value edit box, and click the Add button.
Type 1 in the Time edit box, type 0 in the Value edit box, and click the Add button.
Click the OK buttons on the Time History Function Definition and Define Time History Functions forms to close all of the forms.
Click the Define menu > Load Cases command to access the Define Load Cases form. In that form:
Highlight (select) MODAL in the Case Name list and click the Modify/Show Case button to display the Analysis Case Data - Modal form. In that form:
Type 4 in the Maximum Number of Modes edit box.
Click the OK button to return to the Load Cases form.
Click the Add New Load Case button to access the Load Case Data - Linear Static form. In that form:
Accept the default Load Case Name, ACASE1.
Select Time History from the Load Case Type drop-down list.
In the Time History Motion Type area, select the Periodic option.
In the Loads Applied area, verify that FUNC1 is selected in the Function drop-down list and then click on the Add button.
In the Time Step Data area, type 25 in the Number of Output Time Steps edit box.
In the Time Step Data area, type .01 in the Output Time Step Size edit box.
Click the OK button to return to the Define Load Cases form.
Click the Add New Load Case button to display the Load Case Data - Linear Static form. In that form:
Accept the default Load Case Name, ACASE2.
Select Time History from the Load Case Type drop-down list.
In the Time History Motion Type area, select the Periodic option.
In the Loads Applied area, select FUNC2 from the Function drop-down list and click on the Add button.
In the Time Step Data area, type 50 in the Number of Output Time Steps edit box.
In the Time Step Data area, type .01 in the Output Time Step Size edit box.
Click the OK button to return to the Define Load Cases form.
Click the Add New Load Case button to access the Load Case Data form. In that form:
Accept the default Load Case Name, ACASE3.
Select Time History from the Load Case Type drop-down list.
In the Time History Motion Type area, select the Periodic option.
In the Loads Applied area, select FUNC3 from the Function drop-down list and click on the Add button.
In the Time Step Data area, type 100 in the Number of Output Time Steps edit box.
In the Time Step Data area, type .01 in the Output Time Step Size edit box.
Click the OK buttons on the Load Case Data and Define Load Cases forms to close all forms.
Click the Analyze menu > Set Analysis Options command to access the Analysis Options form.
In that form click the Plane Frame XZ Plane button 
to set the available degrees of freedom.
Click the OK button.
Click the Run Analysis button 
to display the Set Load Cases to Run form. In that form:
Verify that the DEAD load case is set to Run in the Action list.
Verify that the MODAL load case is set to Run in the Action list.
Verify that the ACASE1 load case is set to Run in the Action list.
Verify that the ACASE2 load case is set to Run in the Action list.
Verify that the ACASE3 load case is set to Run in the Action list.
Click the Run Now button to run the analysis.
When the analysis is complete, check the messages in the SAP Analysis Monitor window (there should be no warnings or errors). Note in the messages that the first mode period is about 0.5 second. Click the OK button to close the window. Note again in the window title on the screen that the first mode period is about 0.5 second.
Select the joint labeled D in the problem statement.
Click the Display menu > Show Tables command to access the Choose Tables to Display form. In that form:
Click on the Select Load Cases button to access the Select Load Cases form. In that form:
Click the Clear All button.
Click on the ACASE1 case to highlight it.
Hold down the shift key on the keyboard and click on the ACASE3 case. The ACASE1, ACASE2, and ACASE3 cases should all be highlighted (selected) now.
Click the OK button to close the form.
In the ANALYSIS RESULTS area, click on the + (plus) associated with the Joint Output item to display the Displacements item.
Click the + (plus) associated with Displacements item to display the Table: Joint Displacements and Table: Joint Displacements (Absolute) items.
Click on the Table: Joint Displacements and Table: Joint Displacements (Absolute) items.
Click the OK button to display the Joint Displacements form.
Note that the maximum displacement occurs for ACASE2, as would be expected because the period of Function 2 is close to the first mode period of the structure.
Click the Done button to close the table.
We have viewed the envelopes of the joint displacement at joint D. Now we will view the time histories of the displacement.
Click the Display menu > Show Plot Functions command to access the Plot Function Trace Display Definition form. In that form:
Click the Define Plot Functions button to access the Plot Functions form. In that form:
Highlight Joint 4.
Click the Modify/Show Plot Function button to access the Joint Plot Function form. In that form:
Verify that the Displ option is selected in the Vector Type area.
Verify that the UX option is selected in the Component area.
Click the OK button on the Joint Plot Function and Plot Functions form to return to the Plot Function Trace Display Definition form.
Verify that ACASE1 is selected in the Load Case drop-down list.
Click on Joint 4 in the List of Functions list box to select it.
Click the Add button to move Joint 4 to the Vertical Functions list box.
Click the Display button to display the time history.
Click the OK button to close the time history display and return to the Plot Function Trace Display Definition form.
Select ACASE2 in the Load Case drop-down list.
Click the Display button to display the time history.
Click the OK button to close the time history display and return to the Plot Function Trace Display Definition form.
Select ACASE3 in the Load Case drop-down list.
Click the Display button to display the time history.
Click the OK button to close the time history display and return to the Plot Function Trace Display Definition form.
Click the Done button to close the Plot Function Trace Display Definition form.