A seven-story 2D frame structure is subjected to static lateral loads, static vertical loads and dynamic (seismic) lateral loads. The dynamic loads are represented by a response spectrum. The analysis is performed for two independent static load cases and one dynamic load case. Load combinations are generated to combine the static load cases with the dynamic load condition.

Determine the displacements and element forces for all static and dynamic load conditions. Also, determine the mode shapes and natural frequencies of the structure.

The 2-D model consists of 24 joints and 35 beam elements. This is plane frame problem. The translational displacement in Global Z-direction and rotations about Global X and Y-directions are deleted from the model. The joints 1, 2 and 3 are fixed supports.

The material property data is given:

Modulus of Elasticity = 29,500 ksi

and sectional property data:

Area = 51.17 in2 Izz = 2150 in4 Designation = S1

Area = 62.10 in2 Izz = 2670 in4 Designation = S2

Area = 72.30 in2 Izz = 3230 in4 Designation = S3

Area = 84.40 in2 Izz = 3910 in4 Designation = S4

Area = 50.00 in2 Izz = 3330 in4 Designation = S5

Area = 50.00 in2 Izz = 4020 in4 Designation = S6

Area = 50.00 in2 Izz = 5120 in4 Designation = S7

In the reference, to reduce the size of the system of equations, the lateral (X) displacements of the exterior columns have been constrained to the lateral (X) displacements of the middle column at each corresponding level. This eliminates all axial deformations in the beams. The Master/Slave option in LARSA is used to produce a model similar to Ref [2] for the comparison of the results.

The primary load cases are defined as:

LoadCase	Type	Load Case Definition
1	STATIC	STATIC VERTICAL LOADS
2	STATIC	STATIC LATERAL LOADS
3	RSA	LATERAL DYNAMIC LOADS

The combined (factored) load cases are:

Comb Case	(Primary Load Case x Contribution Factor)
1	(Case 1 x 1.00) + (Case 2 x 1.00)
2	(Case 1 x 1.00) + (Case 3 x 1.00)
3	(Case 1 x 1.00) + (Case 3 x -1.00)

The load combination 1 combines the static vertical and lateral loads. The load combination 2 combines the static vertical load condition with the dynamic load condition. The load combination case 3 combines the static vertical load case with the dynamic load case with the signs reversed.

Load Case 1 (Static Vertical Loads):

The static vertical load is applied on all horizontal beam elements 22 to 35 and it consists of:

Uniform Load W = 0.1 kip/ft (0.008333 kip/in)

Point Load P = 20 kips @ 10 ft from the I-end of the beam

Point Load P = 20 kips @ 20 ft from the I-end of the beam

Load Case 2 (Static Lateral Loads):

In load case 2, the static horizontal loads are applied at each level as joint loads. The joint loads are entered for joints 4, 7, 10, 13, 16, 19 and 22 acting in the X-direction.

Fx = 2.5 kips @ joint 4

Fx = 5.0 kips @ joint 7

Fx = 7.5 kips @ joint 10

Fx = 10 kips @ joint 13

Fx = 12.5 kips @ joint 16

Fx = 15 kips @ joint 19

Fx = 20 kips @ joint 22

Load Case 3 (Seismic Loads):

This load case is defined for RSA (Response Spectra Analysis). The complete quadratic combination (CQC) method of modal combination is selected. The seismic response spectrum table is applied in X-direction with a factor of 1.00. The critical damping ratio of 0.05 is used. The spectrum table is defined using frequency versus acceleration normalized with respect to g

In the Reference, a typical story mass of 0.49 kip-sec2/in has been used in the lateral direction (X) and each floor mass has been assigned to the joints on the exterior columns. To obtain similar effect, we will apply 0.49 kip-sec2/in as the mass in the horizontal direction (X) at joints 4, 7, 10, 13, 16, 19, 22.

Seismic Response Spectrum Data are given as Frequency versus Accelaration and normalized in Gravitation g (386.4):

0.5000	0.160189	0.7855	0.258617	1.0000	0.482251
1.5000	0.641750	2.0000	1.046620	2.3186	0.921167
2.5000	.882996	3.0000	0.880624	3.5000	0.718264
4.0000	0.798052	4.1322	0.704753	4.5000	0.746135
0.5000	0.160189	0.7855	0.258617	1.0000	0.482251
5.5000	0.943909	6.0000	0.787220	6.2422	0.804605
6.5000	0.905796	7.0000	0.636531	7.5000	0.665413
8.0000	0.627807	8.4034	0.588211	8.5000	0.572438
9.0000	0.523663	9.5000	0.564412	10.000	0.581609
10.500	0.530631	10.515	0.527825	11.000	0.477599
11.500	0.493366	12.000	0.518093	12.500	0.520045
12.579	0.519598	13.000	0.505311

Procedure for Analysis:

First the analysis is performed for the static load cases using the Linear Static Analysis option of LARSA. For the static analysis, the program automatically considers only the static load cases.

The next step is to return to the preprocessor and request Unstressed Eigenvalue Analysis for 7 mode shapes. You must select Keep Previous Results option from the Run dialog box to keep the results from static analysis run.

After eigenvalue analysis, return to the preprocessor and request Response Spectra Analysis. The spectrum table for this problem is provided in a file with filename RSATBL03. Use this file as the file for response spectrum data.

All the results from static, eigenvalue and response spectra analysis are in the postprocessor.

Tested Features

Reference

"Static and Dynamic Analysis of Multistory Frame Structure Using DYNAMIC/EASE2," Engineering Analysis Corporation and Computers/Structures International.

Sources

"SAP90, A Series of Computer Programs for the Finite Element Analysis of Structures. Verification Manual", Computers & Structures, 1992.
LARSA 4D

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