S15-1 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation SECTION 15 RESPONSE/SHOCK SPECTRUM ANALYSIS

S15-2 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation

S15-3 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation RESPONSE SPECTRUM METHOD n A response spectra depicts the maximum response of an SDOF oscillator, u i max, as a function of its natural frequency, f i, for a given base excitation, u B (t). u B (t) t u 3 (t) t => u 3 max

S15-4 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n A response spectra is used to provide the maximum response of each of the modes of a structural model. n The (net) response of the structural model is estimated by combining, using various methods, the maximum modal responses. This method, response spectrum, is approximate. RESPONSE SPECTRUM METHOD (Cont.)

S15-5 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n A response spectra curve is created for several values of damping. This is necessary to provide the maximum values of modal response. * Oscillator damping; fraction of critical. CurveDamping (*) 10% 23% 35% RESPONSE SPECTRUM METHOD (Cont.)

S15-6 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation MAXIMUM AND RELATIVE RESPONSE n In addition to determining the maximum absolute displacement response of each oscillator from u i (t), u i max, the maximum relative displacement between each oscillator and the base (a point on the vibrating structure) is computed, u ri max. n Maximum relative velocity and absolute acceleration are approximately related to the maximum relative displacement by the following expressions. n For design, useful variables are u r, u r, u. Design spectra are usually in terms of these variables.... max

S15-7 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation SDOF RESPONSE TO 4 HZ SINE PULSE

S15-8 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation SDOF RESPONSE TO 4 HZ SINE PULSE (Cont.)

S15-9 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n Response spectra capability u Create a response spectra u Use a response spectra to estimate the response of a structure n Create a response spectra by determining the response of a large structure with its small attached structures, e.g. motor with pump. n A response spectra is created, as previously described, by forcing a set of SDOF oscillators to move with the motion of the large structure, at the location where the small attached structure is to be placed, u B (t). The maximum response of each SDOF oscillator is determined from its transient response, u i (t). The base motion u B (t) of the oscillators is obtained from the force or base excitation applied to a substantially larger structure, i.e. building, earth. u Example -- a power plant experiences movement due to an earthquake. Response spectra are calculated for the locations of the floors/levels where mechanical equipment/components (i.e. machinery, piping systems) will be located. The response spectra are then used in the design of the equipment. CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LARGE STR

S15-10 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n An implicit assumption is that a small attached oscillators mass is very small relative to the larger mass of the base structure. Therefore, no dynamic interaction occurs between the base structure and the attached small oscillator. n The transient response calculated for selected degrees-of- freedom of the model can be used as the input time history (base excitation, e.g. u B (t)) for the generation of response spectra curves. n Response spectra may be generated using any transient solution method. u Direct Transient (SOL 109 in MSC.Nastran) u Modal Transient (SOL 112 in MSC.Nastran) n Additional information is in the MSC.Nastran Advanced Dynamics Users Guide. CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LG STR (Cont.)

S15-11 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LG STR (Cont.) n Determine the transient response of a model with an attached small structure (e.g. attached appendage) u The structure can be excited by a force or an enforced motion u SOL 109, SOL 112 n Executive Control Section u SOL 109 u Example

S15-12 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n Case Control Section u OUTPUT(XYPLOT) u XYPLOT DISP SPECTRAL (compute a displacement spectra) u XYPUNCH DISP SPECTRAL (create a file containing the spectra data) l Example n XYPUNCH ACCELERATION SPECTRAL 1/1 (T1RM) This command causes the creation of a.pch file with a set of absolute (RM) acceleration spectra data. They are based on record number (RECNO) 1 of the DTI,SPSEL Bulk Data entry. This is for DOF Grid 1 X(T1) direction. For T1IP, IP refers to relative response spectra. u Example l Must include both DISPLACEMENT and VELOCITY requests CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LG STR (Cont.)

S15-13 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LG STR (Cont.) n Bulk Data Section u PARAM, RSPECTRA, 0 – used to request calculation of spectra u DTI, SPSEL – used to specify the spectral frequency and damping tables, and the Grids for which spectra will be calculated u FREQ – used to specify damping ratios, that are fraction of critical, for the creation of the spectra u FREQ1 – used to specify the frequencies at which the spectra ordinate value will be calculated

S15-14 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CREATE RESPONSE SPECTRA FROM TRANSIENT ANALYSIS OF LG STR (Cont.) n Bulk Data Section (continued) u Example

S15-15 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Rectangular plate with an appendage u 5 x 2 Aluminum plate, clamped along one edge u Beam appendage at end of plate u Transient enforced motion at clamped edge in the Z-direction

S15-16 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Rectangular plate properties u 5 in x 2 in Aluminum plate u Thickness of 0.1 in u Elastic modulus of 10.0 x 10 6 psi u Poisson ratio of 0.3 u Density of lbm/in 3 = x lbf*sec 2 /in 4 n Beam appendage properties u 0.05 in x 0.05 in cross-section Aluminum beam u Length (in X- and Y- direction) of 0.5 in u Elastic modulus of 10.0 x 10 6 psi u Poisson ratio of 0.3 u Density of lbm/in 3 = x lbf*sec 2 /in 4 u Attached to plate at end opposite clamped end of plate

S15-17 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Damping u Structural damping l Coefficient, g, is 0.06 l Instead of using structural damping, must use equivalent viscous damping at 250 Hz. n SOL 109, direct transient response method

S15-18 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Displacement enforced motion at clamped edge in the Z-direction u where Node i = 1, 12, 23, 34, 45

S15-19 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Create the model in MSC.Patran u Geometry, surface and curve u Mesh the surface and curve u Equivalence the nodes u Create a time dependent load case u Create a non-spatial field for the enforced motion u Constrain one short edge of the plate model, using the field u Create material property set u Create element property sets u Write the MSC.Nastran input file, e.g. jobname.bdf u Edit the MSC.Nastran input file, including the entries that are needed to calculate the response spectra (see following pages) u Perform the MSC.Nastran analysis u View the analysis results

S15-20 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Edited MSC.Nastran input file u File name is create_response_spectra.bdf

S15-21 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Edited MSC.Nastran input file (continued)

S15-22 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Edited MSC.Nastran input file (continued)

S15-23 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Transient results displayed using MSC.Patran

S15-24 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: CREATE RESPONSE SPECTRA n Three response spectra in the.pch file

S15-25 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation RESPONSE SPECTRUM ANALYSIS METHOD n Approximate transient. The base excitation (input) response spectra ordinate values are used to determine the exact peak response of each mode. n These peak modal responses are combined to obtain the system (net) response u The only problem is that the peak value for the modes occur, in general, at different times. n Three methods of combining the modal responses are available. They are ABS, SRSS, and NRL.

S15-26 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n A model of the structure to be analyzed is created with the input points identified as SUPORT DOFs. n A large mass (usually 10 3 to 10 6 times the total structural mass) is attached to the SUPORT DOFs. n System modes are obtained for the model (including the 0.0 Hz modes) with the SUPORT DOFs unconstrained. n This approximates the cantilevered modes of the model attached to the exciting structure. RESPONSE SPECTRUM ANALYSIS METHOD (Cont.)

S15-27 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n The 0.0 Hz modes approximate the static motion the model experiences when the supporting structure moves statically. n Participation factors (PF) are calculated using the following expression. where [ is the matrix of fixed base elastic modes [M] is the mass matrix [D m ] contains the rigid body modes (0.0 Hz ) n The PF are used in conjunction with a base excitation response spectra to calculate the peak response of each mode. RESPONSE SPECTRUM ANALYSIS METHOD (Cont.)

S15-28 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n Data recovery quantities (displacements, stresses, forces, etc.) are then calculated for each mode based on its peak motion. n These modal quantities are then combined using one the available methods -- ABS, SRSS, and NRL. n The relative displacement response of a single degree- of-freedom oscillator, u ri (t) due to a base motion, u B (t), is calculated as follows n The (net) transient response in physical space (response is calculated by summing over the modes) is exactly RESPONSE SPECTRUM ANALYSIS METHOD (Cont.)

S15-29 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation ABS option where k corresponds to a physical degree-of-freedom i corresponds to a mode RESPONSE SPECTRUM ANALYSIS METHOD (Cont.)

S15-30 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation SRSS option where the average peak modal coordinate,, is given by NRL option where is > for all RESPONSE SPECTRUM ANALYSIS METHOD (Cont.)

S15-31 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Perform a response spectrum analysis using the beam appendage model, that is attached to the plate model, and the response spectra calculated during the previous case study. Enforced motion at Node 57

S15-32 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Edited MSC.Nastran input file u File name is response_spectrum_analysis.bdf u Specify SOL 103 as the solution sequence u Specify the desired output

S15-33 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Edited MSC.Nastran input file (continued) u Must specify the output to go to the.op2 file u The Bulk Data portion of the appendage model can be in a separate file, INCLUDE appendage.bdf

S15-34 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Edited MSC.Nastran input file (continued)

S15-35 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Edited MSC.Nastran input file (continued)

S15-36 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Edited MSC.Nastran input file (continued)

S15-37 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation n MSC.Nastran Bulk Data for appendage model u File name is appendage.bdf CASE STUDY: RESPONSE SPECTRUM ANALYSIS

S15-38 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Response spectrum analysis results in.f06 file u File name is response_spectrum_analysis.f06

S15-39 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Response spectrum analysis in.f06 file (continued)

S15-40 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Response spectrum analysis in.f06 file (continued)

S15-41 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: RESPONSE SPECTRUM ANALYSIS n Read the.op2 file into MSC.Patran n Display results, i.e. displacement, bending stress

S15-42 NAS122, Section 15, August 2005 Copyright 2005 MSC.Software Corporation EXERCISE Workshop 20 Create Response Spectra for Tower Subjected to an Earthquake in your exercise workbook. Workshop 21 Response Spectrum Analysis for Equipment Mounted on Tower in your exercise workbook.