Use Of Approximate Method Trusses - Lecture Notes
CHAPTER 5Approximate Analysis of Indeterminate StructuresObjectives Portal method Cantilever methodUse of approximate method The analysis of this model is known as an approximateanalysis The preliminary design of the members can be made After which, the more exact indeterminate analysis can beperformed & the design refinedUse of approximate method The analysis when using a model must satisfy both theconditions of: Equilibrium Compatibility of displacements at joints For an initial design, member sizes are not known &statically indeterminate analysis cannot be done A simpler model must be developed,i.e., a staticallydeterminate analysisTrusses The truss used for lateral bracing of a building is notconsidered a primary element It will therefore be analysedusing approximate methods Hence, the truss isindeterminate to the thirddegree
Trusses 3 assumptions must be made in order to reduce the trussto one that is statically determinate Assumptions may be made in regards with the following: When 1 diagonal in the panel is in tension, thecorresponding cross diagonal will be in compression\ Two methods of analysis are generally acceptable: Method 1 If the diagonals are intentionally designed to be long &slender, it is reasonable to assume they cannot supportcompression force Otherwise, they may easily buckle Hence, the compressive diagonal is assumed to be zeroforce memberExample 1Determine (approximately) the forces in themembers of the truss.Trusses Method 2 If the diagonals are intended to be constructed fromlarge rolled sections such as angles or channels, theymay be equally capable of supporting a tensile &compressive force We will assume that tension & compression diagonalseach carry half the panel shearExample 1 cont’d
Example 1 cont’dVertical loads on building frames Building frames often consist of girders that are rigidlyconnected to columns This is to allow the structure to better able to resist theeffects of lateral forces One technique would be to consider only the memberswithin a localised region of the structure This is possible if the deflections of the members withinthe region caused little disturbance to the membersoutside the structure The approximate location of the points of inflection can bespecified These points are zero momentsVertical loads on building frames Assumptions for approximate analysis The column supports at A & B will each exert 3reactions on the girder The girder will be statically indeterminate to the thirddegree 3 assumptions would be needed to perform anapproximate analysisVertical loads on building frames Assumptions for approximate analysis If the columns are stiff, no rotation at A & B will occur However, if the column connections at A & B are veryflexible, then zero moments will occur at the supports In reality, the columns willprovide some flexibilityat the supports
Vertical loads on building frames Assumptions for approximate analysis Therefore, point of zero moment occurs at the averagepoint between the two extremes(0.21L 0) / 2 0.1L from each supportExample 2 Determine (approximately) the moment at thejoints E and C caused by members EF and CD ofthe building bent.Vertical loads on building frames Assumptions for approximate analysis The 3 assumptions are: There is zero moment in the girder, 0.1L from the leftsupport There is zero moment in the girder, 0.1L from the rightsupport The girder does not support an axial forceExample 2 cont’d
Portal Frames & Trusses Portal frames are used to transfer horizontal forces appliedat the top of frame to the foundation Portals can be pin supported, fixed supported orsupported by partial fixityExample 3Determine by approximate methods the forcesacting in the members of the Warren portal.Portal Frames & Trusses We analyse the trussed portals using the sameassumptions as those for simple portal frames For pin-supported column, assume horizontal shear areequal For fixed-supported column, assume horizontal reactionsare equal and an point of inflection occurs on each column,midway between base of column & the lowest point oftruss member connection to columnExample 3 cont’d
Example 3 cont’dLateral loads on building frames:Portal method A building bent deflects in the same way as portal frame Each bent of the frame can be considered as a series ofportals The interior columns would represent the effect of 2 portalcolumns & would carry 2x the shear V as the exteriorcolumnsExample 3 cont’dLateral loads on building frames:Portal method The portal method for analyzing fixed supported buildingframes requires the following assumptions: A hinge is placed at the center of each girder A hinge is placed at the center of each column At a given floor level, the shear at the int column hingesis 2x that at the ext column hinges These assumptions provide an adequate reduction of theframe to one that is statically determinate and yet stableunder loading This method is more suitable for buildings having lowelevation and uniform framing
Example 4Example 4 cont’dDetermine (approximately) the reactions at the baseof the columns of the frame. Use the portal methodof analysis.Example 4 cont’dLateral loads on building frames:Cantilever method This method is based on the same action as a longcantilevered beam subjected to a transverse load This causes a bending stress that varies linearly from thebeam’s neutral axis In a similar manner, the lateral loads on a frame tends to tipthe frame over or cause a rotation about a neutral axis lyingin the horizontal plane that passes through the columns ateach floor level
Lateral loads on building frames:Cantilever method To counter this, the axial forces in the columns will betensile on one side of the neutral axis & compressive onthe other side It is reasonable to assume this axial stress has a linearvariation from the centroid of the neutral axis This method is appropriate if the frame is tall & slenderor has columns with different x-sectional areasExample 5Determine (approximately) the reactions at the baseof the columns of the frame. Use the cantilevermethod of analysis.Lateral loads on building frames:Cantilever method The following assumptions apply for a fixed support frame A hinge is placed at the center of each girder A hinge is placed at the center of each column The axial stress in a column is proportional to itsdistance from the centroid of the cross-sectional areasof the columns at a given floor level Since stress force per area, then in the case of equalcross-sectional areas, the force in a column isproportional to its distance from the centroid These assumptions reduce the frame to one that is bothstable & statically determinateExample 5 cont’d
Example 5 cont’dExample 5 cont’d
CHAPTER 5 Approximate Analysis of Indeterminate Structures Objectives Portal method Cantilever method Use of approximate method The analysis when using a model must satisfy both the conditions of: Equilibrium Compatibility of displacements at joints For an initial design, member sizes are not known & statically indeterminate analysis cannot be done
TYPES OF STEEL ROOF TRUSSES SheelaMalik AP (Civil) GITAM Kablana. Roof Trusses . Types of Roof Truss Pitched roof trusses Parallel chord trusses Trapezoidal trusses. . This allows for efficient design,since the short membersareundercompression. However, the windupliftmaycausereversalof .
Cutting blocks to nail between trusses is another important step to complete before you start setting trusses. In seismic and high-wind areas, code requires blocking between trusses at the plates and often at the ridge as well. I cut 221 2-in. blocks to maintain the Trusses gain their strength from light-weight components assembled in triangu-
b) Measure trusses for the correct pitch, span and any special details. c) Check for damage, broken members, loose plates, etc. 2. Erection Procedure, a) Mark the bearing plates on both walls to the required spacing of trusses, (Normally 24" O/C). b) Hoist the trusses to the roof level, taking care not to bend or twist the trusses.
wood trusses. The versatility of wood trusses makes it an excellent roof framing system in hybrid construction where wood trusses are commonly used with steel, concrete or masonry wall systems. Environmental: Wood, the only renewable building material, has numerous environ-mental advantages. Wood trusses enhance wood's environmental
2. Analyse indeterminate trusses by approximate methods. 3. Analyse industrial frames and portals by approximate methods. 35.1 Introduction In module 2, force method of analysis is applied to solve indeterminate beams, trusses and frames. In modules 3 and 4, displacement based methods are discussed for the analysis of indeterminate structures.
EPA Test Method 1: EPA Test Method 2 EPA Test Method 3A. EPA Test Method 4 . Method 3A Oxygen & Carbon Dioxide . EPA Test Method 3A. Method 6C SO. 2. EPA Test Method 6C . Method 7E NOx . EPA Test Method 7E. Method 10 CO . EPA Test Method 10 . Method 25A Hydrocarbons (THC) EPA Test Method 25A. Method 30B Mercury (sorbent trap) EPA Test Method .
Using approximate methods to analysestatically indeterminate trusses and frames The methods are based on the way the structure deforms under the load Trusses Portal frames with trusses Vertical loads on building frames Lateral loads on building frames – Portal method – Cantilever method
J’ai commencé à apprendre la guitare. Ma copine a choisi d’étudier le théâtre l’année prochaine. J’ai oublié d’acheter un cadeau d‘anniversaire pour ma sœur. Use of comparative and superlative of adjectives and adverbs such as: Je trouve l’espagnol plus facile que le français. Ma meilleure copine est plus petite que moi. La physique est la matière la plus difficile .
