Lecture6 True

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Lecture 6 - Flexure

September 13, 2001

CVEN 444


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Lecture Goals

Class Project Structures Basic Concepts

Rectangular Beams


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Class Project

The structural floor plan of a three-story(ground floor, two suspended floors, anda roof) office building is shown on the

next page. The roof covers the holeused for the elevator shaft and stairwells.The new building will be located inHouston, Texas. The floor systemsconsist of one-way pan joists slabs

supported in one direction by beamslocated on column lines A through F. Inaddition, beams are located on columnlines 1 and 4 as part of the lateral forceresisting system .

0.75L

0.75L

0.75L

0.75L

0.75L

L0.85LL

A

D

E

1 2 3 4

1 1

Pan joist -ribdirection(typ)

C2

2

Plan

View

B

F

Hole forElevatorshafts andstairwells

2 2


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Class Project

The design loads for the floor (inaddition to the self-weight) include asuperimposed dead load (SDL) of 20 psfto account for moveable partitions,ceiling panels, etc. and a superimposedlive load (LL) to be determined fromASCE 7-95. In addition, a 0.5 kip/ft.wall load is applied around the building

perimeter. The design loads for the roof(in addition to the self-weight) include asuperimposed dead load (SDL) of 10

psf.

0.75L

0.75L

0.75L

0.75L

0.75L

L0.85LL

A

D

E

1 2 3 4

1 1

Pan joist -ribdirection(typ)

C2

2

Plan

View

B

F

Hole forElevatorshafts andstairwells

2 2


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Class Project

Follow detailed instructions on separate assignmentsheets!!!


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0.75L

0.75L

0.75L

0.75L

L0.85LL

A

D

E

1 2 3 4

1 1

Pan joist - rib

direction(typ)

C2

2

Plan View

B

F

0.75L

Hole forElevator shaftsand stairwells

2 2

Class Project


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Class ProjectThe Joist detail for section 1-1

The beam detail for section 2-2


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Class ProjectTeam Performance

It is expected that all assignments related to the project will be done in teams.Each assignment must contain computations that are initialed by thecalculators (or originators) and initialed by the checker(s) . Members of theteam will rotate between calculation and checking tasks. It is recommendedthat two persons calculate for each assignment (i.e., In a four-person team,two persons should provide calculation services on odd numberedassignments and checking services on even number assignments. In a three-

person team, each person should rotate so that they are checking every thirdassignment.) Those not performing calculations are responsible for

checking them and must be afforded ample time to thoroughly check thecalculations. If revisions are necessary, those performing thecalculations must make the corrections. Each sheet must be initialed bythe originator and checker. A cover sheet with the signature of each teammember must be included with each assignment. Assignments that are not

signed or initialed by all team members will not be accepted.


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Class Project

Peer Evaluation

Peer evaluation is a common practice in the engineering community. Criticalevaluation is a necessary component of improving the engineering

profession. It is generally believed that honors and awards granted by peersare the highest possible honors. After all, it is our peers who know best whatis required to do an adequate, good, or outstanding job. Your individual

project grade will depend on an evaluation by your peers at the end of thesemester. The evaluation form will have a format similar to the one providedon the back of this sheet. Evaluation forms will also be collected during themiddle of the semester for an unofficial assessment of group performance.


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Class Project


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Class of Structures


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Class of Structures


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Class of Structures


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Class of Structures

Retaining Wall Abutment


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Class of Structures

Deformed Frame

Reinforced Frame


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Flexural StressThe beam is a structural memberused to support the internalmoments and shears. It would becalled a beam-column if acompressive force existed.

C = T

M = C*(jd)

= T*(jd)


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Flexural Stress

The stress in the block is defined as:

s = ( M*y) / I

Sxx = I / (y max)

The equation for Sxx modulus forcalculating maximum compressivestress .


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Flexural Stress

There are 5 stages the concrete through which the beam goes.

Stage 1: No external loadsself weight.

Stage 2: the external load Pcause the bottom fibers toequal to modulus of ruptureof the concrete. Entire

concrete section waseffective, steel bar at tensionside has same strain assurrounding concrete.


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Flexural Stress


Stage 3: The tensile strengthof the concrete exceeds therupture f r and cracksdevelop. The neutral axisshifts upward and cracksextend to neutral axis.Concrete loses tensilestrength and steel startsworking effectively andresists the entire tensile load.


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Flexural Stress


Stage 4: The reinforcementyields.

Stage 5: Failure of the beam.


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Flexural Stress

The three stages of the beam.

Stage 1: No externalloads acting on the beam.

Stage 3: Service loadingon the beam.

Stage 5: Beam failure.


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Flexural StressThe moment-curvature diagramshow the five stages of the

beam . The plot is of thecurvature angle, f , verse themoment.

f = (e / y) = [ s / E ] / y

= [(My /I) / E] / y

f = M / ( E I )


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Flexural Stress

The first beam fails in shear and the second beam failsin bending moment.


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Flexural StressThere are three types of flexuralfailure of a structural member.

Steel may reach its yield strength before theconcrete reaches its maximum. ( Under-

reinforced section ).Steel reaches yield at same time as concretereaches ultimate strength. ( Balancedsection ).

Concrete may fail before the the yield ofsteel due to the presence of a high percentage of steel in the section. ( Over-reinforced section ).


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Flexural Stress

The flexural strain and stress distribution of beam from a test beam .


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Flexural StressStrain measured in test of eccentrically loaded columns for a tiedand spiral columns .


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Flexural Stress

Example

Consider a simple rectangular beam( b x h ) reinforcedwith steel reinforcement of A

s.

(1) Determine the centroid ( neutral axis, NA ) and momentof inertia I xx of the beam for an ideal beam (no cracks).

(2) Determine the NA and moment of inertia, I xx, of beam

if the beam is cracked and tensile forces are in the steelonly.

Lecture6 True

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