Chapter Skim View of:

Currently Skimming:

Pages 718-733

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.

From page 718... ... H-i Appendix H Subassemblage Sectional Calculations and Analyses Read the entire page →
From page 719... ... H-ii H.1: Subassemblage Specimen Design Calculations and Analyses The subassemblage specimens utilized during the current study were primarily considered to provide a comparison of the benefits of particular crack control details relative to one another. To provide an understanding of the expected behavior of each specimen based on its individual measured material properties, geometry, and reinforcement details, a detailed analytical investigation was completed. Read the entire page →
From page 720... ... H-1 Sectional calculations for subassemblage specimens Specimen dimensions and variables are defined in plan and elevation views of the subassemblage specimens in Figures H.1 and H.2, respectively. As shown in Figure H.1, each subassemblage specimen was 120 in. Read the entire page →
From page 721... ... H-2 (a) Subassemblage section view perpendicular to joint (b) Read the entire page →
From page 722... ... H-3 Note: The index number in each array represents the subassemblage specimen number. For example, subassemblage 1 will always be represented as the first entry in any array variable Useful units: kip 1000lbf:= ksi kip in 2 := Specimen range variable: i 1 7..:= Specimen naming includes specimen number - description - maximum distance between perpendicular reinforcement immediately above the precast joint Specimens i "1-Control1-9in." "2-NoCage-18in." "3-HighBars-9in." "4-Deep-9in." "5-No.6Bars-9in." "6-Frosch-4.5in." "7-Control2-9in." := Material Properties Measured material properties have been documented herein. Read the entire page →
From page 723... ... H-4 Specimen and reinforcement geometry and layout Ashook equals the area of a single perpendicular hooked bar equals the area of all horizontally oriented legs of the stirrups in the cage at a given level, i.e.: all the horizontal legs of the stirrups at the bottom of the trough Ascage bss equals nominal width, perpendicular to joint, of specimen hcip equals the nominal depth of CIP concrete between top of precast flange at the joint and the top of the specimen dshook equals the nominal depth of the hooks oriented perpendicular to joint, measured from top of specimen to center of reinforcement, also used as depth of lower horizontal leg of cage reinforcement dtoplegofcage equals the nominal depth of the center of the top horizontal leg of the cage reinforcement from the top of the specimen dsdeck equals the nominal depth of the center of the deck reinforcement oriented perpendicular to the joint from the top of the specimen Area of No. 3 mild reinforcement: Ashooki .2in 2 .2in 2 .2in 2 .2in 2 .44in 2 .2in 2 .2in 2 Ascagei .33in 2 0in 2 .33in 2 .33in 2 .33in 2 1.43in 2 .33in 2 A3 0.11in 2 := bss i 62.75in 67.25in 62.75in 62.75in 62.75in 64.0in 62.75in hcipi 11in 11in 11in 15in 11in 11in 11in dshooki 9.75in 9.75in 7in 13.75in 9.6875in 9.75in 9.75in dsdeck 1.5625in:= dtoplegofcage 2.25in:= Read the entire page →
From page 724... ... H-5 Location of uncracked and cracked neutral axis Method of transformed sections is utilized to calculate neutral axis (NA) location, the modular ratio is the ratio of the elastic modulus of the steel to the elastic modulus of the concrete n i Es EcSSi := n 6.1 5.1 7.4 6.2 7.1 5.5 6.9                   = Depth of neutral axis is measured from top surface of each specimen, as follows: Black box in upper right corner of equation indicates that the equation is not evaluated; only shown for illustration of method of calculation Atotal x  ⋅ i n 1−( ) Read the entire page →
From page 725... ... H-6 Cracked Neutral axis depth is calculated as above; the depth of the concrete in compression is equal to the neutral axis depth, therefore a quadratic equation must be solved. The coefficients of the quadratic equation are as follows: The cracked transformed section is shown in Figure H.3: Figure H.3: Cracked transformed section, with neutral axis, x, measured from top of section The area of the deck reinforcement should be subtracted from the total area of the section by multiplying by (n-1) Read the entire page →
From page 726... ... H-7 The polyroots function is used to evaluate the parabolic function for each specimen. The polyroots function takes the coefficients A,B, and C and returns, for a parabolic function, two roots. Read the entire page →
From page 727... ... H-8 Recalculate the depth of the neutral axis with the area of the deck reinforcement not subtracted from the total area of the section when the deck reinforcement is below the neutral axis depth Coeffs M 0← M 3 i, bss i 2 ← M 2 i, ni 8Ashooki 2Ascagei +    ⋅ n i 5⋅ A3( ) xcracked i dsdeck Read the entire page →
From page 728... ... H-9 Moment of Inertia The moment of inertia of the section is the moment of inertia of the individual components about centroid of component plus area of component multiplied by the distance to centroid of section squared (parallel axis theorem) Read the entire page →
From page 729... ... H-10 Cracked Icracked i 1 12 bss i xcracked i     3 bss i xcracked i ⋅ xcracked i 2 xcracked i −       2 ⋅+ n i 8Ashooki dshooki xcracked i −    2 ⋅ Ascagei dshooki xcracked i −    2 ⋅+ Ascagei dtoplegofcage xcracked i −    2 ⋅+ ...        ⋅+ ... n i 5⋅ A3⋅ dsdeck xcracked i −    2 ⋅    xcracked i dsdeck Read the entire page →
From page 730... ... H-11 β1i 0.85 rounded_fci 4000≤if 0.85 0.05 rounded_fci 4000−    1000 ⋅−       rounded_fci 4000>if 0.65 rounded_fci 8000>if := β1 0.70 0.70 0.80 0.70 0.80 0.70 0.70                   = Mflexurei 4Ashooki 60⋅ ksi dshooki β1i xcracked i ⋅ 2 −       ⋅:= Mflexure 439 444 306 625 918 434 437                   in kip⋅⋅= φ uncracked i Mcracki EcSSi Iuncracked i ⋅ := φ uncracked 0.000032 0.000024 0.000031 0.000022 0.000027 0.000028 0.000032                   1 in ⋅= The same moment is applied immediately before and after cracking: φ cracked i Mcracki EcSSi Icracked i ⋅ := φ cracked 0.000269 0.00029 0.000441 0.000217 0.000118 0.000178 0.00024                   1 in ⋅= Read the entire page →
From page 731... ... H-12 Compare results, normalized by the Control 1 specimen: xuncracked i xuncracked1 1.000 0.998 0.993 1.362 1.013 1.000 1.001                   = xcracked i xcracked1 1.000 0.822 0.909 1.203 1.422 1.157 1.054                   = Iuncracked i Iuncracked1 1.000 1.058 0.981 2.526 1.032 1.035 1.005                   = Icracked i Icracked1 1.000 0.732 0.578 2.084 1.995 1.351 1.112                   = φ uncracked i φ uncracked1 1.000 0.746 0.966 0.665 0.847 0.863 0.986                   = φ cracked i φ cracked1 1.000 1.077 1.641 0.806 0.438 0.661 0.891                   = Read the entire page →
From page 732... ... H-13 µε εsSW 1.881 10 3 × 1.995 10 3 × 3.198 10 3 × 1.633 10 3 × 1.128 10 3 × 1.105 10 3 × 2.134 10 3 ×                           = The yield strength of a representative piece of the mild steel reinforcement was measured in the laboratory to be approximately 70 ksi. Therefore the predicted steel stresses are below the yield and are assumed to be linear elastic. Read the entire page →
From page 733... ... H-14 The strain in the transverse hooks due to self weight and the weight of the clamping system was between 1105 and 3198µε. The largest transverse strain measured in the hooks was approximately 1455µε in SSMBLG1-Control1, in which case the state of strain near that gage was expected to be closer to 3336µε. Read the entire page →

From page 718...

... H-i Appendix H Subassemblage Sectional Calculations and Analyses

Read the entire page →

From page 719...

... H-ii H.1: Subassemblage Specimen Design Calculations and Analyses The subassemblage specimens utilized during the current study were primarily considered to provide a comparison of the benefits of particular crack control details relative to one another. To provide an understanding of the expected behavior of each specimen based on its individual measured material properties, geometry, and reinforcement details, a detailed analytical investigation was completed.

Read the entire page →

From page 720...

... H-1 Sectional calculations for subassemblage specimens Specimen dimensions and variables are defined in plan and elevation views of the subassemblage specimens in Figures H.1 and H.2, respectively. As shown in Figure H.1, each subassemblage specimen was 120 in.

Read the entire page →

From page 721...

... H-2 (a) Subassemblage section view perpendicular to joint (b)

Read the entire page →

From page 722...

... H-3 Note: The index number in each array represents the subassemblage specimen number. For example, subassemblage 1 will always be represented as the first entry in any array variable Useful units: kip 1000lbf:= ksi kip in 2 := Specimen range variable: i 1 7..:= Specimen naming includes specimen number - description - maximum distance between perpendicular reinforcement immediately above the precast joint Specimens i "1-Control1-9in." "2-NoCage-18in." "3-HighBars-9in." "4-Deep-9in." "5-No.6Bars-9in." "6-Frosch-4.5in." "7-Control2-9in." := Material Properties Measured material properties have been documented herein.

Read the entire page →

From page 723...

... H-4 Specimen and reinforcement geometry and layout Ashook equals the area of a single perpendicular hooked bar equals the area of all horizontally oriented legs of the stirrups in the cage at a given level, i.e.: all the horizontal legs of the stirrups at the bottom of the trough Ascage bss equals nominal width, perpendicular to joint, of specimen hcip equals the nominal depth of CIP concrete between top of precast flange at the joint and the top of the specimen dshook equals the nominal depth of the hooks oriented perpendicular to joint, measured from top of specimen to center of reinforcement, also used as depth of lower horizontal leg of cage reinforcement dtoplegofcage equals the nominal depth of the center of the top horizontal leg of the cage reinforcement from the top of the specimen dsdeck equals the nominal depth of the center of the deck reinforcement oriented perpendicular to the joint from the top of the specimen Area of No. 3 mild reinforcement: Ashooki .2in 2 .2in 2 .2in 2 .2in 2 .44in 2 .2in 2 .2in 2 Ascagei .33in 2 0in 2 .33in 2 .33in 2 .33in 2 1.43in 2 .33in 2 A3 0.11in 2 := bss i 62.75in 67.25in 62.75in 62.75in 62.75in 64.0in 62.75in hcipi 11in 11in 11in 15in 11in 11in 11in dshooki 9.75in 9.75in 7in 13.75in 9.6875in 9.75in 9.75in dsdeck 1.5625in:= dtoplegofcage 2.25in:=

Read the entire page →

From page 724...

... H-5 Location of uncracked and cracked neutral axis Method of transformed sections is utilized to calculate neutral axis (NA) location, the modular ratio is the ratio of the elastic modulus of the steel to the elastic modulus of the concrete n i Es EcSSi := n 6.1 5.1 7.4 6.2 7.1 5.5 6.9                   = Depth of neutral axis is measured from top surface of each specimen, as follows: Black box in upper right corner of equation indicates that the equation is not evaluated; only shown for illustration of method of calculation Atotal x  ⋅ i n 1−( )

Read the entire page →

From page 725...

... H-6 Cracked Neutral axis depth is calculated as above; the depth of the concrete in compression is equal to the neutral axis depth, therefore a quadratic equation must be solved. The coefficients of the quadratic equation are as follows: The cracked transformed section is shown in Figure H.3: Figure H.3: Cracked transformed section, with neutral axis, x, measured from top of section The area of the deck reinforcement should be subtracted from the total area of the section by multiplying by (n-1)

Read the entire page →

From page 726...

... H-7 The polyroots function is used to evaluate the parabolic function for each specimen. The polyroots function takes the coefficients A,B, and C and returns, for a parabolic function, two roots.

Read the entire page →

From page 727...

... H-8 Recalculate the depth of the neutral axis with the area of the deck reinforcement not subtracted from the total area of the section when the deck reinforcement is below the neutral axis depth Coeffs M 0← M 3 i, bss i 2 ← M 2 i, ni 8Ashooki 2Ascagei +    ⋅ n i 5⋅ A3( ) xcracked i dsdeck

Read the entire page →

From page 728...

... H-9 Moment of Inertia The moment of inertia of the section is the moment of inertia of the individual components about centroid of component plus area of component multiplied by the distance to centroid of section squared (parallel axis theorem)

Read the entire page →

From page 729...

... H-10 Cracked Icracked i 1 12 bss i xcracked i     3 bss i xcracked i ⋅ xcracked i 2 xcracked i −       2 ⋅+ n i 8Ashooki dshooki xcracked i −    2 ⋅ Ascagei dshooki xcracked i −    2 ⋅+ Ascagei dtoplegofcage xcracked i −    2 ⋅+ ...        ⋅+ ... n i 5⋅ A3⋅ dsdeck xcracked i −    2 ⋅    xcracked i dsdeck

Read the entire page →

From page 730...

... H-11 β1i 0.85 rounded_fci 4000≤if 0.85 0.05 rounded_fci 4000−    1000 ⋅−       rounded_fci 4000>if 0.65 rounded_fci 8000>if := β1 0.70 0.70 0.80 0.70 0.80 0.70 0.70                   = Mflexurei 4Ashooki 60⋅ ksi dshooki β1i xcracked i ⋅ 2 −       ⋅:= Mflexure 439 444 306 625 918 434 437                   in kip⋅⋅= φ uncracked i Mcracki EcSSi Iuncracked i ⋅ := φ uncracked 0.000032 0.000024 0.000031 0.000022 0.000027 0.000028 0.000032                   1 in ⋅= The same moment is applied immediately before and after cracking: φ cracked i Mcracki EcSSi Icracked i ⋅ := φ cracked 0.000269 0.00029 0.000441 0.000217 0.000118 0.000178 0.00024                   1 in ⋅=

Read the entire page →

From page 731...

... H-12 Compare results, normalized by the Control 1 specimen: xuncracked i xuncracked1 1.000 0.998 0.993 1.362 1.013 1.000 1.001                   = xcracked i xcracked1 1.000 0.822 0.909 1.203 1.422 1.157 1.054                   = Iuncracked i Iuncracked1 1.000 1.058 0.981 2.526 1.032 1.035 1.005                   = Icracked i Icracked1 1.000 0.732 0.578 2.084 1.995 1.351 1.112                   = φ uncracked i φ uncracked1 1.000 0.746 0.966 0.665 0.847 0.863 0.986                   = φ cracked i φ cracked1 1.000 1.077 1.641 0.806 0.438 0.661 0.891                   =

Read the entire page →

From page 732...

... H-13 µε εsSW 1.881 10 3 × 1.995 10 3 × 3.198 10 3 × 1.633 10 3 × 1.128 10 3 × 1.105 10 3 × 2.134 10 3 ×                           = The yield strength of a representative piece of the mild steel reinforcement was measured in the laboratory to be approximately 70 ksi. Therefore the predicted steel stresses are below the yield and are assumed to be linear elastic.

Read the entire page →

From page 733...

... H-14 The strain in the transverse hooks due to self weight and the weight of the clamping system was between 1105 and 3198µε. The largest transverse strain measured in the hooks was approximately 1455µε in SSMBLG1-Control1, in which case the state of strain near that gage was expected to be closer to 3336µε.

Read the entire page →

Key Terms

← Previous Chapter Skim

Next Chapter Skim →

This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More information on Chapter Skim is available.