Wood Beam AnalysisConcrete Beam Design Homework 09
Concrete Beam Design Homework 09
Concrete Beam Design Homework 09
Using the strength method, determine the required amount of flexural steel reinforcement, As, for the simple span beam (shown in section). The beam carries a dead and live floor load from a one-way slab in addition to its own self weight at 150 PCF. For the given bar size, determine the number of bars to obtain the required As. Check As,min and epsilon_t. Calculate the strength moment, Mn for the final beam design and check that phi Mn is > Mu.
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Questions 1. Unfactored dead load on beam from slab 2. Unfactored dead load on beam from the beam (beam self weight) 3. Unfactored live load on beam, LL 4. Total factored beam load, wu 5. Factored design moment from the loads, Mu 6. Distance from top beam edge to centroid of flexural steel, d 7. The final calculated area of steel required, As,req 8. Number of rebars used 9. Actual, final area of flexural steel used, As,used 10. Minimum required area of steel, As,min (the greater of the 2 criteria) 11. Depth of concrete stress block, a 12. The factor beta_1 13. Distance to Neutral Axis from top of beam, c 14. Strain in flexural steel, epsilon_t 15. Strength reduction factor, phi 16. Tensile force in the flexural steel, T 17. Nominal bending moment, Mn 18. Factored bending resistance, phi Mn
Concrete Beam Design Homework 09
Main Steps 1. Calculate the factored load and find
factored required moment, Mu
2. Find d = h – cover – stirrup – db/2 (one layer)
3. Estimate moment arm z = jd . For beams j ≈ 0.9 for slabs j ≈ 0.95
4. Estimate As based on estimate of jd .
5. Use As to find a
6. Use a to find As (repeat…until 2% accuracy)
7. Choose bars for As and check As max & min
8. Check that εt ≥ 0.005
9. Check Mu ≤ φ Mn (final condition)
Using the strength method, determine the required amount of flexural steel reinforcement, As, for the simple span beam (shown in section). The beam carries a dead and live floor load from a one-way slab in addition to its own self weight at 150 PCF. For the given bar size, determine the number of bars to obtain the required As. Check As,min and epsilon_t. Calculate the strength moment, Mn for the final beam design and check that phi Mn is > Mu.
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Questions 1. Unfactored dead load on beam from slab 2. Unfactored dead load on beam from the beam (beam self weight) 3. Unfactored live load on beam, LL 4. Total factored beam load, wu 5. Factored design moment from the loads, Mu 6. Distance from top beam edge to centroid of flexural steel, d 7. The final calculated area of steel required, As,req 8. Number of rebars used 9. Actual, final area of flexural steel used, As,used 10. Minimum required area of steel, As,min (the greater of the 2 criteria) 11. Depth of concrete stress block, a 12. The factor beta_1 13. Distance to Neutral Axis from top of beam, c 14. Strain in flexural steel, epsilon_t 15. Strength reduction factor, phi 16. Tensile force in the flexural steel, T 17. Nominal bending moment, Mn 18. Factored bending resistance, phi Mn
1. Calculate the factored load and find factored required moment, Mu
1. Unfactored dead load on beam from slab wDL, Slab, PLF = Density RC x ½ x SpanA x tslab = 150 x ½ x 14 x 9/12 = 787.5 PLF
2. Unfactored dead load on beam from the beam (beam self weight) wDL, Beam, PLF = Density RC x b x h = 150 x 17 x 27 /144 = 478.125 PLF
3. Unfactored live load on beam, LL wLL, PLF = wLL, PSF x ½ x SpanA = 80 x ½ x 14 = 560 PLF
4. Total factored beam load, wu wu, PLF = 1.2 WDL, PLF + 1.6 WLL, PLF = 1.2 x (787.5 +478.125) + 1.6 x 560 = 2414.75 PLF
5. Factored design moment from the loads, Mu Mu = 1/8 x wu, PLF x SpanB2 = 1/8 x 2414.75 x 272 /1000 = 220.04 K-FT
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 1. Unfactored dead load on beam from slab 2. Unfactored dead load on beam from the
beam (beam self weight) 3. Unfactored live load on beam, LL 4. Total factored beam load, wu 5. Factored design moment from the loads, Mu
2. Find d = h – cover – stirrup – db/2 (one layer)
6. Distance from top beam edge to centroid of flexural steel, d dc = protection cover + dstirrup + ½ db = 1.5 + 0.5 + ½ x 1.27 = 2.635 IN d = h – dc = 27 – 2.635 = 24.365 IN
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 6. Distance from top beam edge to centroid of
flexural steel, d
3. Estimate moment arm z = jd . For beams j ≈ 0.9 for slabs j ≈ 0.95
4. Estimate As based on estimate of jd . 5. Use As to find a 6. Use a to find As (repeat…until 2% accuracy)
7. The final calculated area of steel required, As,req
Trail 1 Estimated Z: For beams j ≈ 0.9 Z = j x d = 0.9 x 24.365 = 21.929 IN
Mu = F(As x fy) z As =
F = 220.04 12 1000 0.9 60000 21.929
= 2.230 IN2
= 2.230 60000 0.85 3500 17
= 2.646 IN
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
Related Questions 7. The final calculated area of steel required,
As,req
Trail 2 Z = d – a/2 = 24.365 – 2.646/2 = 23.042 IN As =
F = 220.04 12 1000 0.9 60000 23.042
= 2.122 IN2
= 2.122 60000 0.85 3500 17
= 2.517 IN
(2.230 - 2.122) / 2.122 = 5.09% > 2%
Trail 3 Z = d – a/2 = 24.365 – 2.517/2 = 23.107 IN As =
F = 220.04 12 1000 0.9 60000 23.107
= 2.116 IN2
= 2.116 60000 0.85 3500 17
= 2.510 IN
As,req = 2.116 IN2
7. Choose bars for As and check AS,max&min
8. Number of rebars used As,req / 1.27 = 2.116 / 1.27 = 1.666 Number of rebars = 2
9. Actual, final area of flexural steel used, As,used As,used = 1.27 x 2 = 2.54 IN2
10.Minimum required area of steel, As,min (the greater of the 2 criteria) 3 ′
bw d = 3 3500 60000
x 17 x 24.365 = 1.225 IN2
200
As,min = 1.381 IN2
As,used = 2.54 IN2 > As,min = 1.381 IN2
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 8. Number of rebars used 9. Actual, final area of flexural steel used,
As,used 10.Minimum required area of steel, As,min (the
greater of the 2 criteria)
8. Check that εt ≥ 0.005
11. Depth of concrete stress block, a a = ,
0.85 ′
= 3.013 IN
12. The factor beta_1 β1 = 0.85
13. Distance to Neutral Axis from top of beam, c c = a / β1 = 3.013 / 0.85 = 3.545 IN
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 11. Depth of concrete stress block, a 12. The factor beta_1 13. Distance to Neutral Axis from top of beam, c 14. Strain in flexural steel, epsilon_t
f'c β1 0 0.85
1000 0.85 2000 0.85 3000 0.85 4000 0.85 5000 0.8 6000 0.75 7000 0.7 8000 0.65 9000 0.65
10000 0.65
ca 1β=
8. Check that εt ≥ 0.005
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 11. Depth of concrete stress block, a 12. The factor beta_1 13. Distance to Neutral Axis from top of beam, c 14. Strain in flexural steel, epsilon_t
= −
0.003 ≥ 0.005
14. Strain in flexural steel, epsilon_t t = [(d - c)/c]x0.003 = [(24.365 – 3.545) / 3.545] x 0.003 = 0.018 > 0.005
9. Check Mu ≤ φ Mn (final condition)
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Related Questions 15. Strength reduction factor, phi 16. Tensile force in the flexural steel, T 17. Nominal bending moment, Mn 18. Factored bending resistance, phi Mn
15. Strength reduction factor, phi F= 0.9
16. Tensile force in the flexural steel, T T = As fy = 2.54 x 60000 /1000 = 152.4 Kips
17. Nominal bending moment, Mn Mn = T (d - a/2) = 152.4 x (24.365 – 3.013/2) = 3483.635 Kip-in
18. Factored bending resistance, phi Mn Mu =F Mn = 0.9 x 3483.635/12 = 261.273 Kip-ft
Main Steps 1. Calculate the factored load and find
factored required moment, Mu
2. Find d = h – cover – stirrup – db/2 (one layer)
3. Estimate moment arm z = jd . For beams j ≈ 0.9 for slabs j ≈ 0.95
4. Estimate As based on estimate of jd .
5. Use As to find a
6. Use a to find As (repeat…until 2% accuracy)
7. Choose bars for As and check As max & min
8. Check that εt ≥ 0.005
9. Check Mu ≤ φ Mn (final condition)
Using the strength method, determine the required amount of flexural steel reinforcement, As, for the simple span beam (shown in section). The beam carries a dead and live floor load from a one-way slab in addition to its own self weight at 150 PCF. For the given bar size, determine the number of bars to obtain the required As. Check As,min and epsilon_t. Calculate the strength moment, Mn for the final beam design and check that phi Mn is > Mu.
Datasheet Span of slab, Span A Span of beam, Span B Thickness of slab, t section width, b section height, h max. aggregate size bar size number stirrup bar size number concrete cover concrete ultimate strength, f’c steel yield strength, fy Floor Live Load
14FT 27IN
80PSF
Questions 1. Unfactored dead load on beam from slab 2. Unfactored dead load on beam from the beam (beam self weight) 3. Unfactored live load on beam, LL 4. Total factored beam load, wu 5. Factored design moment from the loads, Mu 6. Distance from top beam edge to centroid of flexural steel, d 7. The final calculated area of steel required, As,req 8. Number of rebars used 9. Actual, final area of flexural steel used, As,used 10. Minimum required area of steel, As,min (the greater of the 2 criteria) 11. Depth of concrete stress block, a 12. The factor beta_1 13. Distance to Neutral Axis from top of beam, c 14. Strain in flexural steel, epsilon_t 15. Strength reduction factor, phi 16. Tensile force in the flexural steel, T 17. Nominal bending moment, Mn 18. Factored bending resistance, phi Mn
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Concrete Beam Design
Datasheet Breadth of beam Depth of beam Quantity of bars Bar number Stirrup number Max. aggregate size Steel yield strength Concrete ultimate strength
15IN 36IN
= 2550 PSI
= 3.922 IN
= 7.843 IN
= 28.663 IN
= 300 K
Three things to do: 1. Calculation Steps for the dimensions, a, c, d, dc 2. Section drawing with dimensions 3. Stress block diagram
1. Bend Diameter = 4db = 4 x 0.5 = 2 IN
2. Straight Extension, 6db = 6 x 0.5 = 3 IN 3 IN text ≥ 3 IN
3. Horizontal Spacing in Beam 1 IN db,main bar = 1.128 IN (Control) 4/3 max aggregate = 4/3 x 0.75 = 1 IN
4. Vertical Spacing in Beam 1IN
Datasheet Breadth of beam Depth of beam Quantity of bars Bar number Stirrup number Max. aggregate size Steel yield strength Concrete ultimate strength
15IN 36IN
1. Bend Diameter = 4db = 4 x 0.5 = 2 IN
2. Straight Extension, 6db = 6 x 0.5 = 3 IN 3 IN text ≥ 3 IN
3. Horizontal Spacing in Beam 1 IN db,main bar = 1.128 IN (Control) 4/3 max aggregate = 4/3 x 0.75 = 1 IN
4. Vertical Spacing in Beam 1IN
Datasheet Breadth of beam Depth of beam Quantity of bars Bar number Stirrup number Max. aggregate size Steel yield strength Concrete ultimate strength
15IN 36IN
∑ = 2 1 1.128+1+0.564 +3(1)(0.564)
5(1) = 1.415 IN
6. Distance from lower beam edge to center of flexural steel dc = d3 + dstirrup + protection cover = 1.415 + 0.5 + 1.5 = 3.415 IN
7. Distance from top beam edge to centroid of flexural steel d = h – dc = 36 – 3.415 = 32.585 IN
Datasheet Breadth of beam Depth of beam Quantity of bars Bar number Stirrup number Max. aggregate size Steel yield strength Concrete ultimate strength
15IN 36IN
0.85 ′
= 7.843 IN
9. factor beta_1 β1 = 0.85
10. Distance to Neutral Axis from top of beam, c c = a / β1 = 7.843 / 0.85 = 9.227 IN
f'c β1 0 0.85
1000 0.85 2000 0.85 3000 0.85 4000 0.85 5000 0.8 6000 0.75 7000 0.7 8000 0.65 9000 0.65
10000 0.65