Presentation on theme: "Chp-6:Lecture Goals Serviceability Deflection calculation"— Presentation transcript:
1Chp-6:Lecture Goals Serviceability Deflection calculation Deflection example
2Structural Design Profession is concerned with: Limit States Philosophy:Strength Limit State(safety-fracture, fatigue, overturning buckling etc.-)ServiceabilityPerformance of structures under normal service load and are concerned the uses and/or occupancy of structures
20Reinforced Concrete Sections - Example Given a doubly reinforced beam with h = 24 in, b = 12 in., d’ = 2.5 in. and d = 21.5 in. with 2# 7 bars in compression steel and 4 # 7 bars in tension steel. The material properties are fc = 4 ksi and fy= 60 ksi.Determine Igt, Icr , Mcr(+), Mcr(-), and compare to the NA of the beam.
21Reinforced Concrete Sections - Example The components of the beam
22Reinforced Concrete Sections - Example The compute the n value and the centroid, I uncracked
23Reinforced Concrete Sections - Example The compute the centroid and I uncracked
24Reinforced Concrete Sections - Example The compute the centroid and I for a cracked doubly reinforced beam.
25Reinforced Concrete Sections - Example The compute the centroid for a cracked doubly reinforced beam.
26Reinforced Concrete Sections - Example The compute the moment of inertia for a cracked doubly reinforced beam.
27Reinforced Concrete Sections - Example The critical ratio of moment of inertia
28Reinforced Concrete Sections - Example Find the components of the beam
29Reinforced Concrete Sections - Example Find the components of the beamThe neutral axis
30Reinforced Concrete Sections - Example The strain of the steelNote: At service loads, beams are assumed to act elastically.
31Reinforced Concrete Sections - Example Using a linearly varying e and s = Ee along the NA is the centroid of the area for an elastic centerThe maximum tension stress in tension is
32Reinforced Concrete Sections - Example The uncracked moments for the beam
33Calculate the Deflections (1) Instantaneous (immediate) deflections(2) Sustained load deflectionInstantaneous Deflectionsdue to dead loads( unfactored) , live, etc.
34Calculate the Deflections Instantaneous DeflectionsEquations for calculating Dinst for common cases
35Calculate the Deflections Instantaneous DeflectionsEquations for calculating Dinst for common cases
36Calculate the Deflections Instantaneous DeflectionsEquations for calculating Dinst for common cases
37Calculate the Deflections Instantaneous DeflectionsEquations for calculating Dinst for common cases
38Sustained Load Deflections Creep causes an increase in concrete strainCurvature increasesCompression steel presentIncrease in compressive strains cause increase in stress in compression reinforcement (reduces creep strain in concrete)Helps limit this effect.
39Sustained Load Deflections Sustain load deflection = l DiInstantaneous deflectionACIat midspan for simple and continuous beamsat support for cantilever beams
40Sustained Load Deflections x = time dependent factor for sustained load5 years or more 12 months months monthsAlso see Figure from ACI code
41Sustained Load Deflections For dead and live loadsDL and LL may have different x factors for LT ( long term ) D calculations
42Sustained Load Deflections The appropriate value of Ic must be used to calculate D at each load stage.Some percentage of DL (if given)Full DL and LL
43Serviceability Load Deflections - Example Show in the attached figure is a typical interior span of a floor beam spanning between the girders at locations A and C. Partition walls, which may be damaged by large deflections, are to be erected at this level. The interior beam shown in the attached figure will support one of these partition walls. The weight of the wall is included in the uniform dead load provided in the figure. Assume that 15 % of the distributed dead load is due to a superimposed dead load, which is applied to the beam after the partition wall is in place. Also assume that 40 % of the live load will be sustained for at least 6 months.
44Serviceability Load Deflections - Example fc = 5 ksify = 60 ksi
45Serviceability Load Deflections - Example Part IDetermine whether the floor beam meets the ACI Code maximum permissible deflection criteria. (Note: it will be assumed that it is acceptable to consider the effective moments of inertia at location A and B when computing the average effective moment of inertia for the span in this example.)Part IICheck the ACI Code crack width provisions at midspan of the beam.
46Serviceability Load Deflections - Example Deflection before glass partition is installed (85 % of DL)
47Serviceability Load Deflections - Example Compute the centroid and gross moment of inertia, Ig.
48Serviceability Load Deflections - Example The moment of inertia
49Serviceability Load Deflections - Example The moment capacity
50Serviceability Load Deflections - Example Determine bending moments due to initial load (0.85 DL) The ACI moment coefficients will be used to calculate the bending moments Since the loading is not patterned in this case, This is slightly conservative
51Serviceability Load Deflections - Example The moments at the two locations
52Serviceability Load Deflections - Example Moment at C will be set equal to Ma for simplicity, as given in the problem statement.
53Serviceability Load Deflections - Example Assume Rectangular Section Behavior and calculate the areas of steel and ratio of Modulus of Elasticity
54Serviceability Load Deflections - Example Calculate the center of the T-beam
55Serviceability Load Deflections - Example The centroid is located at the A’s < 4.5 in. = tf Use rectangular section behavior
56Serviceability Load Deflections - Example The moment of inertia at midspan
57Serviceability Load Deflections - Example Calculate average effective moment of inertia, Ie(avg) for interior span (for 0.85 DL) For beam with two ends continuous and use Ig for the two ends.
58Serviceability Load Deflections - Example Calculate instantaneous deflection due to 0.85 DL:Use the deflection equation for a fixed-fixed beam but use the span length from the centerline support to centerline support to reasonably approximate the actual deflection.