Concept explainers
A reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at d = 105 mm from the top of the slab. The modulus of elasticity for the concrete is Ec= 25 GPa, while that of the steel is £s = 200 G Pa. Assume that allowable stresses for concrete and steel arecrac = 9.2 MPa and
l()5 mm
- Find the maximum permissible positive bending moment for a l-m wide strip of the slab.
What is the required area of steel reinforcement, A^ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)
(a)
The maximum permissible positive bending and balanced condition for both steel and concrete.
Answer to Problem 6.3.16P
The maximum permissible positive pending moment is
Explanation of Solution
Given: .
D =0.13m
Calculation: .
The modular ratio of the momentum is,
The number of reinforcement bar provided is,
Substitute b=100mm, s=160mm
The molecular ratio of the moment is
The area of reinforcement bar is stated as,
Moment of area of concrete section = Moment of area of steel about neutral Axis..
Using Quadratic formula,
Substitute p=
The location of neutral axis for the top layer, y =0.0308m.
Moment of inertia of the transformed section is,
The bending moment at the top layer of concrete..
Substitute y=0.0308m,
The bending moment at the top layer of concrete..
Substitute the value
Conclusion: .
The maximum permissible positive pending moment is
(b)
To find: The allowable value of moment in steel in positive pending.
Answer to Problem 6.3.16P
The allowable value of moment in steel in positive pending is
Explanation of Solution
Calculation: .
Substitute y equation above
Substitute the value n=8,
Take squaring on both sides,
Required area of steel reinforcement
Moment of area of concrete section = Moment of area of steel about neutral Axis..
Use quadratic equation..
Substitute p=
The allowable positive pending moment in concrete is
The allowable positive pending moment in concrete is,
Substitute the value y=0.0371m,
The allowable positive pending moment in steel is,
Conclusion: .
The lesser value of moment in concrete and steel as allowable value of moment..
Allowable positive bending moment in steel is
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Mechanics of Materials (MindTap Course List)
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