Concrete Civil Engineering and Stages of Beam Behavior • True or false: In a simply supported beam, the neutral axis moves upward in the cross section when the beam moves from the uncracked stage to the elastic cracked stage. •
True or false: In a simply supported beam, the neutral axis is at the same point in the ultimate strength stage as in the elastic cracked stage. • What is the definition of failure? • What is the assumption that must be checked about failure? • True or false: The strain distribution is linear at all stages of beam behavior. • True or false: The stress distributions linear at all stages of beam behavior. • Why do we use the Whitney stress block in place of the actual concrete compression stress distribution? • Name three assumptions we use to calculate the ultimate moment. • What is the Whitney stress block calibrated to do? • How large is the uniform stress in the Whitney stress block? • How far does the Whitney stress block extend into the cross section? • What value do we use for β1 if we are using 3500 psi concrete? • What value do we use for β1 if we are using 6000 psi concrete? • Which statics equation do we use to calculate the depth of the equivalent rectangular (i.e. Whitney) stress block a? • How do we find the moment arm of the couple formed by the steel’s tension force and the concrete’s compressive force? • What is the equation for the moment of the couple formed by the steel’s tension force and the concrete’s compressive force? • True or false: The moment arm of the couple formed by the steel force T and the concrete compressive force C is always d-a/2. • What is the steel reinforcement ratio ρ? • What equation(s) is used to find the nominal strength of a beam cross section? • What equation(s) is used to find the design strength of a beam cross section? • True or false: The design strength of a beam cross-section must be at least as big as the factored moment Mu. • Where does the factored moment Mu come from? • What is the equation for the coefficient of resistance Rn? • What is the yield strain for Grade 60 reinforcement? • How is the steel’s yield strain calculated? • How do we find the depth of the neutral axis c if the depth of the stress block a is known? • What does the symbol εt stand for? • What is the difference between it and d? • How do we find the value of the strain in the steel when the concrete reaches its crushing strain? • What is a balanced section or balanced failure? • If you have a cross-section that is reinforced with a steel ratio ρ > ρb would you expect a ductile or a brittle failure? • How does the steel reinforcement have to be adjusted (i.e. do you add more steel or remove steel) to change the failure mode from a brittle compression-controlled failure to a ductile tension-controlled failure mode? • How does ACI 318 Code define a tension-controlled member? • True or false: For beams that have a transition failure mode, steel yields before the concrete crushes. • What value is used for φ in a tension-controlled member? • Is the φ factor for a member in the transition zone greater or less than the φ factor for a tension-controlled member? • What is the smallest value for εt that can be used for a beam according to ACI 318 Code? • What is the largest amount of factored axial compressive load that can act on a cross section and still be classified as a “beam” or bending member, rather than a column member? • What types of members can be designed as compression-controlled? • True or false: The equation for φ for bending moment and axial load is the same for all grades of steel. • True or false: The nominal strength Mn increases for increasing steel ratio ρ. • How do we find the steel ratio ρ that corresponds to a particular value of steel strain εt (i.e. what do we use to find ρ0.005 when εt equals 0.005 or ρ0.004 when εt equals 0.004? • If you wanted to design a cross-section with εt greater than 0.005, would you need to use a steel ratio that was larger or smaller than ρ0.005? • What assumption do we make to use T = Asfy in Example 1? • Why is the compression force C = 0.85f’cab and why is the compression force located at a/2 down from the top of the cross section in Example 1? • How is the assumption that T = Asfy checked in Example 1? • How is the φ factor determined to be 0.9 in Example 1? • Why is Mn calculated as T(d-a/2) in Example 1? • Why is the compression force’s size and location in Example 2 found differently than was used in Example 1? • Why didn’t we calculate a design strength φMn for the cross section in Example
