What is the primary reason for placing reinforcing steel rods in concrete beams in regions of tension?
Explanation
This question connects the concept of deflection and bending moments to a practical application in civil engineering. The shape of the deflected beam (and its corresponding moment diagram) directly informs the placement of reinforcing steel to counteract tension, where concrete is weak.
Other questions
What does the elastic curve of a beam or frame represent?
According to the sign convention discussed in Chapter 8, a positive internal moment tends to bend a horizontal beam member in which direction?
What does a point of inflection on the elastic curve of a beam correspond to?
In the elastic-beam theory, what is the relationship `1/ρ = M/EI` called?
The simplified differential equation for the elastic curve is `d²v/dx² = M/EI`. What key assumption, known as small deflection theory, is made to arrive at this simplified form?
When using the double integration method, what is the purpose of boundary and continuity conditions?
A simply supported beam of length 10 m is subjected to a uniform design loading of 4 kN/m. The support reactions are 20 kN at each end. What is the equation for the internal moment M(x) as a function of x, where x is measured from the left support?
A cantilevered beam of length L is subjected to a couple moment M0 at its free end. What is the maximum slope of the beam in terms of M0, L, and EI?
What does the first moment-area theorem allow you to calculate?
What does the second moment-area theorem state regarding the vertical deviation of tangents?
A cantilever beam is fixed at end A and is 30 ft long. A 2-kip load at the free end C creates a triangular M/EI diagram that is 0 at C and -60/EI at A. Using the first moment-area theorem, what is the slope at point C, θC?
For a cantilever beam fixed at A with length L, a downward point load P at the free end B creates a triangular M/EI diagram. Using the second moment-area theorem, what is the tangential deviation of B with respect to A, t_B/A?
In the conjugate-beam method, what principle from statics is used to find the slope of the real beam?
If a real beam has an internal hinge, what is the corresponding feature on the conjugate beam?
How is the conjugate beam loaded?
A simply supported beam of length 12 m has a moment diagram that results in a positive (upward) parabolic load on its conjugate beam. The total magnitude of this parabolic load is 9000/EI, and its centroid is 6 m from the left end. What is the slope at the left support of the real beam?
A simply supported beam has a pin support at A and a roller at B. For analysis using the conjugate-beam method, what are the supports of the conjugate beam at A' and B'?
A steel beam (E = 200 GPa, I = 60(10^6) mm^4) is subjected to loads that result in a required slope calculation of θ = -112.5 kN-m^2 / EI. What is the final calculated slope in radians?
Which of the following deflection methods is based on a semigraphical technique where the M/EI diagram is used to find the area and moment of the area?
In the context of the moment-area theorems, what does the notation t_A/B represent?
If the M/EI diagram between points A and B on a beam is positive, what does this imply about the change in slope, θ_B/A, according to the first moment-area theorem?
What physical property does the product EI represent for a beam?
A beam has an internal hinge at point B. When drawing the deflected shape (elastic curve), what is a key characteristic at point B?
A cantilever beam fixed at A and free at C is 7 meters long. A couple moment of 500 N-m is applied at C. The beam's EI_BC is half of EI_AB, where B is 4 meters from A. The M/EI diagram relative to EI_BC has a constant value of 250/EI_BC from A to B, and 500/EI_BC from B to C. Using the second moment-area theorem, what is the deflection at C?
For the symmetric, simply supported beam in Figure 8-18a, with a downward load at the center, the tangent to the elastic curve at the center point D is horizontal. How can the slope at the support C, θ_C, be found using moment-area theorems?
Which of the deflection methods covered in Chapter 8 is described as relying 'only on the principles of statics, and hence its application will be more familiar'?
In the double integration method for a beam with discontinuous loads, multiple x coordinates are used for different regions. What condition must be satisfied at the point where two regions meet?
A steel beam (E=29(10^3) ksi, I=800 in^4) has a downward triangular M/EI diagram on its conjugate beam. The area of the diagram is 562.5 k-ft^2/EI and the total length is 30 ft. The beam is a cantilever fixed at A (real). What is the slope at the free end B (real)?
When is it particularly advantageous to use the moment-area theorems?
What type of support on a real beam restricts both displacement and rotation?
A cantilever beam fixed at its left end has a length of 10 m and is subjected to a uniform downward load of 12 kN/m. What is the value of the internal moment M at the fixed support?
In the conjugate-beam method, if the M/EI diagram on the real beam is negative, what is the direction of the distributed load on the conjugate beam?
What does a zero value for the M/EI diagram at a point signify about the elastic curve?
For the compound beam in Figure 8-14a, which has an internal roller at B, why are two x-coordinates required for analysis using the double integration method?
A simply supported beam AB of length L is subjected to a point load P at its center. What is the maximum deflection of the beam in terms of P, L, and EI?
What is a key difference in applicability between the method of virtual work and Castigliano's theorem for finding beam deflections?
In the conjugate-beam method, what does the shear at the free end of a conjugate beam correspond to?
Why must deflections of structures be limited in design?
What are the units of the angular flexibility coefficient, α, as used in the analysis of indeterminate beams?
A beam's M/EI diagram is a rectangle with height 10/EI and length 5m. What is the change in slope between the two ends of this 5m segment?
What is the primary cause of deflection in trusses, as compared to beams and frames?
A fixed-connected joint in a frame deflects under load. What is the relationship between the rotations of the members connected at that joint?
In the context of the conjugate-beam method, a statically determinate real beam will have a conjugate beam that is:
A symmetric beam is symmetrically loaded, causing the M/EI diagram to also be symmetric. Where does the maximum deflection occur?
What is the primary advantage of the tabular method for integrating the product ∫mM dx, as mentioned in Section 9.7?
If the calculated deflection `v` using the double integration method is a positive value, what does this signify about the direction of displacement?
A simply supported beam of length 6m has a concentrated load of 8 kN at its center (3m from the left support). What is the moment M(x) for the left half of the beam (0 < x < 3), where x is measured from the left support?
What does a negative sign for a calculated tangential deviation, such as t_A/B, indicate?
A cantilever beam of length L is subjected to a uniform downward load w. The M(x) function, with x from the free end, is M(x) = -wx^2/2. Using the conjugate-beam method, what is the deflection at the free end?