CEEN 203
A beam in pure bending will have varying curvature and a beam in nonuniform bending will have constant curvature.
False
A beam of rectangular cross section whose height is twice as its width is less efficient in resisting bending than a circular beam that has the same area as the rectangular beam.
False
A positive bending moment compresses the upper part of the beam and a negative bending moment compresses the upper part of the beam.
False
Because length dx is infinitesimally small, equ M1 = P (dx/2)+Vdx+V1dx shows that the increment M1 in bending moment is infinitesimally small. Thus, the magnitude of the bending moment changes as we "pass through" the point of application of a concentrated load.
False
Curvature is a measure of how sharply a beam is bent. If the load in a beam is small, the beam will be nearly straight, the radius of curvature will be very small, and the curvature will be very large.
False
Ex 4-4, pg 391, "Bending moment M may either be positive or negative, depending on the relative magnitudes of loads P and M(not)" If the counterclockwise moments were taken as negative, the answer would be different than the answer given in equation c on pg 391.
False
For each type of loading we can write two equations of equilibrium for an element -- one equ for equilibrium of forces in the vertical direction and one equ for equilibrium of moments. The 1st of these equs gives relationship between load and shear and 2nd gives relationship between shear and non-shearing force.
False
For wide flange beams of typical proportions, the shear force in the flange is 90-99% of the total shear force acting on the cross section: the remainder is carried by shear in the webs. Since the flange resist most of the shear force, designers often calculated an approximate value of the max shear stress by dividing the total shear by the area of the flange.
False
The maximum value of the shear stress occurs at the top or bottom of the beam where the first moment Q has its max value
False
The shear formula applies to prismatic and nonprismatic beams.
False
The shear formula can only be used to determine the shear stress at the top and bottom of the cross section of a rectangular beam
False
dM/dx = V applies only in regions where distributed loads (or no loads) act on the beam. At a point where a concentrated load acts, a sudden change (or discontinuity) in the shear force occurs and the derivative dM/dx is super easy to evaluate at that point
False
First moment of cross sectional area above the level at which the shear stress is being evaluated
Q
A build up beam must be designed so that the beam behaves as a single member. The design of a build up beam involves 2 phases: (a) the beam is designed as though it were made of one piece taking into account bending and shear stresses, and (b) the connections between the parts are designed to ensure that the beam does indeed behave as a single entity.
True
A positive bending moment produces positive curvature and a negative bending moment produces negative curvature.
True
A thin walled open cross section has a wall thickness that is small compared to the height and width of the cross section and is open as in the case of an i-beam or channel beam rather than closed as in case of a hollow box beam
True
Equilibrium of the forces (or moments) shown in Figure 4-29c indicate that M1 = -M0 (Eq. 4-9). Thus, the bending moment decreases by M0 as we move from left to right (according to the convention used in the derivation of the equation) through the point of load applications, which means that the bending moment changes abruptly at the point of application of a couple
True
Ex: shear stress on free surface inside face of top flange must be 0,whereas the shear stress across web is not 0. These observations indicate that the distribution of the shear stresses at the junction of the web and the flange is quite simple and can be investigated by elementary methods.
True
If dV/dx = 0 there is no distributed load on that segment of the beam and the shear is constant in that part of the beam.
True
If the shear force applied to a thin-walled open cross section acts through the shear center but is inclined to the y and/or z axes (see figure 6-39 for reference), the shear force can be resolved into components parallel to the principal axes, which will then require two separate analyses and the superposition of the results
True
If the transformed beam is to be equivalent to the original beam, its neutral axis must be located in the same place and its moment resisting capacity must be the same.
True
Nonuniform bending refers to flexure in the presence of the shear forces, which means that the bending moments changes as we move along the axis of the beam.
True
Shear force formulas have been developed based on some simplified assumptions, therefore they give approximate results. Even though this is the case, the results differ by only a few percent from those obtained using exact theory of elasticity. Consequently, these two equations can be used to determine the maximum shear stresses in circular beams under ordinary circumstances.
True
The beam theory described in ch 5 of the book was derived for prismatic beams. However, nonprismatic beams are commonly used to reduce weight and improve appearance. Fortunately, the flexure formula gives reasonably accurate values for bending stresses in nonprismatic beams whenever the changes in cross-sectional dimensions are gradual.
True
The design of the connections between the parts of a build up beam involves calculating the shear that "flows" between parts. The shear that "flows" between the parts is calculated using the shear-flow formula
True
The fact that cross sections of a beam in pure bending remain plane is so fundamental to beam theory that it is often called an assumption
True
The neutral axis passes through the centroid of the cross-sectional area when the material follows Hooke's law and there is no axial force acting on the cross section.
True
The strains in a beam in pure bending vary linearly with distance from the neutral surface regardless of the shape of the stress-strain curve of the material.
True
The transformed section method consists of transforming the cross section of a composite beam into an equivalent cross section of an imaginary beam that is composed of only one material.
True
To avoid misusing the shear formula, we must keep in mind that the edges of the cross section must be parallel to the y axis (so that the shear stresses act parallel to the y axis)
True
To minimize the amount of material and thereby have the lightest possible beam, we can vary the dimensions of the cross section so as to have the maximum allowable bending stress at very section. A beam in this condition is called a beam of constant strength.
True
We dont usually bother with sign conventions for V and Q. Instead, we treat all terms in shear formula as positive quantities and determine the direction of the shear stresses by inspection, since stresses act in the same direction as the shear force.
True
When determining stresses on a doubly symmetric beam with inclined loads, the sign convention for the bending moments and the orientation of the axes are extremely important.
True
horizontal shear
identical beams on simple supports with load P