Load and Stress Analysis

What conditions must be met for a system to be in static equilibrium?

What is the mathematical relationship between load intensity q(x), shear force V, and bending moment M in a beam?

According to the singularity functions defined in Table 3-1, what is the value of the unit step function <x - a>^0 when x is less than a?

What is the primary characteristic of plane stress?

In Mohr's circle for plane stress, what do the two points where the circle intersects the normal stress (horizontal) axis represent?

For a plane stress element with σx = 14 MPa, σy = -10 MPa, and τxy = -16 MPa, what are the two principal stresses, σ1 and σ2?

What is the relationship between Young's modulus (E), the shear modulus (G), and Poisson's ratio (ν) for a linear, isotropic, homogeneous material?

The flexure formula for normal stress in a straight beam subjected to a bending moment M is σx = -My/I. What does the variable 'I' represent?

A T-section beam has a total area of 1956 mm^2 and is subjected to a bending moment of 1600 N·m. The distance from the neutral axis to the top fiber (c1) is 32.99 mm, and the second moment of area (I) is 1.907 x 10^6 mm^4. What is the maximum tensile stress, which occurs at the top surface?

Where does the maximum transverse shear stress typically occur in a beam with a solid rectangular cross section?

What is the formula for the maximum shear stress in a beam with a rectangular cross section?

What is the formula for the angle of twist, θ, in radians for a solid round bar of length l, subject to a torque T, with shear modulus G and polar second moment of area J?

A rectangular bar with a cross section of width b and thickness c (where b is the longer side) is subjected to a torque T. Where does the maximum shearing stress occur?

A crank arm made of a rectangular bar (1.25 in by 0.25 in) is subjected to a torsional moment of 450 lbf-in. Using the approximate formula τ_T = (T/bc^2) * (3 + 1.8/(b/c)), where b=1.25 in and c=0.25 in, what is the torsional shear stress?

What is a theoretical stress-concentration factor (Kt or Kts) used for?

For a brittle material under static loading, how should a geometric stress-concentration factor Kt be treated?

A 2-mm-thick brittle bar, 40 mm wide, has a 4-mm diameter hole and is subjected to a tensile load. The nominal stress is 139 MPa and the theoretical stress concentration factor Kt is 2.7. What is the maximum stress?

For a thick-walled cylinder under internal pressure only, where do the maximum magnitudes of the tangential (σt) and radial (σr) stresses occur?

For a thin-walled cylindrical pressure vessel with inside diameter di, wall thickness t, and internal pressure pi, what is the approximate formula for the longitudinal stress (σl)?

In a press or shrink fit between two cylindrical members of the same material, the interference contact pressure 'p' is given by the simplified formula p = [Eδ / (2R^3)] * [(ro^2 - R^2)(R^2 - ri^2) / (ro^2 - ri^2)]. What does the term 'δ' represent?

A straight bar is restrained at its ends and subjected to a uniform increase in temperature (ΔT). What is the formula for the resulting compressive thermal stress, σ?

In the analysis of a curved beam, what is the key difference between the neutral axis and the centroidal axis?

A crane hook with a rectangular cross-section is modeled as a curved beam. The inner radius is 2 in, outer radius is 6 in, centroidal radius is 4 in, and the neutral axis radius is calculated to be 3.641 in. What is the eccentricity 'e'?

What type of stress distribution does a curved beam exhibit under pure bending?

When two solid spheres are pressed together by a force F, what is the shape of the pressure distribution within the circular contact area?

In Hertzian contact stress theory for two contacting spheres, where does the maximum shear stress occur?

A 1-in-long strip of steel, 1/8 in thick, is subjected to a torque. Using the open thin-walled section formula τ = Gθ1c, where the formula T = Lc^2τ / 3 applies, and an allowable shear stress of 11500 psi, what is the allowable torque T? The length of the median line L is 1 in and thickness c is 0.125 in.

What is the primary purpose of using a free-body diagram in force analysis?

For a simply supported beam with a uniform load w over its length l, the moment equation is M = (wl/2)x - (w/2)x^2. If the reactions R1 and R2 are 210 lbf and 90 lbf respectively, a 200 lbf load is at x=4 and a 100 lbf load is at x=10 on a 20 inch beam, what is the bending moment at x slightly larger than 20 inches?

In the notation for Cartesian shear stress components, such as τxy, what does the first subscript 'x' indicate?

For a three-dimensional state of stress, what is the relationship between the cross-shears τyx and τxy?

On a Mohr's circle diagram, if the x-face has stresses (σx, τxy) and the y-face has stresses (σy, τyx), how many degrees apart are these two points on the circle?

For a general 3D stress state with principal stresses ordered σ1 >= σ2 >= σ3, what is the formula for the absolute maximum shear stress (τ_max)?

What does Poisson's ratio (ν) represent?

What is the section modulus, Z, for a beam in bending?

A beam with a solid circular cross-section of diameter d is subjected to bending moments My and Mz. What is the formula for the maximum bending stress?

In the analysis of transverse shear stress, what does the term Q represent?

For a thin-walled structural I-beam, the maximum transverse shear stress is approximately equal to what?

What is the primary power transmission equation in U.S. Customary units relating power H (hp), torque T (lbf-in), and speed n (rev/min)?

A steel shaft with a 0.75 in diameter is fixed at one end. A force at the other end creates a maximum bending moment of 1950 lbf-in. What is the bending stress at this location? The formula is σx = 32M / (πd^3).

For a solid 1.5-in-diameter steel shaft, the maximum combined bending moment is 8246 lbf-in and the maximum torsional shear stress is 2.414 kpsi. What is the maximum compressive stress at the point of maximum moment?

What is the formula for shear stress τ in a closed thin-walled tube subjected to a torque T, where Am is the area enclosed by the section median line and t is the wall thickness?

A welded rectangular steel tube is 40 in long with a 1/8-in wall thickness. The area enclosed by the median line is 8.253 in^2. If the allowable shear stress is 11500 psi, what is the allowable torque T? The relevant formula is T = 2*Am*t*τ.

Why should open thin-walled sections be avoided in design for torsional loading?

What is the defining characteristic of a state of plane strain?

How many independent stress components are required to define a general three-dimensional state of stress, assuming cross-shears are equal?

For the plane stress state with σx = 80 MPa, σy = 0, and τxy = 50 MPa (cw), what is the radius of the Mohr's circle, which also represents the maximum in-plane shear stress τ1?

A steel flywheel with an outer diameter of 36 in and an inner diameter of 8 in rotates at 6000 rpm. What is the angular velocity ω in radians per second?

For the steel flywheel in Example 3-15 with an inner radius of 4 in, what is the maximum tangential stress (σt)? The relevant formula is σt = 118.68 * (340 + 5184/r^2 - 0.5699*r^2).

What is the primary assumption made in the analysis of uniformly distributed stresses, such as in a tension rod, described by the formula σ = F/A?