Draw the shear-force and bending-moment diagram for the beam shown. Assume the upward reaction provided by the ground to be uniformly distributed. Let a = 3.3 ft, b=3.2 ft, P = 20 kips, and w= 3.0 kips/ft. Label all significant points on each diagram. Determine the maximum value of (a) the internal shear force and (b) the internal bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. A a P B b W IC b P D a E

For the beam and loading shown,(a) Use discontinuity functions to write the expression for w(x).  Include the beam reactions in this expression.(b) Integrate w(x) twice to determine V(x) and M(x).(c) Use V(x) and M(x) to plot the shear-force and bending-moment diagrams.Let a = 3.8 m, b = 1.3 m, wA = 17 kN/m, and wB = 51 kN/m. Label all significant points on each diagram and identify the maximum shear force and bending moment along with their respective locations.  Clearly differentiate straight-line and curved portions of the diagrams.Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number.

A 240mm diameter circular simply supported beam carries a concentrated load, uniformly distributed load and a triangular load as shown in the figure. Using Area Moment Method, Solve the following unknowns. Let P = 195KN, a = 2m, and the modulus of elasticity of beam is 100GPA. NOTE: WRONG SIGN IS WRONG. WRONG UNITS IS WRONG. w w B Im If the shear at a point 1m from the roller support is equal to -182.66666666667KN, determine the value of "w". kN/m Determine the deflection at point 2n from the hinge support. (Note: Put a negative sign if the deflection is going down) III

Solve with Free body diagram

For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. Place the origin at point A. Let a=4.00 m, b=5.25 m, c= 2.50 m, P = 26kN and M = 160kN-m. Construct the shear-force and bending-moment diagrams. Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below.

A simply supported beam carries a moment applied to one end as shown. El is constant. a) Calculate the support reaction forces for the beam b) Write out the M(x) equation using discontinuity functions. c) Determine the slope and deflection equations by integrating the M(x) equation as needed and using two B.C. to solve for the integration constants, C1 and C2. d) Calculate the deflection at the mid-span of the beam. e) Check: Calculate the deflection at point B (right support). A 12A

For the beam and loading shown,(a) Use discontinuity functions to write the expression for w(x).  Include the beam reactions in this expression.(b) Integrate w(x) twice to determine V(x) and M(x).(c) Use V(x) and M(x) to plot the shear-force and bending-moment diagrams.Let a = 3.2 m, b = 1.1 m, wA = 25 kN/m, and wB = 55 kN/m. Label all significant points on each diagram and identify the maximum shear force and bending moment along with their respective locations.  Clearly differentiate straight-line and curved portions of the diagrams.Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number.

Part C

Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN

Determine the variation in the width w as a function of x for the cantilevered beam that supports a concentrated force P at its end so that it has a maximum bending stress sallow throughout its length. The beam has aconstant thickness t.