A beam supports both a uniform distributed load and a concentrated force, as shown in the figure below. The uniform distributed load has a magnitude q = 700 lb/ft and extends across the entire beam. The concentrated force has a magnitude F = 22 kip and acts L = 9 ft to the right of point A. The beam has an overall length L = 24 ft, and is held in equilibrium by a pin at point A and a roller at point B. Neglect the height and weight of the beam for this analysis. Determine the internal shear force (V) and internal bending moment (M) at the following locations: F A ΑΙ V₁ = M₁ = LE F number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) (b) A point x₂ = 22 ft to the right of point A. V₂ = M2 = Note: Express your answers following the standard positive sign convention described in the Internal Loads - Positive Sign Convention document. (a) A point x₁ = 4 ft to the right of point A. L number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) kip kip - ft kip q kip - ft B 77

A beam supports both a uniform distributed load and a concentrated force, as shown in the figure below. The uniform distributed load has a magnitude q = 700 lb/ft and extends across the entire beam. The concentrated force has a magnitude F = 22 kip and acts L = 9 ft to the right of point A. The beam has an overall length L = 24 ft, and is held in equilibrium by a pin at point A and a roller at point B. Neglect the height and weight of the beam for this analysis. Determine the internal shear force (V) and internal bending moment (M) at the following locations: F A ΑΙ V₁ = M₁ = LE F number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) (b) A point x₂ = 22 ft to the right of point A. V₂ = M2 = Note: Express your answers following the standard positive sign convention described in the Internal Loads - Positive Sign Convention document. (a) A point x₁ = 4 ft to the right of point A. L number (rtol=0.01, atol=1e-05) number (rtol=0.01, atol=1e-05) kip kip - ft kip q kip - ft B 77

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.4.39P: A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A,...

See similar textbooks

Similar questions

Find support reactions at 4 and Band then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN.
Space Frame ABC is clamped at A, except it is free to rotate at A about the x and y axes. Cables DC and EC support the frame at C. Force Py= - 50 lb is applied at the mid-span of AS, and a concentrated moment Mx= -20 in-lb acts at joint B. (a) Find reactions at support A. (b) Find cable tension Forces.
A soccer goal is subjected to gravity loads (in the - z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the mid-height of member DG. Find reactions at sup ports C, D, and H.
A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
The inclined beam represents a ladder with the Following applied loads: the weight (W) of the house painter and the distributed weight (u) of the ladder itself. Find support reactions at A and B: then plot axial force (N), shear (V), and moment (M) diagrams. Label all critical N, V, and M values and also the distance to points where any critical ordmates are zero. Plot N, V, and M diagrams normal to the inclined ladder. Repeat part (a) for the case of the ladder suspended from a pin at B and traveling on a roller support perpendicular to the floor at A.
Find expressions for shear force V and moment M at v = L/2 of beam AB in structure (a). Express V and M in terms of peak load intensity q0and beam length variable L. Repeat for structure (b) but find Fand M at m id-span of member BC.
The plane frame shown in the figure is part of an elevated freeway system. Supports at A and D arc fixed, but there are moment releases at the base of both columns (AB and DE) as well as in column BC and at the end of beam BE. Find all support reactions; then plot axial-force (N), shear (F), and moment (M) diagrams for all beam and column members. Label all critical N, V, and M values and also the distance to points where any critical ordinatcs are zero.
A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in the cable.
A cable with force P is attached to a frame at A and runs over a frictionless pulley at D. Find expressions for shear force V and moment M at x = LI2 of beam BC.
An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2. (a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables). (b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.) (c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.
A long, slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight (see figure). The weight of the cone is W and the modulus of elasticity of the material is E. Derive a formula for the increase S in the length of the bar due to its own weight. (Assume that the angle of taper of the cone is small.)
The main cables of a suspension bridge (see figure part a) follow a curve that is nearly parabolic because the primary load on the cables is the weight of the bridge deck, which is uniform in intensity along the horizontal. Therefore, represent the central region AOB of one of the main cables (see part b of the figure) as a parabolic cable supported at points A and B and carrying a uniform load of intensity q along the horizontal. The span of the cable is L, the sag is /i, the axial rigidity is EA\ and the origin of coordinates is at mid span. (a) Derive the following formula for the elongation of cable AOB shown in part b or the figure: (b) Calculate the elongation 5 of the central span of one of the main cables of the Golden Gate Bridge for which the dimensions and properties are L = 4200 ft,h = 470 ft, q = 12,700 lb/ft, and E = 23,300,000 psi The cable consists of 27,572 parallel wires of diameter 0.196 in. Hint: Determine the tensile force Tal any point in the cable from a free-body diagram of part of the cable; then determine the elongation of an element of the cable of length ds: finally, integrate along the curve of the cable to obtain an equation for the elongation £.