4. An I beam column with fixed ends (at x = 0 and x = 12 m) is braced at midpoint C as shown below and loaded in compression by a force P. Buckling can potentially occur in either xy plane or xz plane (out of the page). The bracing acts as a simple support (i.e. pinned support) in the xy plane, and there is no such midspan support for buckling in the xz plane. 6 m 6 m a. Which plane is more likely to buckle and why? Include relevant calculations to support your choice. b. Given your answer to part a, find the allowable axial force P assuming a safety factor of 2. Material Properties: E = 200 GPa; S = 280 MPa y Important properties of the cross-section: A = 27.5×10³ (mm)² I = 712×106 (mm) yy 1zz 282×10° (mm) =

4. An I beam column with fixed ends (at x = 0 and x = 12 m) is braced at midpoint C as shown below and loaded in compression by a force P. Buckling can potentially occur in either xy plane or xz plane (out of the page). The bracing acts as a simple support (i.e. pinned support) in the xy plane, and there is no such midspan support for buckling in the xz plane. 6 m 6 m a. Which plane is more likely to buckle and why? Include relevant calculations to support your choice. b. Given your answer to part a, find the allowable axial force P assuming a safety factor of 2. Material Properties: E = 200 GPa; S = 280 MPa y Important properties of the cross-section: A = 27.5×10³ (mm)² I = 712×106 (mm) yy 1zz 282×10° (mm) =

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 10.4.1P: A two-span, continuous wood girder (E = 1700 ksi) supports a roof patio structure (figure part a). A...

See similar textbooks

Similar questions

A two-span, continuous wood girder (E = 1700 ksi) supports a roof patio structure (figure part a). A uniform load of intensity q acts on the girder, and each span is of length 8 ft. The girder is made up using two 2×8 wood members (see figure part b). Ignore the weight of the beam. Use the nominal dimensions of the beam in your calculations. Find the reactions at A, B, and C. Use the method of superposition to calculate the displacement of the beam at the mid-sapn of segment AB. Hind: See Figs. 10-14c and 10-14d in Example 10-3.
Segments AB and BCD of beam ABCD are pin connected at x = 10 ft. The beam is supported by a pin support at A and roller supports at C and D; the roller at D is rotated by 30* from the x axis (see figure). A trapezoidal distributed load on BC varies in intensity from 5 lb/ft at B to 2.5 lb/ft at C. A concentrated moment is applied at joint A, and a 40-lb inclined load is applied at the mid-span or CD. (a) Find reactions at supports A, C, and D. (b) Find the resultant force in the pin connection at B. (c) Repeat parts (a) and (b) if a rotational spring(kr= 50 ft-lb/radian ) is added at A and the roller at C is removed.
The horizontal beam ABC shown in the figure is supported by columns BD and CE. The beam is prevented from moving horizontally by the pin support at end A. Each column is pinned at its upper end to the beam, but at the lower ends, support D is a sliding support and support E is pinned. Both co lu in us arc solid steel bars (E = 30 × 106 psi) of square cross section with width equal to 0.625 in. A load Q acts at distance a from column BD. If the distance a = 12 in., what is the critical value Qcr of the load? If the distance a can be varied between 0 and 40 in., what is the maximum possible value of Qcr? What is the corresponding value of the distance a?
Continuous cable A DB runs over a small friction less pulley al D to support beam OABC, which is part of an entrance canopy for a building (see figure}. The canopy segment has a weight W = 1700 lb that acts as a concentrated load in the middle of segment AB. (a) What is the maximum permissible value of load P at C if the allowable force in the cable is 4200 lb? (b) If P = 2300 lb, what is the required diameter of pins A, B, and D? Assume that the pins are in double shear and the allowable shear stress in the pins is 10 ksi.
A T-frame structure is composed of prismatic beam ABC and nonprismatic column DBF that are joined at B by a friction less pin connection. The beam has a sliding, support at A and the column is pin supported at F (see figure). Beam ABC and. column segment DB have cross-sectional area A; column segment BF has area 2A. The modulus of elasticity E is the same for both members. Load 2P is applied downward at C, and load P acts at D. Find expressions for the downward displacements of column DBF at D (5D) and also at B (
Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
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.
Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively. What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?
A horizontal beam AB is pin-supported at end A and carries a clockwise moment M at joint B, as shown in the figure. The beam is also supported at C by a pinned-end column of length L: the column is restrained laterally at 0.6Z, from the base at D. Assume the column can only buckle in the plane of the frame. The column is a solid steel bar (E = 200 GPa) of square cross section having length L = 2.4 m and side dimensions h = 70 mm. Let dimensions d = LI2. Based upon the critical load of the column, determine the allowable moment M if the factor of safety with respect to buckling is n = 2.0.
A column ABC is supported at ends A and C and compressed by an axial load P (figure a). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 × 8.2) back to back (see figure b). The modulus of elasticity of the column is E = 29,500 ksi and the proportional limit is 50 ksi. The height of the column is L = 15 ft. Find the allowable value of load P using a factor of safety of 2.5.
A column, pinned at top and bottom, is made up of two C 6 x 13 steel shapes (see figure) that act together. Find the buckling load (kips) if the gap is zero. Find required separation distance d(inches) so that the buckling load is the same in y and z directions. Assume that E = 30,000 ksi and L = 18 ft. Note that distance d is measured between the centroids of the two C shapes.
A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length L = 4 m. The top of each log is trimmed to form the walking surface (see Fig, b)LA simplified model of the bridge is shown in Fig. g. Each log must carry its own weight w = 1.2 kN/m and the weight (P = 850 N) of a person at mid-span, (see Fig. b). Determine the maximum tensile and compressive stresses in the beam (Fig, b) due to bending. If load h is unchanged, find the maximum permissible value of load ... if the allowable normal stress in tension and compression is 2.5 M Pa.