Combined Axial and Bending

Problem 920 | Additional Centroidal Load to Eliminate Tensile Stress Anywhere Over the Cross Section

Problem 920
A compressive load P = 100 kN is applied, as shown in Fig. 9-8a, at a point 70 mm to the left and 30 mm above the centroid of a rectangular section for which h = 300 mm and b = 250 mm. What additional load, acting normal to the cross section at its centroid, will eliminate tensile stress anywhere over the cross section?
 

920-eccentrically-loaded-rectangular-section.jpg

 

Problem 919 | Additional Axial Compression Load for the Section to Carry No Tensile Stress

Problem 919
From the data in Prob. 918, what additional load applied at the centroid is necessary so that no tensile stress will exist anywhere on the cross-section?
 

Solution 919

Problem 918 | Stress at Each Corner of Eccentrically Loaded Rectangular Section

Problem 918
A compressive load P = 12 kips is applied, as in Fig. 9-8a, at a point 1 in. to the right and 2 in. above the centroid of a rectangular section for which h = 10 in. and b = 6 in. Compute the stress at each corner and the location of the neutral axis. Illustrate the answers with a sketch.
 

figure_9-8a_eccentrically_loaded_column.jpg

 

Eccentrically Loaded Short Compression Member

Consider the cross-section below. A compressive load P is applied at any point (ex, ey) with respect to the principal axes x and y. The moment of P about these axes are respectively
 

$M_x = Pe_y$     and     $M_y = Pe_x$

 

figure_9-9a_eccentrically_loaded_section.jpg

 

Problem 917 | Combined Axial and Bending

Problem 917
For the structure in Problem 916, calculate the maximum compressive stress in bar ABC if its cross section is 200 mm square.
 

916-fbd-member-abc.gif

 

Problem 916 | Combined Axial and Bending

Problem 916
For the structure shown in Figure P-916 is hinged to fixed supports at A and E. Compute the maximum compressive stress developed in bar BDE if its cross section is 200 mm square. Neglect the weights of the members.
 

916-given-structural-assembly.gif

 

Problem 915 | Combined Axial and Bending

Problem 915
For the structure in Problem 914, compute the maximum tensile stress developed in bar CB.
 

914-two-bar-structure.gif

 

Problem 914 | Combined Axial and Bending

Problem 914
The structure shown in Figure P-914 is hinged to fixed is hinged to fixed supports at A and C. Assume that the pin connections at A, B, and C are frictionless. The bars are each 4 in. by 4 in. in section. Compute the maximum compressive stress developed in bar AD.
 

914-two-bar-structure.gif

 

Problem 912 | Combined Axial and Bending

Problem 912
Compute the stresses at A and B on the link loaded as shown in Figure P-912 if P = 9000 lb and F = 3000 lb.
 

912-rectangular-link.gif

 

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