Axial Deformation

Cross-Sectional Dimensions of Steel Rod to Elongate 1-mm when Subjected to 8,000 kg of Tension Force

Problem
A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 106 kg/cm2. What is the dimension of a side of the rod?

A.   5 cm C.   2 cm
B.   1 cm D.   4 cm

Solution to Problem 257 Statically Indeterminate

Problem 257
Three bars AB, AC, and AD are pinned together as shown in Fig. P-257. Initially, the assembly is stress free. Horizontal movement of the joint at A is prevented by a short horizontal strut AE. Calculate the stress in each bar and the force in the strut AE when the assembly is used to support the load W = 10 kips. For each steel bar, A = 0.3 in.2 and E = 29 × 106 psi. For the aluminum bar, A = 0.6 in.2 and E = 10 × 106 psi.
 

Figure 257

 

Solution to Problem 256 Statically Indeterminate

Problem 256
Three rods, each of area 250 mm2, jointly support a 7.5 kN load, as shown in Fig. P-256. Assuming that there was no slack or stress in the rods before the load was applied, find the stress in each rod. Use Est = 200 GPa and Ebr = 83 GPa.
 

Figure P-256

 

Solution to Problem 255 Statically Indeterminate

Problem 255
Shown in Fig. P-255 is a section through a balcony. The total uniform load of 600 kN is supported by three rods of the same area and material. Compute the load in each rod. Assume the floor to be rigid, but note that it does not necessarily remain horizontal.
 

Figure P-255

 

Solution to Problem 254 Statically Indeterminate

Problem 254
As shown in Fig. P-254, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assuming that the rods were initially stress-free, what maximum load P can be applied without exceeding stresses of 150 MPa in the steel rod and 70 MPa in the bronze rod.
 

Figure P-254

 

Solution to Problem 253 Statically Indeterminate

Problem 253
As shown in Fig. P-253, a rigid beam with negligible weight is pinned at one end and attached to two vertical rods. The beam was initially horizontal before the load W = 50 kips was applied. Find the vertical movement of W.
 

Figure P-253

 

Solution to Problem 252 Statically Indeterminate

Problem 252
The light rigid bar ABCD shown in Fig. P-252 is pinned at B and connected to two vertical rods. Assuming that the bar was initially horizontal and the rods stress-free, determine the stress in each rod after the load after the load P = 20 kips is applied.
 

Figure P-252

 

Solution to Problem 251 Statically Indeterminate

Problem 251
The two vertical rods attached to the light rigid bar in Fig. P-251 are identical except for length. Before the load W was attached, the bar was horizontal and the rods were stress-free. Determine the load in each rod if W = 6600 lb.
 

Figure P-251

 

Solution to Problem 247 Statically Indeterminate

Problem 247
The composite bar in Fig. P-247 is stress-free before the axial loads P1 and P2 are applied. Assuming that the walls are rigid, calculate the stress in each material if P1 = 150 kN and P2 = 90 kN.
 

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