Deformation of Axially Loaded Members - Single Member

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Presentation transcript:

Deformation of Axially Loaded Members - Single Member P P Assumptions: uniform cross section (A is a constant) homogeneous material (E is a constant) loads are applied at ends only

Axially Loaded Members - Multiple Members C Rob consists of several portions of various cross sections and possibly different materials. Assumptions: uniform cross section and homogeneous material within each portion loads are applied at ends of each portion In general: Fi is the internal axial force inside the ith portion.

Axially Loaded Members - Continuously Varied Members P

Axially Loaded Members - Applications: Design Design Considerations: Stress - deformation Factor of Safety n: Allowable stress: Allowable load:

Axially Loaded Members - Applications: Design Example 1: A circular bar made of steel is subject to the loading system indicated in the figure. The maximum elastic deformation has to be limited to 10 mm. And the factor of safety, based on slip failure, is to be 1.8. Determine the minimum diameter of the bar required to support the loads.

Axially Loaded Members - Applications: Statically Indeterminate Problems Statically indeterminate structures: reactions acting on the structures can’t be found by solving static equations. Example 2: Find reactions of the bar.

Axially Loaded Members - Applications: Statically Indeterminate Problems Example 3: A horizontal rigid bar AB is pinned at end A and supported by two wires (CD and EF) at points D and F. A vertical load P acts at end B of the bar. The length of the bar is 3b and the lengths of wires CD and EF are L1 and L2 respectively. Also wire CD has a diameter of d1 and a modulus of elasticity of E1. Wire EF has a diameter of d2 and a modulus of E2. Find the allowable load P if the allowable stresses in wires CD and EF are s1 and s2.

Axially Loaded Members - Temperature Effects

Axially Loaded Members - Temperature Effects Total strain: L P P

Axially Loaded Members - Temperature Effects Example 4: In the structure (a Thermostat) shown below, find the horizontal movement of A if the temperature decrease about 45 oC. The thermal expansion coefficients for steel and aluminum are 11.9 x 10-6 /oC and 22.5 x 10-6 /oC respectively. Assume the thermal expansion coefficient for bar CE is zero and it is very soft.

Axially Loaded Members - Temperature Effects Example 5: A bar is fixed between two walls. Find the stress inside the bar when the temperature is decreased about . Aluminum bar: Steel bar: Al Steel

Axially Loaded Members- Stresses in an Inclined Plane Stresses at section pq: q h P P q F V P

Axially Loaded Members - Maximum Normal Stress and Maximum Shear Stress P P P P P P Maximum normal stress: Maximum shear stress:

Axially Loaded Members- Stresses in an Inclined plane Example 6: A circular brass of diameter d is composed of two segments brazed together on a plane pq making an angle a = 30o with the axis of the bar. The allowable stresses in the brass are 13,000 psi in tension and 7000 psi in shear. On the brazed joint, the allowable stresses are 6000 psi in tension and 3000 psi in shear. If the bar must resist a tensile force P = 6500 lb, what is the minimum required diameter dmin of the bar? (1 psi = 1 lb/in2)