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Statically indeterminate problems

Determination of the load distribution in the joint is a statically indeterminate problem which depends on a number of factors ... [Pg.423]

The upper and lower adherends are denoted by 1 and 2, respectively. Each adherend has a Young s modulus , and a thickness r,. The adhesive has a shear modulus of G and a thickness of h. The joint length is I, as shown in Fig. 12a. Solving this statically indeterminate problem involves the equilibrium equations based on a differential element as shown in Fig. 12a ... [Pg.24]

Rigid Systems. Literature pertaining to the theoretical analysis of the three-plane rigid piping system is voluminous (30). This literature is expanding steadily and, as it is becoming more abstract, tends to obscure the basic problem which is the analysis of a three-dimensional statically indeterminate structure. [Pg.61]

The simultaneous solution of Eqs. (4.2) and (4.3) allows the forces and stresses in the various rods to be determined. It should be noted that even though linear elasticity is assumed, the terms for stresses do not involve the elastic constants. This is not true, however, for the strains. In the last chapter, the geometry shown in Fig. 3.25 was statically indeterminate, and to solve the problem the rods were assumed to be linear elastic. [Pg.107]

Experimental creep data for ceramics have been obtained using mainly flexural or uniaxial compression loading modes. Both approaches can present some important difficulties in the interpretation of the data. For example, in uniaxial compression it is very difficult to perform a test without the presence of friction between the sample and the loading rams. This effect causes specimens to barrel and leads to the presence of a non-uniform stress field. As mentioned in Section 4.3, the bend test is statically indeterminate. Thus, the actual stress distribution depends on the (unknown) deformation behavior of the material. Some experimental approaches have been suggested for dealing with this problem. Unfortunately, the situation can become even more intractable if asymmetric creep occurs. This effect will lead to a shift in the neutral axis during deformation. It is now recommended that creep data be obtained in uniaxial tension and more workers are taking this approach. [Pg.204]

However, Eq. (6.9) cannot be solved for the m actuator forces because m> n (i.e., the matrix of actuator moment arms is nonsquare). Static optimization theory is usually used to solve this indeterminate problem (Seireg and Arvikar, 1975 Hardt, 1978 Crowninshield and Brand, 1981). Here, a cost function is hypothesized, and an optimal set of actuator forces is found, subject to the equality constraints defined by Eq. (6.9) plus additional inequality constraints that bound the values of the actuator forces. If, for example, actuator stress is to be minimized, then the static optimization problem can be stated as follows (Seireg and Arvikar, 1975 Crowninshield and Brand, 1981) Find the set of actuator forces that minimizes the sum of the squares of actuator stresses ... [Pg.162]

The present study shows that It is possible to evaluate the variability of statically determinate and statically indeterminate structures due to spatial variation of elastic properties without resort to finite element analysis. If a Green s function formulation is used, the mean square statistics of the indeterminate forces are obtained in a simple Integral form which is evaluated by numerical methods in negligible computer time. It was shown that the response variability problem becomes a problem Involving only few random variables, even if the material property is considered to constitute stochastic fields. The response variability was estimated using two methods, the First-Order Second Moment method, and the Monte Carlo simulation technique. [Pg.80]

Suppose you have a four-leg bridle. The loads in the slings vary because the shngs are almost always unequal in length. The loads are statically indeterminate, meaning that the true load in each shng cannot be mathematically solved. In reality, the load is carried by two slings, while the other two act to balance the load. To solve this problem, you must size the bridle such that just two legs carry the fuU load, or you must use a spreader. [Pg.116]


See other pages where Statically indeterminate problems is mentioned: [Pg.106]    [Pg.288]    [Pg.158]   
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