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Curve C is a concave failure criterion Some of the volume under curve C lies on the safe side of curve A, so the linear estimate is unconservative Of course, the failure criterion could be convex on one side of the point of tangency and concave on the other It could be a complicated wavy curve The relations become more complicated when more than two variables are involved Two issues have to be addressed First is the question of how adequate is the linear approximation Figure 167 shows the failure criterion for the Culmann problem It as a hyperbolic paraboloid, so it is curved everywhere However, comparisons between the results of Hasofer-Lind analyses and Monte Carlo simulation for the example problems show that the differences between the probabilities of failure computed from the linearized Hasofer Lind approach (FORM) and from simulation are not large.

7C962513 7C962514 7C962517 7C962519 DEC MOV JNZ JMP ESI EAX,DWORD PTR [EAX+4] SHORT ntdll.7C962513 SHORT ntdll.7C96254E

Additional weight should come from muscle. Being stronger has additional bene ts: you can lift heavier sheet loads more easily. Increasing body fat means that you have to carry all that weight around without the additional strength to do so. You should aim to maximise the lean tissue weight gain. This means combining a healthy diet (see 15) with exercise (see 14). Aiming for a maximum of around 0.5 1 kg of lean tissue per week would require an additional 500 1000 extra calories per day. A weight-training programme to gain weight means little rest and lots of sets of the compound exercises those involving several muscle groups (squat, deadlift, chin-ups, shoulder and chest press) for around 10 repetitions for

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The most important thing to notice about this loop is that it is using a different pointer in the element s header. The backward-searching loops you encountered earlier were both using offset +4 in the element s header, and this one is using offset +0. That s really an easy one this is clearly a linked list of some sort, where offset +0 stores the NextElement pointer and offset +4 stores the PrevElement pointer. Also, this loop is using EDI as the counter,

For most geotechnical problems the Hasofer-Lind approach gives satisfactory results Secondly, if the Hasofer Lind approach does not give adequate results, what is to be done next As suggested above and described in more detail in 17, Monte Carlo simulation with variance reduction can be used to improve the estimate of the probability of failure A second approach is to compute directly the probability volume.

There is one other significant search case that hasn t been covered yet. Remember how before we got into the first backward-searching loop we tested for a case where the index was lower than LastIndexFound / 2 Let s see what the function does when we get there:

THE HASOFER LIND APPROACH (FORM)

7C96251B 7C96251D 7C962520 7C962522 7C962524 7C962525 7C962527 7C962529 TEST EBX,EBX LEA EAX,DWORD PTR [ECX+4] JE SHORT ntdll.7C96254E MOV EDX,EBX DEC EDX MOV EAX,DWORD PTR [EAX] JNZ SHORT ntdll.7C962524 JMP SHORT ntdll.7C96254E

This sequence starts with the element at offset +4 in the root data structure, which is the one we ve previously defined as the last element in the list. It then starts looping on elements using offset +0 in each element s header. Offset +0 has just been established as the element s NextElement pointer, so what s going on How could we possibly be going forward from the last element in the list It seems that we must revise our definition of offset +4 in the root data structure a little bit. It is not really the last element in the list, but it is the head of a circular linked list. The term circular means that the NextElement pointer in the last element of the list points back to the beginning and that the PrevElement pointer in the first element points to the last element. Because in this case the index is lower than LastIndexFound / 2, it would just be inefficient to start our search from the last element found. Instead, we start the search from the first element in the list and move forward until we find the right element.

Figure 16.6 Joint probability distribution of two independent Normal variables and a non-linear failure criterion.

16

This concludes the detailed analysis of RtlGetElementGenericTable. It is not a trivial function, and it includes several slightly confusing control flow constructs and some data structure manipulation. Just to demonstrate the power of reversing and just how accurate the analysis is, I ve attempted to reconstruct the source code of that function, along with a tentative declaration of what must be inside the TABLE data structure. Listing 5.3 shows what you currently know about the TABLE data structure. Listing 5.4 contains my reconstructed source code for RtlGetElementGenericTable.

5

g H/2

struct TABLE { PVOID Unknown1; LIST_ENTRY *LLHead; LIST_ENTRY *SomeEntry; LIST_ENTRY *LastElementFound; ULONG LastElementIndex; ULONG NumberOfElements; ULONG Unknown1; ULONG Unknown2; ULONG Unknown3; ULONG Unknown4; };

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